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Abstract
In this work, we proposed a black phosphorus (BP) achiral metasurface and theoretically study the chiroptical response arising from extrinsic 2D-chirality in the mid-infrared regime. The achiral metasurface is composed of a monolayer BP sheet sandwiched by a silver ring array and dielectric spacer stacking on a silver substrate. The giant circular conversion dichroism (CCD) of the achiral metasurface is allowed at oblique incidence for the cooperative interaction of BP anisotropic surface plasmon modes and localized surface plasmons in metal rings, and the integrated BP can dynamically modulate the chiroptical response by controlling the doping concentration of BP. Furthermore, we found that a multiband phenomenon for CCD response occurs when tuning the thickness of the spacer. The proposed hybrid achiral metasurface provides more flexible opportunities to realize active polarization modulator, biosensor and chiral detection.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Chirality refers to an intrinsic feature that an object cannot be brought to coincide with its mirror image [1]. Intrinsically chiral objects are ubiquitous in nature, such as amino acids [2], quartz crystals [3], carbohydrates and DNA. Chirality is of great significance in spectroscopy, analytical chemistry, biomedicine, optics and so on. Therefore, studies on chirality have attached more and more attention in recent years. In the field of optics, it is well known that chiral objects interacting with circularly polarized light (CPL) with different polarities have different optical responses. For 3D chirality, circular birefringence (CB) and circular dichroism (CD), collectively referred to as optical activity [4], are two important optical effects in 3D chiral materials. Furthermore, the phenomena of asymmetric transmission [5–12] can be observed in 2D chiral materials, which is result from the circular conversion dichroism (CCD) effect. However, the chiral responses of natural chiral materials are usually weak. With the advancement of nanotechnology, chiral metamaterials have been intensively studied [13–20]. Chiral metamaterials can exhibit much stronger chiral responses compared with the materials in nature. Especially, plasmonic metallic nanostructures have greatly promoted the development of the design of optical chiral metamaterials due to extraordinary optical properties, such as metallic helices [21–26], dual-layer twisted-arc [27], twisted planar metal rosettes [28], U/L-shaped split ring resonators [29,30], gammadions [31] and so on.
Although chiral metamaterials can achieve much stronger chiral responses, complexities in fabrication towards the realization of chiral metamaterials, especially 3D chiral metamaterials, have so far hindered their application. Here is a question whether planar achiral structures with the advantage of easy fabrication can also produce strong chiral responses? The answer is yes. A chiral response can occur in planar achiral structure when the planar achiral structure forms an extrinsic chiral arrangement with the incident circularly polarized wave under an oblique incidence [32,33]. This phenomenon is called extrinsic chirality. Compared with intrinsic chirality, the extrinsic chirality is readily tunable, as the magnitude of CCD can be continuously varied by changing the angle of incidence [34]. To obtain strong extrinsic chiral responses in achiral structures, various kinds of achiral metasurfaces have been proposed. For example, it has been demonstrated that achiral planar metamaterial consisting of a 2D array of metal split rings show a strong extrinsic optical chiral response [32–36]. A large CCD = 0.39 in the mid-infrared region can be observed in highly symmetric plasmonic square arrays based on metal-dielectric-metal multilayers [37]. Similarly, dual-band strong extrinsic 2D chirality occurs in a highly symmetric metal-dielectric-metal (MDM) achiral metasurface consisting of circular holes array penetrating through an MDM structure [38]. In addition, a lot of active materials, such as semiconductors [39], phase-change materials [40], 2D materials [41], have also been added into chiral metamaterials to achieve dynamic manipulation of the chiral response. For instance, a multilayer stack achiral phase-change metamaterial was proposed to actively control the CD spectrum in the infrared region by changing the phase from amorphous to crystalline [42]. Metamaterials with graphene sheet layer and nonlinear photonic graphene also have been studied to achieve the tunable extrinsic chirality [43–46]. Recently, optical activity in unpatterned monolayer black phosphorus has been reported due to extrinsic chirality [47], in which the maximal value of CD is 0.147. Plasmonic metallic nanostructures can greatly increase the chiral response of metamaterial, but lack dynamical tunability. BP as a 2D material has dynamical tunability, and can achieve extrinsic chirality at oblique incidence due to the intrinsic material anisotropy [47], but the chiral effect is not strong. Therefore, a tunable strong external chiral response can be expected by combining the metal nanostructures and BP.
In this work, we propose a BP-integrated achiral metasurface and theoretically investigate chiral responses arising from extrinsic 2D chirality in mid-infrared regime. Under oblique incidence, a giant and dynamical tunable CCD response will be achieved in the mid-infrared region if the incident plane neither parallel nor perpendicular to a mirror symmetry line of the proposed metasurface. The magnitude of CCD for the proposed metasurface change by the incident angle, and can reach a maximal value of 0.863 at a tilted angle $\theta =80^{\circ }$, $\phi =49^{\circ }$. Furthermore, dynamical tunable CCD spectra can be obtained by altering the doping concentration of BP. Due to the Fabry-Pérot resonance between the BP sheet and the silver substrate, a multiband phenomenon for CCD response will be clearly observed when we adjust the thickness of spacer.
2. Structure and design
Fig. 1 shows the unit cell of the proposed BP-integrated achiral metasurface to be studied, which composed of four stacked layers. The top layer is silver rings array, the second layer is a monolayer BP sheet, the third layer is a dielectric spacer and the bottom layer is a silver reflector. The detailed geometrical parameters are given in the caption of Fig. 1. Circularly polarized waves are incident upon the proposed achiral metasurface at a tilted angle ($\theta$, $\phi$). Due to the intrinsic material anisotropy of BP, the achiral metasurface will exhibit extrinsic chirality at oblique incidence provided that the plane of incidence does not contain the crystal axis of BP. The numerical simulations are performed by a fully 3D finite element technique (COMSOL Multiphysics). In the simulations, the periodic boundary conditions are set along $x$ and $y$ directions. The refractive index $n_d$ of the dielectric layer is 1.45. The permittivity of silver is taken as Drude model: $\epsilon =\epsilon _\infty -\frac {\omega _p^2}{\omega ^2+i\omega \gamma }$, where $\omega$ is the angular frequency, and $\omega _p=1.39\times 10^{16}$ rad/s is the plasma frequency, $\gamma =2.7\times 10^{13}$ rad/s is the scattering rate, and $\epsilon _\infty =3.4$ is the high-frequency constant. In addition, the optical conductivity of monolayer BP can be described by employing a simple semi-classical Drude model:
where $j$ denotes the $x$ or $y$ direction, $D_j$ is the Drude weight, and $m_j$ is the electron mass along the $j$ direction. For monolayer BP, we have $m_x\approx 0.15m_0$, $m_y\approx 0.7m_0$ ($m_0$ is the static electron mass) [48]. Moreover, we choose the electron doping $n_s=9\times 10^{13}$ cm$^{-2}$ and the relaxation rate $\eta$ = 10 meV.3. Results and discussion
In our simulation, the circularly polarized waves are incident on the achiral metasurface at oblique incidence. Since the achiral metasurface forms an extrinsically 2D chiral arrