Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Goos-Hänchen shifts for Airy beams impinging on graphene-substrate surfaces

Open Access Open Access

Abstract

The spatial (ΔGH) and the angular (ΘGH) Goos-Hänchen (GH) shifts for an Airy beam impinging upon a weakly absorbing medium coated with the monolayer graphene are theoretically investigated. The influence of the GH shift on the incident angle, the incident wavelength, the Fermi energy, and the decay factors of Airy beams is discussed. A significant magnification of ΔGH, which reaches its maximum of about three orders of wavelengths, is predicted. Our findings may provide a feasible tool to obtain a huge ΔGH in experiments.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The Airy wave packet, a solution to the the potential-free Schrödinger equation, was predicted for the first time theoretically by Balazs and Berry in 1979 [1], which carries infinite energy and thus is not realizable physically. The first finite energy Airy beams were reported theoretically and verified experimentally by Siviloglou and Chiristodoulides in 2007 [2,3]. Airy beams have been extensively applied in various areas, such as optical routing [4], optical cleaning of the micro particles [5], light bullet and soliton pairs generation [6,7], bio-optical tweezers [8], vacuum electron acceleration [9,10] and so on, owing to their novel and unique properties such as self-acceleration [2,3], self-healing [11], and nondiffraction [12].

On the other hand, graphene, a one-atom-thick layer of carbon atoms with a hexagonal honeycomb lattice [13,14], has attracted tremendous interest, due to its unique optical and electronic properties [15,16], and its broad applications spanning from Klein tunneling [17], tunable plasmonic devices [18], polarizers [19], and modulators [20]. Moreover, the Fermi energy of graphene can be adjusted by varying the gate voltage or the doping concentration [21].

In geometric optics, as we all know, reflection and refraction of light on an interface are strictly governed by the Fresnel equations and Snell’s law [22]. When the wave properties of the physical beam are taken into account, the nonsecular reflection phenomena will occur and be observed, the most important ones are the Goos-Hänchen (GH) shift [23] and Imbert-Fedorov (IF) shifts [24], which occur in the plane of incidence and the plane normal to the plane of incidence, respectively. In addition, there have been lots of investigations about the photonic spin Hall effect (SHE), which is also the IF shift connected with the law of conservation of angular momentum, in the past few years [2528]. These beam shifts have been studied for different kinds of incident beams, including Gaussian beams [2934], Hermite-Gaussian beams [3537], Laguerre-Gaussian beams [38,39], nondiffracting Bessel beams [40], Airy beams [4144], and vortex beams [45,46]. Meanwhile, there have been numerous intriguing materials as reflection surfaces to investigate beam shifts as well, such as graphene [32,37,4761], weakly absorbing media [6264], photonic crystals [6567], ferromagnets [68], and epsilon near-zero materials [6971]. Importantly, these beam shifts have many practical applications in physics. Using the quantum weak measurement techniques, the GH shift and the photonic SHE hold great potential for precision metrology, such as measuring precisely the optical conductivity of graphene [56] and identifying the layer of graphene [57,58] as well as topological phase transitions [59]. Moreover, unique applications of the GH shift in optical differential operation and image edge detection have been reported recently [60]. However, the GH shift value always has the same order of magnitude as the incident wavelength, which is too extremely small to be easily observed and measured in experiment. Thus, the weak measurements have been introduced, which can enhance the magnitude of shift effectively [57,58,7274]. Furthermore, giant GH shifts have been produced in graphene theoretically and experimentally. Cheng et al. have predicted a huge GH shift with a graphene layer at the excited surface plasmon resonance [48]. Li et al. have presented experimentally a giant GH shift using a beam splitter scanning method [49]. In addition, Airy beams can also raise the magnitude of GH shift, which is clearly seen in the analytical solution of the shift derived by Gao et al. [44], compared to the case of Gaussian beams. Whether the GH shifts are greatly enhanced for Airy beams impinging on graphene coated surfaces? There is still no any investigation on it, where some intriguing phenomena may occur.

The purpose of this paper is to study theoretically the spatial GH shift (GHS) and the angular one (GHA) for Airy beams impinging on weakly absorbing media coated with the monolayer graphene. The dependence of the GH shift on the incident angle, the incident wavelength, the Fermi energy, and the decay factors of Airy beams is investigated. A huge GH shift which is up to three orders of wavelengths is obtained.

This paper is organized as follow. In Sec. 2, we present the analytical expressions of the GHS and the GHA for Airy beams and the Fresnel reflection coefficients in the graphene-substrate system. The results and discussions of the simulations are presented in Sec. 3. We conclude some useful results in Sec. 4.

2. Theoretical model

To start our analysis, we consider a monochromatic, paraxial electric field impinging on a weakly absorbing semi-infinite medium coated with the monolayer graphene, as illustrated in Fig. 1. $\varepsilon _{1}=1$ and $\varepsilon _{2}=\varepsilon _{2r}+\varepsilon _{2i}i$ represent the relative permittivity of air and the absorbing medium. The laboratory frame $\{\hat {\mathbf {x}},\hat {\mathbf {y}},\hat {\mathbf {z}}\}$ is established at the graphene-coated surface, where the $\hat {\mathbf {z}}$ axis is normal to the interface pointing to the absorbing medium. $\{\hat {\mathbf {x}}_i,\hat {\mathbf {y}}_i,\hat {\mathbf {z}}_i\}$ and $\{\hat {\mathbf {x}}_r,\hat {\mathbf {y}}_r,\hat {\mathbf {z}}_r\}$ denote the incident and the reflected field coordinates, respectively.

The electric field intensity of position $\mathbf {r}$ for the incident and the reflected beams can be expressed as [75]:

$$\textbf{E}_\mu(\textbf{r}_\mu)=\frac{1}{2\pi}{\iint}\widetilde{\textbf E}_\mu(\textbf{k}_\mu)e^{i(\textbf{k}_\mu{\cdot}\textbf{r}_\mu)}dk_{x_{\mu}}dk_{y_{\mu}},$$
where the subscript $\mu =I,R$ denotes the incident or the reflected coordinate system, $\textbf {k}_I=k_{x_I} \hat {\mathbf {x}} +k_{y_I} \hat {\mathbf {y}} +k_{z_I} \hat {\mathbf {z}}$ represents the wave vector of the incident coordinate system. Meanwhile, $U=k_{x_I}/k_1$, $V=k_{y_I}/k_1$, and $W=k_{z_I}/k_1$, the dimensionless components of the $\mathbf {k}_I$ are introduced in the incident frame, where $k_1=|\textbf {k}_I|=2 \pi / \lambda$ with the wavelength $\lambda$ of incident beams, and let $\hat {\mathbf {X}}_I=k_1 \hat {\mathbf {x}}_I, \hat {\mathbf {Y}}_I=k_1 \hat {\mathbf {y}}_I, \hat {\mathbf {Z}}_I=k_1 \hat {\mathbf {z}}_I$. According to the law of specular reflection [76], the relationship between $\hat {\mathbf {k}}_I$ and $\hat {\mathbf {k}}_R$ is $\hat {\mathbf {k}}_R=\hat {\mathbf {k}}_I-2 \hat {\mathbf {z}} (\hat {\mathbf {z}} \cdot \hat {\mathbf {k}}_I)$= $k_1(-U\hat {\mathbf {x}}_R+V\hat {\mathbf {y}}_R+ W\hat {\mathbf {z}}_R)$. Thus, the electric fields of the incident and the reflected beams can be described as
$$\textbf{E}_I(k_1\textbf{r}_I)=\frac{k_1^2}{2\pi}{\iint}\widetilde{\textbf E}_I(U,V;\theta)e^{i(U\hat{\textbf X}_I+V\hat{\textbf Y}_I+W\hat{\textbf Z}_I)}dUdV,$$
$$\textbf{E}_R(k_1\textbf{r}_R)=\frac{k_1^2}{2\pi}{\iint}\widetilde{\textbf E}_R(U,V;\theta)e^{i(-U\hat{\textbf X}_R+V\hat{\textbf Y}_R+W\hat{\textbf Z}_R)}dUdV,$$
whose the angular spectrums can be written as
$$\widetilde{\textbf E}_\mu(U,V;\theta)=\sum_{\lambda}^{p,s}\hat{\textbf e}_\lambda(\textbf{k}_\mu)\alpha_\lambda(U,V;\theta)\widetilde{\textbf A}_{\mu}(U,V;\theta),$$
in which $\lambda =p,s$ denote p or s polarization, and $\hat {\mathbf {e}}_\lambda (\mathbf {k}_\mu )$ represents the polarization unit basis vectors written as
$$\hat{\mathbf{e}}_p(\mathbf{k}_\mu)=\frac{\hat{\mathbf{e}}_s(\mathbf{k}_\mu){\times}\mathbf{k}_\mu}{|\hat{\mathbf{e}}_s(\mathbf{k}_\mu){\times}\mathbf {k}_\mu|},$$
$$\hat{\mathbf{e}}_s(\mathbf {k}_\mu)=\frac{\hat{\mathbf{z}}{\times}\mathbf{k}_\mu}{|\hat{\mathbf{z}}{\times}\mathbf{k}_\mu|}.$$
The polarized vector spectral amplitudes $\alpha _\lambda (U,V;\theta )=\hat {\mathbf {e}}_\lambda (\mathbf {k}_I) \cdot \hat {f}$, where $\hat {f}=f_p\hat {\mathbf {x}}_I+f_s\hat {\mathbf {y}}_I$, and $f_p=a_p$, $f_s=a_se^{i\eta }$ with the phase difference $\eta$ between p and s polarization. The initial incident and the reflected angular spectrums are $\widetilde {A}_I(U,V;\theta )=\widetilde {A}(U,V;0)$, and $\widetilde {A}_R(U,V;\theta )=r_\lambda (U,V;\theta )\widetilde {A}(U,V;Z_I^0)$, respectively, where $Z_I^0$ corresponds to the transmission distance before reflecting along $Z_I$, and $r_\lambda (U,V;\theta )=R_\lambda e^{i\phi _\lambda }$ is the Fresnel reflection coefficients with the modulus value $R_\lambda$ as well as the phase $\phi _\lambda$. Using Taylor expansion method at $U=0, V=0$, the Fresnel reflection coefficients can also be expressed as follow [22]:
$$r_\lambda(U,V;\theta){\simeq}r_\lambda+Ur^{\prime}_\lambda+\frac{1}{2}U^2r^{\prime\prime}_\lambda+\frac{1}{2}V^2r^{\prime}_\lambda,$$
where $r_\lambda^{\prime}$ and $r_\lambda^{\prime\prime}$ represent the first and the second order differentials of ordinary reflection coefficients to the incident angle $\theta$ respectively. In this case, the angular spectrum of the finite energy Airy beams is expressed as
$$\widetilde{A}(U,V)=\frac{w_0^2}{2\pi}\mathrm{exp}(\frac{\alpha^3+\beta^3}{3})\mathrm{exp}(-\frac{\alpha U^2+\beta V^2}{\vartheta^2}) \mathrm{exp}[i(\frac{U^3+V^3}{3\vartheta^3}-\frac{\alpha^2U+\beta^2V}{\vartheta})],$$
where $\alpha$ and $\beta$ are the decay factors, $\vartheta =1/(k_1w_0)$, and $w_0$ is the length parameter of Airy beams.

 figure: Fig. 1.

Fig. 1. Schematic plot of the GH shift at the graphene-coated surface between air ($z<0$) and a semi-infinite weakly absorbing medium ($z>0$). The single graphene layer (characterized by its optical conductivity $\sigma$) is located on the interface at $z = 0$. $\varepsilon _{1}=1$ and $\varepsilon _{2}=\varepsilon _{2r}+\varepsilon _{2i}i$ represent the relative permittivity of air and the absorbing medium, respectively.

Download Full Size | PPT Slide | PDF

According to the definition of the GH shift in Refs. [44,77], the shift can be written as

$$\bar{X}=\bar{X}_R-\bar{X}_I,$$
where $\bar {X}_R$ and $\bar {X}_I$ can be expressed in the Fourier form:
$$\bar X_R=\frac{{\iint}\mathrm{Im}[\widetilde{\mathbf{E}}_R^*\frac{\partial}{\partial U}\widetilde{\mathbf{E}}_R]dUdV}{{\iint}|\widetilde{\mathbf{E}}_R|^2dUdV}-(Z_R+Z_I)\frac{{\iint}\frac{U}{W}{|\widetilde{\mathbf{E}}_R|^2dUdV}}{{\iint}|\widetilde{\mathbf{E}}_R|^2dUdV},$$
$$\bar X_I=\frac{-{\iint}\mathrm{Im}[\widetilde{\mathbf{E}}_I^*\frac{\partial}{\partial U}\widetilde{\mathbf{E}}_I]dUdV}{{\iint}|\widetilde{\mathbf{E}}_I|^2dUdV}-Z_I\frac{{\iint}\frac{U}{W}{|\widetilde{\mathbf{E}}_I|^2dUdV}}{{\iint}|\widetilde{\mathbf{E}}_I|^2dUdV}.$$
The GHS and the GHA can be written separately as follows:
$$\Delta_{\mathrm{GH}}=\frac{{\iint}\mathrm{Im}[\widetilde{\mathbf{E}}_R^*\frac{\partial}{\partial{U}}\widetilde{\mathbf{E}}_R]dUdV}{k_1{\iint}|\widetilde{\mathbf{E}}_R|^2dUdV} +\frac{{\iint}\mathrm{Im}[\widetilde{\mathbf{E}}_I^*\frac{\partial}{\partial V}\widetilde{\mathbf{E}}_I]dUdV}{k_1{\iint}|\widetilde{\mathbf{E}}_I|^2dUdV},$$
$$\Theta_{\mathrm{GH}}=\partial\bar{X}_R/\partial{Z_R}=-\frac{{\iint}\frac{U}{W}{|\widetilde{\mathbf{E}}_R|^2dUdV}}{{\iint}|\widetilde{\mathbf{E}}_R|^2dUdV}.$$
After straightforward calculations, the GHS and the GHA can be modified as [44]
$$\Delta_{\mathrm{GH}}^\mathrm{Airy}=\frac{1}{\Lambda}(\Delta_{\mathrm{GH}}^g+\frac{\vartheta}{8\alpha^2k_1}\sum_{\lambda}^{p,s}\omega_{\lambda_{1}}),$$
$$\Theta_{\mathrm{GH}}^\mathrm{Airy}=\frac{1}{4\alpha\Lambda}\Theta_{\mathrm{GH}}^g,$$
where $\Delta _{\mathrm {GH}}^g=\omega _p\partial \phi _p/\partial \theta +\omega _s\partial \phi _s/\partial \theta$ is the GHS for Gaussian beams, with the fractional energy in each polarization $w_\lambda =a_\lambda ^2R_\lambda ^2/(a_p^2R_p^2+a_s^2R_s^2)$, $\Lambda =1+\frac {\vartheta ^2}{4\alpha }\sum _{\lambda }^{p,s}\omega _{\lambda _{1}}+\frac {\vartheta ^2}{4\beta }\sum _{\lambda }^{p,s}\omega _{\lambda _{2}}$ with $\omega _{\lambda _{1}}=a_\lambda ^2(R_\lambda ^2+\mathrm {Re}[r^{\prime\prime}_\lambda r^*_\lambda ])/(a_p^2R_p^2+a_s^2R_s^2)$ as well as $\omega _{\lambda _2}=a_\lambda ^2(\mathrm {cot}\theta \mathrm {Re}[r^{\prime}_\lambda r^*_\lambda ]+\mathrm {cot}^2\theta R^2_{\bar \lambda })/(a_p^2R_p^2+a_s^2R_s^2)$, $\bar \lambda =s,p$ when $\lambda =p,s$, and $\Theta _{\mathrm {GH}}^g=-2\vartheta ^2(\omega _p\frac {\partial }{\partial \theta }\mathrm {ln}R_p+\omega _s\frac {\partial }{\partial \theta }\mathrm {ln}R_s)$ is the GHA of Gaussian beams.

On the other hand, the transfer matrix method is employed to calculate the Fresnel reflection coefficient in this system with the monolayer graphene [78,79]. We consider the p polarized incident light propagating in the absorbing medium, whose magnetic field is polarized along $\hat {\mathbf {y}}$ direction, written as:

$$H_{1y}=(a_1 e^{k_{1z}z}+b_1 e^{-k_{1z}z})e^{k_{1x}x} \quad (z<0),$$
$$H_{2y}=(a_2 e^{k_{2z}z}+b_2 e^{-k_{2z}z})e^{k_{2x}x} \quad (z>0),$$
where $k_{jx} (k_{jz})$ $(j=1,2)$ is the $x (z)$ componet of the wave vector $\mathbf {k}_j$, with $|\mathbf {k}_j|= \sqrt {\varepsilon _{j}} \omega /c$ having the angular frequency $\omega$ of the incident beam and the speed $c$ of light in vacuum; $a_j$ and $b_j$ are the field coefficients. Meanwhile, it is obvious that from the well-known Snell’s law [22]:
$$k_{1x}=k_{2x}.$$
The transmission matrix of the graphene surface can be derived with the help of the boundary conditions at $z=0$ and Ohm’s law, as follow [79]:
$$D_{p(1\rightarrow2)}=\frac{1}{2} \left[ \begin{array}{cc} 1+\eta_p+\xi_p & 1-\eta_p-\xi_p \\ 1-\eta_p+\xi_p & 1+\eta_p-\xi_p \\ \end{array} \right],$$
for p polarization, where $\eta _p=(\varepsilon _{1}k_{2z})/(\varepsilon _{2}k_{1z})$ and $\xi _p= (\sigma \omega k_{2z})/(\varepsilon _{0}\varepsilon _{2} \omega )$, as well as
$$D_{s(1\rightarrow2)}=\frac{1}{2} \left[ \begin{array}{cc} 1+\eta_s+\xi_s & 1-\eta_s+\xi_s \\ 1-\eta_s-\xi_s & 1+\eta_s-\xi_s \\ \end{array} \right],$$
for s polarization, where $\eta _s=k_{2z}/k_{1z}$ and $\xi _p=\sigma \mu _0\omega /k_{1z}$; $\sigma$ is the optical conductivity of graphene, $\varepsilon _{0}$ and $\mu _0$ are the permittivity and permeability in vacuum, respectively. The propagation matrix in this system is
$$P(0)= \left[ \begin{array}{cc} 1 & 0 \\ 0 & 1 \\ \end{array} \right].$$
The transfer matrix of the graphene-coating system can be written as
$$P(0)= M_{p,s}=D_{p,s(1\rightarrow 2)} P(0)=D_{p,s(1\rightarrow2)} .$$
Hence, the Fresnel reflection coefficients for p and s polarizations can be derived as follow [79]:
$$r_p=\frac{M_{p,21}}{M_{p,11}}=\frac{\varepsilon_2/k_{2z}-\varepsilon_1/k_{1z}+\sigma/(\varepsilon_0 \omega)}{\varepsilon_2/k_{2z}+\varepsilon_1/k_{1z}+\sigma/(\varepsilon_0\omega)},$$
$$r_s=\frac{M_{s,21}}{M_{s,11}}=\frac{k_{1z}-k_{2z}-k_1\sigma/(\varepsilon_0 c)}{k_{1z}+k_{2z}+k_1\sigma/(\varepsilon_0 c)}.$$
In addition, according to the semiconductor theory, the optical conductivity of graphene can be written as the form [80]:
$$\sigma(\omega,E_f)=\frac{e^2 E_f}{\pi \hbar^2} \frac{i}{\omega+i \tau^{-1}}+ \frac{e^2}{4 \hbar^2} \Bigg [H(\hbar \omega-2 E_f)+\frac{i}{\pi} \ln \bigg|\frac{\hbar \omega-2 E_f}{\hbar \omega+2 E_f} \bigg| \Bigg],$$
where $H(x)$ denotes the step function, $e=1.60 \times 10^{-19}$ C and $\hbar =h/(2\pi )=1.05 \times 10^{-34} \, \mathrm {J \cdot s}$ represent the elementary charge and the reduce Plank’s constants, accordingly, $E_f$ is the Fermi energy, $\tau =(\mu E_f)/(e v_f^2)$ indicates the electron-phonon relaxation time with the mobility $\mu =10^4\, \mathrm {cm^2 V/s}$ and the Fermi velocity $v_f=10^6$ m/s. Moreover, $E_f= \hbar v_f \sqrt {\pi n_{2D}}$ can be controlled by changing the charge density $n_{2D}$, manipulated by the external gate voltage, which gives an easy tool to control the GH shift in experiment.

3. Results and discussions

3.1 Spatial GH shift

In the following simulation, the case of p polarization is only considered, due to the extremely small value of the GHS for s polarizaion. First, to illustrate the meaning of this study, we plot the comparison of the GHSs ($\Delta _{\mathrm {GH}}$) for four different cases: in Fig. 2(a) Gaussian beam without graphene (solid line), Gaussian beam with monolayer graphene (dashed line), Airy beam without graphene (dotted line); in Fig. 2(b) Airy beam with the monolayer graphene, at fixed parameters: $\varepsilon _2=2+0.02i$, $\lambda =850$ nm, $E_f=0.5$ eV, and $\alpha =\beta =0.1$. It is clear that using the monolayer graphene or the Airy beam can enhance the GHS, compared to the case of the Gaussian beam without graphene. Meanwhile, the effect of the former is a little larger than the latter. It is should be noted that the GHS without graphene is maximal at the Brewster angle $\theta _B=54.74^\circ$, while it increases to $\theta _B=55.43^\circ$ in the case with the monolayer graphene, owing to the fact that the position of $\theta _B$ is determined by the real part of the graphene conductivity [54], where Re$(\sigma )=0.6\times 10^{-4}$ S/m at $E_f=0.5$ eV, as shown below in Fig. 4(b). Interestingly, in Fig. 2(b), the GHS for the Airy beam with the monolayer graphene can be enhanced significantly, which far exceeds the above two cases, achieving about 390 times of the incident wavelength $\lambda$.

Next, in Eq. (25), the surface conductivity $\sigma$ of graphene depends strongly on the incident wavelength $\lambda$, which has also influence on the GHS value. In Fig. 3, we plot the dependence of GHS ($\Delta _{\mathrm {GH}}$) of the monolayer graphene on $\theta$ with different incident wavelengths: $\lambda =325$ nm (solid line), $\lambda =488$ nm (dashed line), $\lambda =633$ nm (dotted line), and $\lambda =850$ nm (dash-dotted line) for two cases of Fig. 3(a) Gaussian beams and Fig. 3(b) Airy beams. It is indicated that for a bigger value of the wavelength $\lambda$, a larger maximal value of the GH shift is obtained. Meanwhile, the difference of the maximal GHSs between Gaussian and Airy beams also increases with the increasing $\lambda$, by comparing Figs. 3(a) and 3(b). Therefore, enlarging $\lambda$ of the Airy beam impinging on the graphene-coating surface can produce a larger GH shift. In the next discussion, we only consider $\lambda =850$ nm in order to obtain a larger GHS.

 figure: Fig. 2.

Fig. 2. The GHS ($\Delta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ for (a) Gaussian beam without graphene (solid line), Gaussian beam with the monolayer graphene (dashed line), Airy beam without graphene (dotted line), and (b) Airy beam with the monolayer graphene. Here, $\varepsilon _2=2+0.02i$, $\lambda =850$ nm, $E_f=0.5$ eV, and $\alpha =\beta =0.1$.

Download Full Size | PPT Slide | PDF

 figure: Fig. 3.

Fig. 3. The GHS ($\Delta _{\mathrm {GH}}$) with the monolayer graphene in dependence on the incident angle $\theta$, with different incident wavelengths: $\lambda =325$ nm (solid line), $\lambda =488$ nm (dashed line), $\lambda =633$ nm (dotted line), and $\lambda =850$ nm (dash-dotted line) for two cases of (a) Gaussian beams and (b) Airy beams. Here, $\varepsilon _2=2+0.02i$, $E_f=0.5$ eV, and $\alpha =\beta =0.1$.

Download Full Size | PPT Slide | PDF

 figure: Fig. 4.

Fig. 4. (a) GHS ($\Delta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ and the Fermi energy $E_f$ for Airy beams with the monolayer graphene. (b) The real part (solid line) and imaginary part (dashed line) of the conductivity $\sigma$ of graphene as the function of $E_f$. Here, $\varepsilon _2=2+0.02i$, $\lambda =850$ nm, and $\alpha =\beta =0.1$.

Download Full Size | PPT Slide | PDF

Moreover, the surface conductivity $\sigma$ of graphene has a strong dependence on the Fermi energy $E_f$ as well. Figure 4(a) depicts the GHS ($\Delta _{\mathrm {GH}}$) for Airy beams with the monolayer graphene as a function of the incident angle $\theta$ and the Fermi energy $E_f$. Far away from $\theta _B$, the GHS is always small but non-zero. Near $\theta _B$, the GHS rises sharply. It is found that with the increasing $E_f$, the variations of $\Delta _{\mathrm {GH}}$ are not monotonous both at $\theta _B=55.43^\circ$ and $\theta _B=54.74^\circ$. The maximal value of $\Delta _{\mathrm {GH}}$ at $\theta _B=55.43^\circ$ appears at $E_f=0.58$ eV while one at $\theta _B=54.74^\circ$ exists at $E_f=0.82$ eV. The former one is a little bigger than the latter one. Figure 4(b) shows the conductivity $\sigma$ of graphene in dependence on the Fermi energy $E_f$. It is clear that the real part of the graphene conductivity is Re$(\sigma )=0.6\times 10^{-4}$ S/m at $E_f<0.73$ eV, while it becomes 0 at $E_f>0.73$ eV, leading to the two different $\theta _B=55.43^\circ$ and $\theta _B=54.74^\circ$ at both sides of 0.73 eV. Therefore, we can control a considerable GHS from $\theta _B=55.43^\circ$ to $\theta _B=54.74^\circ$ easily by adjusting the Fermi energy from $E_f=0.58$ eV to $E_f=0.82$ eV.

The above discussions in Figs. 3 and 4 involve only the influence of the monolayer graphene on the GH shift. Now, we consider the effect of Airy beams on the GHS. The dependences of the GHSs on the incident angle $\theta$ and the decay factors $\alpha$ $(\beta =\alpha )$ of Airy beams without graphene and with the monolayer graphene are demonstrated in Figs. 5(a) and 5(b), respectively. In fact, as the decay factor $\alpha$ decreases, the value of 1/$\Lambda$ in Eq. (14) also decreases discussed in the recent paper [44]. However, the decrease of $\alpha$ results in an increase of $\Delta _{\mathrm {GH}}$ at $\theta _B$ both in cases of with and without graphene, so the maximal value of $\Delta _{\mathrm {GH}}$ at $\theta _B$ exists at $\alpha =0.02$. It is revealed that the second term in the brackets in Eq. (14) is dominant to $\Delta _{\mathrm {GH}}$ when $\alpha$ is extremely small. Obviously, we find from Figs. 5(a) and 5(b) that using graphene coating can promote the enhancement of $\Delta _{\mathrm {GH}}$ with the decreasing $\alpha$ of Airy beams. Further, by comping Figs. 35, using Airy beams to enhance $\Delta _{\mathrm {GH}}$ is more strongly than inserting the monolayer graphene, which can arrive at $10^3$ $\lambda$.

 figure: Fig. 5.

Fig. 5. The GHS ($\Delta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ and the decay factor $\alpha$ $(\beta =\alpha )$ of Airy beams (a) without graphene and (b) with the monolayer graphene ($E_f=0.3$ eV). Here, $\varepsilon _2=2+0.02i$, and $\lambda =850$ nm.

Download Full Size | PPT Slide | PDF

3.2 Angular GH shift

The GHA ($\Theta _{\mathrm {GH}}$) is depicted in Fig. 6, and the initial beam width for Gaussian and Airy beams is $w_0=1$ mm. Other parameters are the same as those in Fig. 2. There are a pair of positive and opposite GHA peaks for all cases. Similar to the case of the GHS, using the Airy beam with no coating and inserting graphene coating for the Gaussian beam can also promote the GHA, compared to the case for the Gaussian beam without graphene (shown in Fig. 6(a)). In addition, the enhancement of the GHA for the Airy beam with graphene is more significant than the above two cases, by comparing Figs. 6(a) and 6(b). However, it is still an extremely small value of the GHA ( $\simeq 10^{-5}$ rad) which can not be easily observed and measured in experiment. Hence, there is not any more discussion about the GHA in this case.

 figure: Fig. 6.

Fig. 6. The GHA ($\Theta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ for (a) Gaussian beam without graphene (solid line), Gaussian beam with the monolayer graphene (dashed line), Airy beam without graphene (dotted line), and (b) Airy beam with the monolayer graphene. Here, $w_0=1$ mm, $\varepsilon _2=2+0.02i$, $\lambda =1550$ nm, $E_f=0.3$ eV, and $\alpha =\beta =0.1$.

Download Full Size | PPT Slide | PDF

4. Conclusion

In conclusion, we have reported the GHS and the GHA for the p polarized Airy beams impinging onto weakly absorbing media coated with a single layer of graphene for the first time. The influence of the GHS on the incident angle, the incident wavelength, the Fermi energy, and the decay factors of Airy beams is studied and discussed. The simulation results show that the GHS can be significantly enlarged, compared to the case of only using Airy beams or the monolayer graphene. The maximal value of the GHS reaches about three orders of wavelengths, which can be experimentally observed and measured without difficulty. As we all know, Airy beams and graphene are hot research topics in the optical field, and thus employing them can become an easy way to generate a giant GHS in experiment.

Funding

National Natural Science Foundation of China (11374108, 11775083).

Disclosures

The authors declare no conflicts of interest.

References

1. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979). [CrossRef]  

2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef]  

3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef]  

4. P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013). [CrossRef]  

5. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008). [CrossRef]  

6. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010). [CrossRef]  

7. Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013). [CrossRef]  

8. Z. Zheng, B.-F. Zhang, H. Chen, J. Ding, and H.-T. Wang, “Optical trapping with focused Airy beams,” Appl. Opt. 50(1), 43–49 (2011). [CrossRef]  

9. J.-X. Li, W.-P. Zang, and J.-G. Tian, “Vacuum laser-driven acceleration by Airy beams,” Opt. Express 18(7), 7300–7306 (2010). [CrossRef]  

10. J.-X. Li, X.-L. Fan, W.-P. Zang, and J.-G. Tian, “Vacuum electron acceleration driven by two crossed Airy beams,” Opt. Lett. 36(5), 648–650 (2011). [CrossRef]  

11. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008). [CrossRef]  

12. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008). [CrossRef]  

13. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef]  

14. A. K. Geim, “Graphene: Status and Prospects,” Science 324(5934), 1530–1534 (2009). [CrossRef]  

15. L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008). [CrossRef]  

16. A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009). [CrossRef]  

17. C. W. J. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene,” Rev. Mod. Phys. 80(4), 1337–1354 (2008). [CrossRef]  

18. X. Y. Dai, L. Y. Jiang, and Y. J. Xiang, “Tunable optical bistability of dielectric/nonlinear graphene/dielectric heterostructures,” Opt. Express 23(5), 6497–6508 (2015). [CrossRef]  

19. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011). [CrossRef]  

20. B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012). [CrossRef]  

21. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012). [CrossRef]  

22. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

23. F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947). [CrossRef]  

24. F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465 (1955).

25. M. Onoda, S. Murakami, and N. Nagaosa, “Hall Effect of Light,” Phys. Rev. Lett. 93(8), 083901 (2004). [CrossRef]  

26. K. Y. BliokhY. P. Bliokh, Conservation of Angular Momentum, “Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet,” Phys. Rev. Lett. 96(7), 073903 (2006). [CrossRef]  

27. K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007). [CrossRef]  

28. X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017). [CrossRef]  

29. O. Emile, T. Galstyan, A. L. Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995). [CrossRef]  

30. A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008). [CrossRef]  

31. M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for bounded wavepackets of light,” J. Opt. 15(1), 014004 (2013). [CrossRef]  

32. S. Grosche, M. Ornigotti, and A. Szameit, “Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces,” Opt. Express 23(23), 30195–30203 (2015). [CrossRef]  

33. W. Zhen and D. Deng, “Goos-Hänchen and Imbert-Fedorov shifts in temporally dispersive attenuative materials,” J. Phys. D: Appl. Phys. 53(25), 255104 (2020). [CrossRef]  

34. F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019). [CrossRef]  

35. D. Golla and S. D. Gupta, “Goos-Hänchen shift for higher-order Hermite-Gaussian beams,” Pramana 76(4), 603–612 (2011). [CrossRef]  

36. C. Prajapati and D. Ranganathan, “Goos-Hanchen and Imbert-Fedorov shifts for Hermite-Gauss beams,” J. Opt. Soc. Am. A 29(7), 1377–1382 (2012). [CrossRef]  

37. W. Zhen and D. Deng, “Goos-Hänchen shift for elegant Hermite-Gauss light beams impinging on dielectric surfaces coated with a monolayer of graphene,” Appl. Phys. B 126(3), 35 (2020). [CrossRef]  

38. K. N. Pichugin, D. N. Maksimov, and A. F. Sadreev, “Goos-Hänchen and Imbert-Fedorov shifts of higher-order Laguerre-Gaussian beams reflected from a dielectric slab,” J. Opt. Soc. Am. A 35(8), 1324–1329 (2018). [CrossRef]  

39. X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019). [CrossRef]  

40. A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam,” Opt. Lett. 36(4), 543–545 (2011). [CrossRef]  

41. P. Chamorro-Posada, J. Sánchez-Curto, A. B. Aceves, and G. S. McDonald, “Widely varying giant Goos-Hänchen shifts from Airy beams at nonlinear interfaces,” Opt. Lett. 39(6), 1378–1381 (2014). [CrossRef]  

42. M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for Airy beams,” Opt. Lett. 43(6), 1411–1414 (2018). [CrossRef]  

43. C. Zhai and S. Zhang, “Goos-Hänchen shift of an Airy beam reflected in an epsilon-near-zero metamaterial,” Optik 184, 234–240 (2019). [CrossRef]  

44. M. Gao and D. Deng, “Spatial Goos-Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy Airy beams,” Opt. Express 28(7), 10531–10541 (2020). [CrossRef]  

45. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hänchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009). [CrossRef]  

46. Z. Xiao, H. Luo, and S. Wen, “Goos-Hänchen and Imbert-Fedorov shifts of vortex beams at air-left-handed-material interfaces,” Phys. Rev. A 85(5), 053822 (2012). [CrossRef]  

47. C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009). [CrossRef]  

48. M. Cheng, P. Fu, X. Chen, X. Zeng, S. Feng, and R. Chen, “Giant and tunable Goos-Hänchen shifts for attenuated total reflection structure containing graphene,” J. Opt. Soc. Am. B 31(10), 2325–2329 (2014). [CrossRef]  

49. X. Li, P. Wang, F. Xing, X. Chen, Z. Liu, and J. Tian, “Experimental observation of a giant Goos-Hänchen shift in graphene using a beam splitter scanning method,” Opt. Lett. 39(19), 5574–5577 (2014). [CrossRef]  

50. Y. Chen, Y. Ban, Q.-B. Zhu, and X. Chen, “Graphene-assisted resonant transmission and enhanced Goos-Hänchen shift in a frustrated total internal reflection configuration,” Opt. Lett. 41(19), 4468–4471 (2016). [CrossRef]  

51. J. Guo, L. Jiang, X. Dai, and Y. Xiang, “Tunable Fano resonances of a graphene/waveguide hybrid structure at mid-infrared wavelength,” Opt. Express 24(5), 4740–4748 (2016). [CrossRef]  

52. A. Farmani, M. Miri, and M. H. Sheikhi, “Tunable resonant Goos-Hänchen and Imbert-Fedorov shifts in total reflection of terahertz beams from graphene plasmonic metasurfaces,” J. Opt. Soc. Am. B 34(6), 1097–1106 (2017). [CrossRef]  

53. C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017). [CrossRef]  

54. X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise control of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019). [CrossRef]  

55. W. Kong, Y. Sun, and Y Lu, “Enhanced Goos-Hänchen shift of graphene coated on one-dimensional photonic crystal,” Results Phys. 17, 103107 (2020). [CrossRef]  

56. S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Phys. Rev. Appl. 13(1), 014057 (2020). [CrossRef]  

57. X. Zhou, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012). [CrossRef]  

58. S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017). [CrossRef]  

59. W. Wu, W. Zhang, S. Chen, X. Ling, W. Shu, H. Luo, S. Wen, and X. Yin, “Transitional Goos-Hänchen effect due to the topological phase transitions,” Opt. Express 26(18), 23705–23713 (2018). [CrossRef]  

60. D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020). [CrossRef]  

61. W. Wu, S. Chen, C. Mi, W. Zhang, H. Luo, and S. Wen, “Giant quantized Goos-Hänchen effect on the surface of graphene in the quantum Hall regime,” Phys. Rev. A 96(4), 043814 (2017). [CrossRef]  

62. H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. 27(9), 680–682 (2002). [CrossRef]  

63. L.-G. Wang, H. Chen, and S.-Y. Zhu, “Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 30(21), 2936–2938 (2005). [CrossRef]  

64. L.-G. Wang and S.-Y. Zhu, “Large positive and negative Goos-Hänchen shifts from a weakly absorbing left-handed slab,” J. Appl. Phys. 98(4), 043522 (2005). [CrossRef]  

65. J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index,” Opt. Express 14(7), 3024–3029 (2006). [CrossRef]  

66. A. Matthews and Y. Kivshar, “Tunable Goos-Hänchen shift for self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372(17), 3098–3101 (2008). [CrossRef]  

67. I. V. Soboleva, V. V. Moskalenko, and A. A. Fedyanin, “Giant Goos-Hänchen Effect and Fano Resonance at Photonic Crystal Surfaces,” Phys. Rev. Lett. 108(12), 123901 (2012). [CrossRef]  

68. W. Zhen and D. Deng, “Giant Goos-Hänchen shift of a reflected spin wave from the ultrathin interface separating two antiferromagnetically coupled ferromagnets,” Opt. Commun. 474, 126067 (2020). [CrossRef]  

69. J. Wen, J. Zhang, L.-G. Wang, and S.-Y. Zhu, “Goos-Hänchen shifts in an epsilon-near-zero slab,” J. Opt. Soc. Am. B 34(11), 2310–2316 (2017). [CrossRef]  

70. C. Wang, F. Wang, R. Liang, Z. Wei, H. Meng, H. Dong, H. Cen, and N. Lin, “Electrically tunable Goos-Hänchen shifts in weakly absorbing epsilon-near-zero slab,” Opt. Mater. Express 8(4), 718–726 (2018). [CrossRef]  

71. A. Nieminen, A. Marini, and M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for epsilon-near-zero materials,” J. Opt. 22(3), 035601 (2020). [CrossRef]  

72. G. Jayaswal, G. Mistura, and M. Merano, “Weak measurement of the Goos-Hänchen shift,” Opt. Lett. 38(8), 1232–1234 (2013). [CrossRef]  

73. O. J. S. Santana, S. A. Carvalho, S. de Leo, and L. E. E. de Araujo, “Weak measurement of the composite Goos-Hänchen shift in the critical region,” Opt. Lett. 41(16), 3884–3887 (2016). [CrossRef]  

74. S. Goswami, S. Dhara, M. Pal, A. Nandi, P. K. Panigrahi, and N. Ghosh, “Optimized weak measurements of Goos-Hänchen and Imbert-Fedorov shifts in partial reflection,” Opt. Express 24(6), 6041–6051 (2016). [CrossRef]  

75. L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

76. R. F. Gragg, “The total reflection of a compact wave group: long-range trasmission in a waveguide,” Am. J. Phys. 56(12), 1092–1094 (1988). [CrossRef]  

77. A. Aiello and J. Woerdman, “Theory of angular Goos-Hänchen shift near brewster incidence,” arXiv preprint arXiv:0903.3730 (2009).

78. J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73(15), 2084–2086 (1998). [CrossRef]  

79. T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013). [CrossRef]  

80. F. H. L. Koppens, D. E. Chang, and F. J. Garcĺa de Abajo, “Graphene plasmonics: A platform for strong lightmatter interactions,” Nano Lett. 11(8), 3370–3377 (2011). [CrossRef]  

References

  • View by:

  1. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
    [Crossref]
  2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
    [Crossref]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
    [Crossref]
  4. P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
    [Crossref]
  5. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
    [Crossref]
  6. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
    [Crossref]
  7. Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
    [Crossref]
  8. Z. Zheng, B.-F. Zhang, H. Chen, J. Ding, and H.-T. Wang, “Optical trapping with focused Airy beams,” Appl. Opt. 50(1), 43–49 (2011).
    [Crossref]
  9. J.-X. Li, W.-P. Zang, and J.-G. Tian, “Vacuum laser-driven acceleration by Airy beams,” Opt. Express 18(7), 7300–7306 (2010).
    [Crossref]
  10. J.-X. Li, X.-L. Fan, W.-P. Zang, and J.-G. Tian, “Vacuum electron acceleration driven by two crossed Airy beams,” Opt. Lett. 36(5), 648–650 (2011).
    [Crossref]
  11. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
    [Crossref]
  12. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
    [Crossref]
  13. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
    [Crossref]
  14. A. K. Geim, “Graphene: Status and Prospects,” Science 324(5934), 1530–1534 (2009).
    [Crossref]
  15. L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
    [Crossref]
  16. A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
    [Crossref]
  17. C. W. J. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene,” Rev. Mod. Phys. 80(4), 1337–1354 (2008).
    [Crossref]
  18. X. Y. Dai, L. Y. Jiang, and Y. J. Xiang, “Tunable optical bistability of dielectric/nonlinear graphene/dielectric heterostructures,” Opt. Express 23(5), 6497–6508 (2015).
    [Crossref]
  19. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
    [Crossref]
  20. B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
    [Crossref]
  21. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
    [Crossref]
  22. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  23. F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
    [Crossref]
  24. F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465 (1955).
  25. M. Onoda, S. Murakami, and N. Nagaosa, “Hall Effect of Light,” Phys. Rev. Lett. 93(8), 083901 (2004).
    [Crossref]
  26. K. Y. Bliokh and Y. P. Bliokh, Conservation of Angular Momentum, “Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
    [Crossref]
  27. K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
    [Crossref]
  28. X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
    [Crossref]
  29. O. Emile, T. Galstyan, A. L. Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
    [Crossref]
  30. A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
    [Crossref]
  31. M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for bounded wavepackets of light,” J. Opt. 15(1), 014004 (2013).
    [Crossref]
  32. S. Grosche, M. Ornigotti, and A. Szameit, “Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces,” Opt. Express 23(23), 30195–30203 (2015).
    [Crossref]
  33. W. Zhen and D. Deng, “Goos-Hänchen and Imbert-Fedorov shifts in temporally dispersive attenuative materials,” J. Phys. D: Appl. Phys. 53(25), 255104 (2020).
    [Crossref]
  34. F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
    [Crossref]
  35. D. Golla and S. D. Gupta, “Goos-Hänchen shift for higher-order Hermite-Gaussian beams,” Pramana 76(4), 603–612 (2011).
    [Crossref]
  36. C. Prajapati and D. Ranganathan, “Goos-Hanchen and Imbert-Fedorov shifts for Hermite-Gauss beams,” J. Opt. Soc. Am. A 29(7), 1377–1382 (2012).
    [Crossref]
  37. W. Zhen and D. Deng, “Goos-Hänchen shift for elegant Hermite-Gauss light beams impinging on dielectric surfaces coated with a monolayer of graphene,” Appl. Phys. B 126(3), 35 (2020).
    [Crossref]
  38. K. N. Pichugin, D. N. Maksimov, and A. F. Sadreev, “Goos-Hänchen and Imbert-Fedorov shifts of higher-order Laguerre-Gaussian beams reflected from a dielectric slab,” J. Opt. Soc. Am. A 35(8), 1324–1329 (2018).
    [Crossref]
  39. X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
    [Crossref]
  40. A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam,” Opt. Lett. 36(4), 543–545 (2011).
    [Crossref]
  41. P. Chamorro-Posada, J. Sánchez-Curto, A. B. Aceves, and G. S. McDonald, “Widely varying giant Goos-Hänchen shifts from Airy beams at nonlinear interfaces,” Opt. Lett. 39(6), 1378–1381 (2014).
    [Crossref]
  42. M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for Airy beams,” Opt. Lett. 43(6), 1411–1414 (2018).
    [Crossref]
  43. C. Zhai and S. Zhang, “Goos-Hänchen shift of an Airy beam reflected in an epsilon-near-zero metamaterial,” Optik 184, 234–240 (2019).
    [Crossref]
  44. M. Gao and D. Deng, “Spatial Goos-Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy Airy beams,” Opt. Express 28(7), 10531–10541 (2020).
    [Crossref]
  45. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hänchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009).
    [Crossref]
  46. Z. Xiao, H. Luo, and S. Wen, “Goos-Hänchen and Imbert-Fedorov shifts of vortex beams at air-left-handed-material interfaces,” Phys. Rev. A 85(5), 053822 (2012).
    [Crossref]
  47. C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
    [Crossref]
  48. M. Cheng, P. Fu, X. Chen, X. Zeng, S. Feng, and R. Chen, “Giant and tunable Goos-Hänchen shifts for attenuated total reflection structure containing graphene,” J. Opt. Soc. Am. B 31(10), 2325–2329 (2014).
    [Crossref]
  49. X. Li, P. Wang, F. Xing, X. Chen, Z. Liu, and J. Tian, “Experimental observation of a giant Goos-Hänchen shift in graphene using a beam splitter scanning method,” Opt. Lett. 39(19), 5574–5577 (2014).
    [Crossref]
  50. Y. Chen, Y. Ban, Q.-B. Zhu, and X. Chen, “Graphene-assisted resonant transmission and enhanced Goos-Hänchen shift in a frustrated total internal reflection configuration,” Opt. Lett. 41(19), 4468–4471 (2016).
    [Crossref]
  51. J. Guo, L. Jiang, X. Dai, and Y. Xiang, “Tunable Fano resonances of a graphene/waveguide hybrid structure at mid-infrared wavelength,” Opt. Express 24(5), 4740–4748 (2016).
    [Crossref]
  52. A. Farmani, M. Miri, and M. H. Sheikhi, “Tunable resonant Goos-Hänchen and Imbert-Fedorov shifts in total reflection of terahertz beams from graphene plasmonic metasurfaces,” J. Opt. Soc. Am. B 34(6), 1097–1106 (2017).
    [Crossref]
  53. C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017).
    [Crossref]
  54. X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise control of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
    [Crossref]
  55. W. Kong, Y. Sun, and Y Lu, “Enhanced Goos-Hänchen shift of graphene coated on one-dimensional photonic crystal,” Results Phys. 17, 103107 (2020).
    [Crossref]
  56. S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Phys. Rev. Appl. 13(1), 014057 (2020).
    [Crossref]
  57. X. Zhou, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
    [Crossref]
  58. S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017).
    [Crossref]
  59. W. Wu, W. Zhang, S. Chen, X. Ling, W. Shu, H. Luo, S. Wen, and X. Yin, “Transitional Goos-Hänchen effect due to the topological phase transitions,” Opt. Express 26(18), 23705–23713 (2018).
    [Crossref]
  60. D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
    [Crossref]
  61. W. Wu, S. Chen, C. Mi, W. Zhang, H. Luo, and S. Wen, “Giant quantized Goos-Hänchen effect on the surface of graphene in the quantum Hall regime,” Phys. Rev. A 96(4), 043814 (2017).
    [Crossref]
  62. H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. 27(9), 680–682 (2002).
    [Crossref]
  63. L.-G. Wang, H. Chen, and S.-Y. Zhu, “Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 30(21), 2936–2938 (2005).
    [Crossref]
  64. L.-G. Wang and S.-Y. Zhu, “Large positive and negative Goos-Hänchen shifts from a weakly absorbing left-handed slab,” J. Appl. Phys. 98(4), 043522 (2005).
    [Crossref]
  65. J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index,” Opt. Express 14(7), 3024–3029 (2006).
    [Crossref]
  66. A. Matthews and Y. Kivshar, “Tunable Goos-Hänchen shift for self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372(17), 3098–3101 (2008).
    [Crossref]
  67. I. V. Soboleva, V. V. Moskalenko, and A. A. Fedyanin, “Giant Goos-Hänchen Effect and Fano Resonance at Photonic Crystal Surfaces,” Phys. Rev. Lett. 108(12), 123901 (2012).
    [Crossref]
  68. W. Zhen and D. Deng, “Giant Goos-Hänchen shift of a reflected spin wave from the ultrathin interface separating two antiferromagnetically coupled ferromagnets,” Opt. Commun. 474, 126067 (2020).
    [Crossref]
  69. J. Wen, J. Zhang, L.-G. Wang, and S.-Y. Zhu, “Goos-Hänchen shifts in an epsilon-near-zero slab,” J. Opt. Soc. Am. B 34(11), 2310–2316 (2017).
    [Crossref]
  70. C. Wang, F. Wang, R. Liang, Z. Wei, H. Meng, H. Dong, H. Cen, and N. Lin, “Electrically tunable Goos-Hänchen shifts in weakly absorbing epsilon-near-zero slab,” Opt. Mater. Express 8(4), 718–726 (2018).
    [Crossref]
  71. A. Nieminen, A. Marini, and M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for epsilon-near-zero materials,” J. Opt. 22(3), 035601 (2020).
    [Crossref]
  72. G. Jayaswal, G. Mistura, and M. Merano, “Weak measurement of the Goos-Hänchen shift,” Opt. Lett. 38(8), 1232–1234 (2013).
    [Crossref]
  73. O. J. S. Santana, S. A. Carvalho, S. de Leo, and L. E. E. de Araujo, “Weak measurement of the composite Goos-Hänchen shift in the critical region,” Opt. Lett. 41(16), 3884–3887 (2016).
    [Crossref]
  74. S. Goswami, S. Dhara, M. Pal, A. Nandi, P. K. Panigrahi, and N. Ghosh, “Optimized weak measurements of Goos-Hänchen and Imbert-Fedorov shifts in partial reflection,” Opt. Express 24(6), 6041–6051 (2016).
    [Crossref]
  75. L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).
  76. R. F. Gragg, “The total reflection of a compact wave group: long-range trasmission in a waveguide,” Am. J. Phys. 56(12), 1092–1094 (1988).
    [Crossref]
  77. A. Aiello and J. Woerdman, “Theory of angular Goos-Hänchen shift near brewster incidence,” arXiv preprint arXiv:0903.3730 (2009).
  78. J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73(15), 2084–2086 (1998).
    [Crossref]
  79. T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013).
    [Crossref]
  80. F. H. L. Koppens, D. E. Chang, and F. J. Garcĺa de Abajo, “Graphene plasmonics: A platform for strong lightmatter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
    [Crossref]

2020 (8)

W. Zhen and D. Deng, “Goos-Hänchen and Imbert-Fedorov shifts in temporally dispersive attenuative materials,” J. Phys. D: Appl. Phys. 53(25), 255104 (2020).
[Crossref]

W. Zhen and D. Deng, “Goos-Hänchen shift for elegant Hermite-Gauss light beams impinging on dielectric surfaces coated with a monolayer of graphene,” Appl. Phys. B 126(3), 35 (2020).
[Crossref]

M. Gao and D. Deng, “Spatial Goos-Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy Airy beams,” Opt. Express 28(7), 10531–10541 (2020).
[Crossref]

W. Kong, Y. Sun, and Y Lu, “Enhanced Goos-Hänchen shift of graphene coated on one-dimensional photonic crystal,” Results Phys. 17, 103107 (2020).
[Crossref]

S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Phys. Rev. Appl. 13(1), 014057 (2020).
[Crossref]

D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
[Crossref]

W. Zhen and D. Deng, “Giant Goos-Hänchen shift of a reflected spin wave from the ultrathin interface separating two antiferromagnetically coupled ferromagnets,” Opt. Commun. 474, 126067 (2020).
[Crossref]

A. Nieminen, A. Marini, and M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for epsilon-near-zero materials,” J. Opt. 22(3), 035601 (2020).
[Crossref]

2019 (4)

C. Zhai and S. Zhang, “Goos-Hänchen shift of an Airy beam reflected in an epsilon-near-zero metamaterial,” Optik 184, 234–240 (2019).
[Crossref]

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise control of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
[Crossref]

2018 (4)

2017 (6)

J. Wen, J. Zhang, L.-G. Wang, and S.-Y. Zhu, “Goos-Hänchen shifts in an epsilon-near-zero slab,” J. Opt. Soc. Am. B 34(11), 2310–2316 (2017).
[Crossref]

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

W. Wu, S. Chen, C. Mi, W. Zhang, H. Luo, and S. Wen, “Giant quantized Goos-Hänchen effect on the surface of graphene in the quantum Hall regime,” Phys. Rev. A 96(4), 043814 (2017).
[Crossref]

A. Farmani, M. Miri, and M. H. Sheikhi, “Tunable resonant Goos-Hänchen and Imbert-Fedorov shifts in total reflection of terahertz beams from graphene plasmonic metasurfaces,” J. Opt. Soc. Am. B 34(6), 1097–1106 (2017).
[Crossref]

C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

2016 (4)

2015 (2)

2014 (3)

2013 (5)

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for bounded wavepackets of light,” J. Opt. 15(1), 014004 (2013).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
[Crossref]

G. Jayaswal, G. Mistura, and M. Merano, “Weak measurement of the Goos-Hänchen shift,” Opt. Lett. 38(8), 1232–1234 (2013).
[Crossref]

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013).
[Crossref]

2012 (6)

C. Prajapati and D. Ranganathan, “Goos-Hanchen and Imbert-Fedorov shifts for Hermite-Gauss beams,” J. Opt. Soc. Am. A 29(7), 1377–1382 (2012).
[Crossref]

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos-Hänchen and Imbert-Fedorov shifts of vortex beams at air-left-handed-material interfaces,” Phys. Rev. A 85(5), 053822 (2012).
[Crossref]

X. Zhou, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

I. V. Soboleva, V. V. Moskalenko, and A. A. Fedyanin, “Giant Goos-Hänchen Effect and Fano Resonance at Photonic Crystal Surfaces,” Phys. Rev. Lett. 108(12), 123901 (2012).
[Crossref]

2011 (6)

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam,” Opt. Lett. 36(4), 543–545 (2011).
[Crossref]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

D. Golla and S. D. Gupta, “Goos-Hänchen shift for higher-order Hermite-Gaussian beams,” Pramana 76(4), 603–612 (2011).
[Crossref]

Z. Zheng, B.-F. Zhang, H. Chen, J. Ding, and H.-T. Wang, “Optical trapping with focused Airy beams,” Appl. Opt. 50(1), 43–49 (2011).
[Crossref]

J.-X. Li, X.-L. Fan, W.-P. Zang, and J.-G. Tian, “Vacuum electron acceleration driven by two crossed Airy beams,” Opt. Lett. 36(5), 648–650 (2011).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. Garcĺa de Abajo, “Graphene plasmonics: A platform for strong lightmatter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref]

2010 (2)

J.-X. Li, W.-P. Zang, and J.-G. Tian, “Vacuum laser-driven acceleration by Airy beams,” Opt. Express 18(7), 7300–7306 (2010).
[Crossref]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

2009 (4)

A. K. Geim, “Graphene: Status and Prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref]

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hänchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009).
[Crossref]

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref]

2008 (7)

A. Matthews and Y. Kivshar, “Tunable Goos-Hänchen shift for self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372(17), 3098–3101 (2008).
[Crossref]

C. W. J. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene,” Rev. Mod. Phys. 80(4), 1337–1354 (2008).
[Crossref]

L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[Crossref]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[Crossref]

2007 (3)

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

2006 (2)

K. Y. Bliokh and Y. P. Bliokh, Conservation of Angular Momentum, “Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index,” Opt. Express 14(7), 3024–3029 (2006).
[Crossref]

2005 (2)

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 30(21), 2936–2938 (2005).
[Crossref]

L.-G. Wang and S.-Y. Zhu, “Large positive and negative Goos-Hänchen shifts from a weakly absorbing left-handed slab,” J. Appl. Phys. 98(4), 043522 (2005).
[Crossref]

2004 (2)

M. Onoda, S. Murakami, and N. Nagaosa, “Hall Effect of Light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

2002 (1)

1998 (1)

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73(15), 2084–2086 (1998).
[Crossref]

1995 (1)

O. Emile, T. Galstyan, A. L. Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

1988 (1)

R. F. Gragg, “The total reflection of a compact wave group: long-range trasmission in a waveguide,” Am. J. Phys. 56(12), 1092–1094 (1988).
[Crossref]

1979 (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

1955 (1)

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465 (1955).

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

Aceves, A. B.

Aiello, A.

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for bounded wavepackets of light,” J. Opt. 15(1), 014004 (2013).
[Crossref]

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam,” Opt. Lett. 36(4), 543–545 (2011).
[Crossref]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[Crossref]

A. Aiello and J. Woerdman, “Theory of angular Goos-Hänchen shift near brewster incidence,” arXiv preprint arXiv:0903.3730 (2009).

Akhmerov, A. R.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref]

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Ban, Y.

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Beenakker, C. W. J.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref]

C. W. J. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene,” Rev. Mod. Phys. 80(4), 1337–1354 (2008).
[Crossref]

Belic, M. R.

Berry, M. V.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hänchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, Conservation of Angular Momentum, “Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, Conservation of Angular Momentum, “Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

Boguslawski, M.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Bretenaker, F.

O. Emile, T. Galstyan, A. L. Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

Broky, J.

Cai, L.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

Carvalho, S. A.

Castro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Cen, H.

Chamorro-Posada, P.

Chan, S. W.

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. Garcĺa de Abajo, “Graphene plasmonics: A platform for strong lightmatter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref]

Chen, H.

Chen, R.

Chen, S.

S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Phys. Rev. Appl. 13(1), 014057 (2020).
[Crossref]

D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
[Crossref]

W. Wu, W. Zhang, S. Chen, X. Ling, W. Shu, H. Luo, S. Wen, and X. Yin, “Transitional Goos-Hänchen effect due to the topological phase transitions,” Opt. Express 26(18), 23705–23713 (2018).
[Crossref]

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

W. Wu, S. Chen, C. Mi, W. Zhang, H. Luo, and S. Wen, “Giant quantized Goos-Hänchen effect on the surface of graphene in the quantum Hall regime,” Phys. Rev. A 96(4), 043814 (2017).
[Crossref]

C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017).
[Crossref]

Chen, X.

Chen, Y.

Chen, Z.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

Cheng, M.

Christodoulides, D. N.

Dai, X.

Dai, X. Y.

Dai, Y.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013).
[Crossref]

de Araujo, L. E. E.

de Leo, S.

Deng, D.

W. Zhen and D. Deng, “Goos-Hänchen and Imbert-Fedorov shifts in temporally dispersive attenuative materials,” J. Phys. D: Appl. Phys. 53(25), 255104 (2020).
[Crossref]

M. Gao and D. Deng, “Spatial Goos-Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy Airy beams,” Opt. Express 28(7), 10531–10541 (2020).
[Crossref]

W. Zhen and D. Deng, “Goos-Hänchen shift for elegant Hermite-Gauss light beams impinging on dielectric surfaces coated with a monolayer of graphene,” Appl. Phys. B 126(3), 35 (2020).
[Crossref]

W. Zhen and D. Deng, “Giant Goos-Hänchen shift of a reflected spin wave from the ultrathin interface separating two antiferromagnetically coupled ferromagnets,” Opt. Commun. 474, 126067 (2020).
[Crossref]

Denz, C.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

Dhara, S.

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Diebel, F.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

Ding, J.

Ding, Y.

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise control of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

Dogariu, A.

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Dong, H.

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Emile, O.

O. Emile, T. Galstyan, A. L. Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

Falkovsky, L. A.

L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]

Fan, X.-L.

Fang, T.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Farmani, A.

Fedorov, F. I.

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465 (1955).

Fedyanin, A. A.

I. V. Soboleva, V. V. Moskalenko, and A. A. Fedyanin, “Giant Goos-Hänchen Effect and Fano Resonance at Photonic Crystal Surfaces,” Phys. Rev. Lett. 108(12), 123901 (2012).
[Crossref]

Fei, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Feng, S.

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Floch, A. L.

O. Emile, T. Galstyan, A. L. Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

Fogler, M. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Fu, P.

Galstyan, T.

O. Emile, T. Galstyan, A. L. Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

Gao, M.

M. Gao and D. Deng, “Spatial Goos-Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy Airy beams,” Opt. Express 28(7), 10531–10541 (2020).
[Crossref]

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

Garcla de Abajo, F. J.

F. H. L. Koppens, D. E. Chang, and F. J. Garcĺa de Abajo, “Graphene plasmonics: A platform for strong lightmatter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref]

Geim, A. K.

A. K. Geim, “Graphene: Status and Prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref]

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Ghosh, N.

Golla, D.

D. Golla and S. D. Gupta, “Goos-Hänchen shift for higher-order Hermite-Gaussian beams,” Pramana 76(4), 603–612 (2011).
[Crossref]

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

Goswami, S.

Gragg, R. F.

R. F. Gragg, “The total reflection of a compact wave group: long-range trasmission in a waveguide,” Am. J. Phys. 56(12), 1092–1094 (1988).
[Crossref]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Grosche, S.

Guan, H.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

Guinea, F.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Guo, J.

Guo, X.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

Guo, Z.

F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
[Crossref]

Gupta, S. D.

D. Golla and S. D. Gupta, “Goos-Hänchen shift for higher-order Hermite-Gaussian beams,” Pramana 76(4), 603–612 (2011).
[Crossref]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

He, J.

He, S.

D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
[Crossref]

J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index,” Opt. Express 14(7), 3024–3029 (2006).
[Crossref]

Huang, K.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

Hwang, W. S.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Jayaswal, G.

Jena, D.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Jiang, H.

F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
[Crossref]

Jiang, L.

Jiang, L. Y.

Keilmann, F.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Kelly, M. M.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Kivshar, Y.

A. Matthews and Y. Kivshar, “Tunable Goos-Hänchen shift for self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372(17), 3098–3101 (2008).
[Crossref]

Kivshar, Y. S.

Kong, W.

W. Kong, Y. Sun, and Y Lu, “Enhanced Goos-Hänchen shift of graphene coated on one-dimensional photonic crystal,” Results Phys. 17, 103107 (2020).
[Crossref]

Koppens, F. H. L.

F. H. L. Koppens, D. E. Chang, and F. J. Garcĺa de Abajo, “Graphene plasmonics: A platform for strong lightmatter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref]

Lai, H. M.

Lau, C. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Li, J.-X.

Li, X.

Li, Y.

F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
[Crossref]

Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
[Crossref]

Liang, R.

Lin, N.

Ling, X.

S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Phys. Rev. Appl. 13(1), 014057 (2020).
[Crossref]

W. Wu, W. Zhang, S. Chen, X. Ling, W. Shu, H. Luo, S. Wen, and X. Yin, “Transitional Goos-Hänchen effect due to the topological phase transitions,” Opt. Express 26(18), 23705–23713 (2018).
[Crossref]

C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

Liu, L.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Liu, M.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

Liu, S.

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise control of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

Liu, X.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013).
[Crossref]

Liu, Y.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

Liu, Z.

Loh, K. P.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Long, W.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

Lu, H.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

Lu, K.

Lu, Y

W. Kong, Y. Sun, and Y Lu, “Enhanced Goos-Hänchen shift of graphene coated on one-dimensional photonic crystal,” Results Phys. 17, 103107 (2020).
[Crossref]

Luo, H.

D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
[Crossref]

S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Phys. Rev. Appl. 13(1), 014057 (2020).
[Crossref]

W. Wu, W. Zhang, S. Chen, X. Ling, W. Shu, H. Luo, S. Wen, and X. Yin, “Transitional Goos-Hänchen effect due to the topological phase transitions,” Opt. Express 26(18), 23705–23713 (2018).
[Crossref]

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

W. Wu, S. Chen, C. Mi, W. Zhang, H. Luo, and S. Wen, “Giant quantized Goos-Hänchen effect on the surface of graphene in the quantum Hall regime,” Phys. Rev. A 96(4), 043814 (2017).
[Crossref]

C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos-Hänchen and Imbert-Fedorov shifts of vortex beams at air-left-handed-material interfaces,” Phys. Rev. A 85(5), 053822 (2012).
[Crossref]

X. Zhou, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

Luo, Y.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

Luo, Z.

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise control of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

Maksimov, D. N.

Mandel, L.

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

Marini, A.

A. Nieminen, A. Marini, and M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for epsilon-near-zero materials,” J. Opt. 22(3), 035601 (2020).
[Crossref]

Matthews, A.

A. Matthews and Y. Kivshar, “Tunable Goos-Hänchen shift for self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372(17), 3098–3101 (2008).
[Crossref]

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

McDonald, G. S.

McLeod, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Meng, H.

Merano, M.

Mi, C.

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

W. Wu, S. Chen, C. Mi, W. Zhang, H. Luo, and S. Wen, “Giant quantized Goos-Hänchen effect on the surface of graphene in the quantum Hall regime,” Phys. Rev. A 96(4), 043814 (2017).
[Crossref]

C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017).
[Crossref]

Min, L.

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise control of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

Miri, M.

Mistura, G.

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Moskalenko, V. V.

I. V. Soboleva, V. V. Moskalenko, and A. A. Fedyanin, “Giant Goos-Hänchen Effect and Fano Resonance at Photonic Crystal Surfaces,” Phys. Rev. Lett. 108(12), 123901 (2012).
[Crossref]

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall Effect of Light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall Effect of Light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

Nandi, A.

Neto, A. H. C.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Ni, Z.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Nieminen, A.

A. Nieminen, A. Marini, and M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for epsilon-near-zero materials,” J. Opt. 22(3), 035601 (2020).
[Crossref]

Novoselov, K. S.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall Effect of Light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

Ornigotti, M.

A. Nieminen, A. Marini, and M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for epsilon-near-zero materials,” J. Opt. 22(3), 035601 (2020).
[Crossref]

M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for Airy beams,” Opt. Lett. 43(6), 1411–1414 (2018).
[Crossref]

S. Grosche, M. Ornigotti, and A. Szameit, “Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces,” Opt. Express 23(23), 30195–30203 (2015).
[Crossref]

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for bounded wavepackets of light,” J. Opt. 15(1), 014004 (2013).
[Crossref]

Pal, M.

Panigrahi, P. K.

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

Peres, N. M. R.

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Pichugin, K. N.

Prajapati, C.

Qiu, C.-W.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

Ranganathan, D.

Ren, J.

F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
[Crossref]

Rodin, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Rose, P.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

Sadreev, A. F.

Sánchez-Curto, J.

Santana, O. J. S.

Sensale-Rodriguez, B.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Sepkhanov, R. A.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref]

Shadrivov, I. V.

Sheikhi, M. H.

Shi, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013).
[Crossref]

Shu, W.

Siviloglou, G. A.

Soboleva, I. V.

I. V. Soboleva, V. V. Moskalenko, and A. A. Fedyanin, “Giant Goos-Hänchen Effect and Fano Resonance at Photonic Crystal Surfaces,” Phys. Rev. Lett. 108(12), 123901 (2012).
[Crossref]

Sun, Y.

W. Kong, Y. Sun, and Y Lu, “Enhanced Goos-Hänchen shift of graphene coated on one-dimensional photonic crystal,” Results Phys. 17, 103107 (2020).
[Crossref]

F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
[Crossref]

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

Szameit, A.

Tahy, K.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Tang, D. Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Thiemens, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Tian, J.

Tian, J.-G.

Tworzydlo, J.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

Wagner, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Wan, J.

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73(15), 2084–2086 (1998).
[Crossref]

Wang, B.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Wang, C.

Wang, F.

Wang, H.-T.

Wang, L.-G.

Wang, P.

Wang, Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Wei, Z.

Wen, J.

Wen, S.

S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Phys. Rev. Appl. 13(1), 014057 (2020).
[Crossref]

D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
[Crossref]

W. Wu, W. Zhang, S. Chen, X. Ling, W. Shu, H. Luo, S. Wen, and X. Yin, “Transitional Goos-Hänchen effect due to the topological phase transitions,” Opt. Express 26(18), 23705–23713 (2018).
[Crossref]

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

W. Wu, S. Chen, C. Mi, W. Zhang, H. Luo, and S. Wen, “Giant quantized Goos-Hänchen effect on the surface of graphene in the quantum Hall regime,” Phys. Rev. A 96(4), 043814 (2017).
[Crossref]

C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos-Hänchen and Imbert-Fedorov shifts of vortex beams at air-left-handed-material interfaces,” Phys. Rev. A 85(5), 053822 (2012).
[Crossref]

X. Zhou, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

Woerdman, J.

A. Aiello and J. Woerdman, “Theory of angular Goos-Hänchen shift near brewster incidence,” arXiv preprint arXiv:0903.3730 (2009).

Woerdman, J. P.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

Wu, F.

F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
[Crossref]

Wu, J.

F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
[Crossref]

Wu, W.

Wu, Z.

X. Lim, C. H. Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Xiang, Y.

Xiang, Y. J.

Xiao, Z.

Z. Xiao, H. Luo, and S. Wen, “Goos-Hänchen and Imbert-Fedorov shifts of vortex beams at air-left-handed-material interfaces,” Phys. Rev. A 85(5), 053822 (2012).
[Crossref]

Xing, F.

Xing, H. G.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Xu, D.

D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
[Crossref]

Yan, R.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Yi, J.

Yin, X.

Yu, J.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

Zang, W.-P.

Zeng, X.

Zhai, C.

C. Zhai and S. Zhang, “Goos-Hänchen shift of an Airy beam reflected in an epsilon-near-zero metamaterial,” Optik 184, 234–240 (2019).
[Crossref]

Zhan, T.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013).
[Crossref]

Zhang, B.-F.

Zhang, C.

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73(15), 2084–2086 (1998).
[Crossref]

Zhang, H.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Zhang, J.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

J. Wen, J. Zhang, L.-G. Wang, and S.-Y. Zhu, “Goos-Hänchen shifts in an epsilon-near-zero slab,” J. Opt. Soc. Am. B 34(11), 2310–2316 (2017).
[Crossref]

Zhang, L. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Zhang, S.

C. Zhai and S. Zhang, “Goos-Hänchen shift of an Airy beam reflected in an epsilon-near-zero metamaterial,” Optik 184, 234–240 (2019).
[Crossref]

Zhang, W.

Zhang, Y.

Zhao, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Zhen, W.

W. Zhen and D. Deng, “Goos-Hänchen and Imbert-Fedorov shifts in temporally dispersive attenuative materials,” J. Phys. D: Appl. Phys. 53(25), 255104 (2020).
[Crossref]

W. Zhen and D. Deng, “Goos-Hänchen shift for elegant Hermite-Gauss light beams impinging on dielectric surfaces coated with a monolayer of graphene,” Appl. Phys. B 126(3), 35 (2020).
[Crossref]

W. Zhen and D. Deng, “Giant Goos-Hänchen shift of a reflected spin wave from the ultrathin interface separating two antiferromagnetically coupled ferromagnets,” Opt. Commun. 474, 126067 (2020).
[Crossref]

Zheng, H.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
[Crossref]

Zheng, Z.

Zhou, J.

D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
[Crossref]

Zhou, X.

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise control of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

X. Zhou, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

Zhu, Q.-B.

Zhu, S.-Y.

Zhu, W.

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

Zi, J.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013).
[Crossref]

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73(15), 2084–2086 (1998).
[Crossref]

Am. J. Phys. (2)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

R. F. Gragg, “The total reflection of a compact wave group: long-range trasmission in a waveguide,” Am. J. Phys. 56(12), 1092–1094 (1988).
[Crossref]

Ann. Phys. (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

W. Zhen and D. Deng, “Goos-Hänchen shift for elegant Hermite-Gauss light beams impinging on dielectric surfaces coated with a monolayer of graphene,” Appl. Phys. B 126(3), 35 (2020).
[Crossref]

Appl. Phys. Lett. (5)

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
[Crossref]

X. Zhou, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73(15), 2084–2086 (1998).
[Crossref]

Carbon (1)

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise control of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

Dokl. Akad. Nauk SSSR (1)

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465 (1955).

J. Appl. Phys. (1)

L.-G. Wang and S.-Y. Zhu, “Large positive and negative Goos-Hänchen shifts from a weakly absorbing left-handed slab,” J. Appl. Phys. 98(4), 043522 (2005).
[Crossref]

J. Opt. (2)

A. Nieminen, A. Marini, and M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for epsilon-near-zero materials,” J. Opt. 22(3), 035601 (2020).
[Crossref]

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for bounded wavepackets of light,” J. Opt. 15(1), 014004 (2013).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (3)

J. Phys. D: Appl. Phys. (1)

W. Zhen and D. Deng, “Goos-Hänchen and Imbert-Fedorov shifts in temporally dispersive attenuative materials,” J. Phys. D: Appl. Phys. 53(25), 255104 (2020).
[Crossref]

J. Phys.: Condens. Matter (1)

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013).
[Crossref]

J. Phys.: Conf. Ser. (1)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]

Nano Lett. (1)

F. H. L. Koppens, D. E. Chang, and F. J. Garcĺa de Abajo, “Graphene plasmonics: A platform for strong lightmatter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref]

Nat. Commun. (1)

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Nat. Photonics (2)

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Nature (1)

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Opt. Commun. (2)

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

W. Zhen and D. Deng, “Giant Goos-Hänchen shift of a reflected spin wave from the ultrathin interface separating two antiferromagnetically coupled ferromagnets,” Opt. Commun. 474, 126067 (2020).
[Crossref]

Opt. Express (9)

S. Grosche, M. Ornigotti, and A. Szameit, “Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces,” Opt. Express 23(23), 30195–30203 (2015).
[Crossref]

X. Y. Dai, L. Y. Jiang, and Y. J. Xiang, “Tunable optical bistability of dielectric/nonlinear graphene/dielectric heterostructures,” Opt. Express 23(5), 6497–6508 (2015).
[Crossref]

J.-X. Li, W.-P. Zang, and J.-G. Tian, “Vacuum laser-driven acceleration by Airy beams,” Opt. Express 18(7), 7300–7306 (2010).
[Crossref]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref]

S. Goswami, S. Dhara, M. Pal, A. Nandi, P. K. Panigrahi, and N. Ghosh, “Optimized weak measurements of Goos-Hänchen and Imbert-Fedorov shifts in partial reflection,” Opt. Express 24(6), 6041–6051 (2016).
[Crossref]

J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index,” Opt. Express 14(7), 3024–3029 (2006).
[Crossref]

W. Wu, W. Zhang, S. Chen, X. Ling, W. Shu, H. Luo, S. Wen, and X. Yin, “Transitional Goos-Hänchen effect due to the topological phase transitions,” Opt. Express 26(18), 23705–23713 (2018).
[Crossref]

J. Guo, L. Jiang, X. Dai, and Y. Xiang, “Tunable Fano resonances of a graphene/waveguide hybrid structure at mid-infrared wavelength,” Opt. Express 24(5), 4740–4748 (2016).
[Crossref]

M. Gao and D. Deng, “Spatial Goos-Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy Airy beams,” Opt. Express 28(7), 10531–10541 (2020).
[Crossref]

Opt. Lett. (16)

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hänchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009).
[Crossref]

X. Li, P. Wang, F. Xing, X. Chen, Z. Liu, and J. Tian, “Experimental observation of a giant Goos-Hänchen shift in graphene using a beam splitter scanning method,” Opt. Lett. 39(19), 5574–5577 (2014).
[Crossref]

Y. Chen, Y. Ban, Q.-B. Zhu, and X. Chen, “Graphene-assisted resonant transmission and enhanced Goos-Hänchen shift in a frustrated total internal reflection configuration,” Opt. Lett. 41(19), 4468–4471 (2016).
[Crossref]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[Crossref]

C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017).
[Crossref]

H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. 27(9), 680–682 (2002).
[Crossref]

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 30(21), 2936–2938 (2005).
[Crossref]

G. Jayaswal, G. Mistura, and M. Merano, “Weak measurement of the Goos-Hänchen shift,” Opt. Lett. 38(8), 1232–1234 (2013).
[Crossref]

O. J. S. Santana, S. A. Carvalho, S. de Leo, and L. E. E. de Araujo, “Weak measurement of the composite Goos-Hänchen shift in the critical region,” Opt. Lett. 41(16), 3884–3887 (2016).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[Crossref]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref]

J.-X. Li, X.-L. Fan, W.-P. Zang, and J.-G. Tian, “Vacuum electron acceleration driven by two crossed Airy beams,” Opt. Lett. 36(5), 648–650 (2011).
[Crossref]

Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
[Crossref]

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam,” Opt. Lett. 36(4), 543–545 (2011).
[Crossref]

P. Chamorro-Posada, J. Sánchez-Curto, A. B. Aceves, and G. S. McDonald, “Widely varying giant Goos-Hänchen shifts from Airy beams at nonlinear interfaces,” Opt. Lett. 39(6), 1378–1381 (2014).
[Crossref]

M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for Airy beams,” Opt. Lett. 43(6), 1411–1414 (2018).
[Crossref]

Opt. Mater. Express (1)

Optik (1)

C. Zhai and S. Zhang, “Goos-Hänchen shift of an Airy beam reflected in an epsilon-near-zero metamaterial,” Optik 184, 234–240 (2019).
[Crossref]

Phys. Lett. A (1)

A. Matthews and Y. Kivshar, “Tunable Goos-Hänchen shift for self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372(17), 3098–3101 (2008).
[Crossref]

Phys. Rev. A (2)

W. Wu, S. Chen, C. Mi, W. Zhang, H. Luo, and S. Wen, “Giant quantized Goos-Hänchen effect on the surface of graphene in the quantum Hall regime,” Phys. Rev. A 96(4), 043814 (2017).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos-Hänchen and Imbert-Fedorov shifts of vortex beams at air-left-handed-material interfaces,” Phys. Rev. A 85(5), 053822 (2012).
[Crossref]

Phys. Rev. Appl. (2)

S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Phys. Rev. Appl. 13(1), 014057 (2020).
[Crossref]

F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
[Crossref]

Phys. Rev. E (1)

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

Phys. Rev. Lett. (7)

O. Emile, T. Galstyan, A. L. Floch, and F. Bretenaker, “Measurement of the nonlinear Goos-Hänchen effect for Gaussian optical beams,” Phys. Rev. Lett. 75(8), 1511–1513 (1995).
[Crossref]

M. Onoda, S. Murakami, and N. Nagaosa, “Hall Effect of Light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, Conservation of Angular Momentum, “Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydło, “Quantum Goos-Hänchen effect in graphene,” Phys. Rev. Lett. 102(14), 146804 (2009).
[Crossref]

I. V. Soboleva, V. V. Moskalenko, and A. A. Fedyanin, “Giant Goos-Hänchen Effect and Fano Resonance at Photonic Crystal Surfaces,” Phys. Rev. Lett. 108(12), 123901 (2012).
[Crossref]

Pramana (1)

D. Golla and S. D. Gupta, “Goos-Hänchen shift for higher-order Hermite-Gaussian beams,” Pramana 76(4), 603–612 (2011).
[Crossref]

Rep. Prog. Phys. (1)

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

Results Phys. (1)

W. Kong, Y. Sun, and Y Lu, “Enhanced Goos-Hänchen shift of graphene coated on one-dimensional photonic crystal,” Results Phys. 17, 103107 (2020).
[Crossref]

Rev. Mod. Phys. (2)

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

C. W. J. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene,” Rev. Mod. Phys. 80(4), 1337–1354 (2008).
[Crossref]

Science (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

A. K. Geim, “Graphene: Status and Prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref]

Other (3)

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

A. Aiello and J. Woerdman, “Theory of angular Goos-Hänchen shift near brewster incidence,” arXiv preprint arXiv:0903.3730 (2009).

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1. Schematic plot of the GH shift at the graphene-coated surface between air ($z<0$) and a semi-infinite weakly absorbing medium ($z>0$). The single graphene layer (characterized by its optical conductivity $\sigma$) is located on the interface at $z = 0$. $\varepsilon _{1}=1$ and $\varepsilon _{2}=\varepsilon _{2r}+\varepsilon _{2i}i$ represent the relative permittivity of air and the absorbing medium, respectively.
Fig. 2.
Fig. 2. The GHS ($\Delta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ for (a) Gaussian beam without graphene (solid line), Gaussian beam with the monolayer graphene (dashed line), Airy beam without graphene (dotted line), and (b) Airy beam with the monolayer graphene. Here, $\varepsilon _2=2+0.02i$, $\lambda =850$ nm, $E_f=0.5$ eV, and $\alpha =\beta =0.1$.
Fig. 3.
Fig. 3. The GHS ($\Delta _{\mathrm {GH}}$) with the monolayer graphene in dependence on the incident angle $\theta$, with different incident wavelengths: $\lambda =325$ nm (solid line), $\lambda =488$ nm (dashed line), $\lambda =633$ nm (dotted line), and $\lambda =850$ nm (dash-dotted line) for two cases of (a) Gaussian beams and (b) Airy beams. Here, $\varepsilon _2=2+0.02i$, $E_f=0.5$ eV, and $\alpha =\beta =0.1$.
Fig. 4.
Fig. 4. (a) GHS ($\Delta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ and the Fermi energy $E_f$ for Airy beams with the monolayer graphene. (b) The real part (solid line) and imaginary part (dashed line) of the conductivity $\sigma$ of graphene as the function of $E_f$. Here, $\varepsilon _2=2+0.02i$, $\lambda =850$ nm, and $\alpha =\beta =0.1$.
Fig. 5.
Fig. 5. The GHS ($\Delta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ and the decay factor $\alpha$ $(\beta =\alpha )$ of Airy beams (a) without graphene and (b) with the monolayer graphene ($E_f=0.3$ eV). Here, $\varepsilon _2=2+0.02i$, and $\lambda =850$ nm.
Fig. 6.
Fig. 6. The GHA ($\Theta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ for (a) Gaussian beam without graphene (solid line), Gaussian beam with the monolayer graphene (dashed line), Airy beam without graphene (dotted line), and (b) Airy beam with the monolayer graphene. Here, $w_0=1$ mm, $\varepsilon _2=2+0.02i$, $\lambda =1550$ nm, $E_f=0.3$ eV, and $\alpha =\beta =0.1$.

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

E μ ( r μ ) = 1 2 π E ~ μ ( k μ ) e i ( k μ r μ ) d k x μ d k y μ ,
E I ( k 1 r I ) = k 1 2 2 π E ~ I ( U , V ; θ ) e i ( U X ^ I + V Y ^ I + W Z ^ I ) d U d V ,
E R ( k 1 r R ) = k 1 2 2 π E ~ R ( U , V ; θ ) e i ( U X ^ R + V Y ^ R + W Z ^ R ) d U d V ,
E ~ μ ( U , V ; θ ) = λ p , s e ^ λ ( k μ ) α λ ( U , V ; θ ) A ~ μ ( U , V ; θ ) ,
e ^ p ( k μ ) = e ^ s ( k μ ) × k μ | e ^ s ( k μ ) × k μ | ,
e ^ s ( k μ ) = z ^ × k μ | z ^ × k μ | .
r λ ( U , V ; θ ) r λ + U r λ + 1 2 U 2 r λ + 1 2 V 2 r λ ,
A ~ ( U , V ) = w 0 2 2 π e x p ( α 3 + β 3 3 ) e x p ( α U 2 + β V 2 ϑ 2 ) e x p [ i ( U 3 + V 3 3 ϑ 3 α 2 U + β 2 V ϑ ) ] ,
X ¯ = X ¯ R X ¯ I ,
X ¯ R = I m [ E ~ R U E ~ R ] d U d V | E ~ R | 2 d U d V ( Z R + Z I ) U W | E ~ R | 2 d U d V | E ~ R | 2 d U d V ,
X ¯ I = I m [ E ~ I U E ~ I ] d U d V | E ~ I | 2 d U d V Z I U W | E ~ I | 2 d U d V | E ~ I | 2 d U d V .
Δ G H = I m [ E ~ R U E ~ R ] d U d V k 1 | E ~ R | 2 d U d V + I m [ E ~ I V E ~ I ] d U d V k 1 | E ~ I | 2 d U d V ,
Θ G H = X ¯ R / Z R = U W | E ~ R | 2 d U d V | E ~ R | 2 d U d V .
Δ G H A i r y = 1 Λ ( Δ G H g + ϑ 8 α 2 k 1 λ p , s ω λ 1 ) ,
Θ G H A i r y = 1 4 α Λ Θ G H g ,
H 1 y = ( a 1 e k 1 z z + b 1 e k 1 z z ) e k 1 x x ( z < 0 ) ,
H 2 y = ( a 2 e k 2 z z + b 2 e k 2 z z ) e k 2 x x ( z > 0 ) ,
k 1 x = k 2 x .
D p ( 1 2 ) = 1 2 [ 1 + η p + ξ p 1 η p ξ p 1 η p + ξ p 1 + η p ξ p ] ,
D s ( 1 2 ) = 1 2 [ 1 + η s + ξ s 1 η s + ξ s 1 η s ξ s 1 + η s ξ s ] ,
P ( 0 ) = [ 1 0 0 1 ] .
P ( 0 ) = M p , s = D p , s ( 1 2 ) P ( 0 ) = D p , s ( 1 2 ) .
r p = M p , 21 M p , 11 = ε 2 / k 2 z ε 1 / k 1 z + σ / ( ε 0 ω ) ε 2 / k 2 z + ε 1 / k 1 z + σ / ( ε 0 ω ) ,
r s = M s , 21 M s , 11 = k 1 z k 2 z k 1 σ / ( ε 0 c ) k 1 z + k 2 z + k 1 σ / ( ε 0 c ) .
σ ( ω , E f ) = e 2 E f π 2 i ω + i τ 1 + e 2 4 2 [ H ( ω 2 E f ) + i π ln | ω 2 E f ω + 2 E f | ] ,

Metrics

Select as filters


Select Topics Cancel
© Copyright 2022 | Optica Publishing Group. All Rights Reserved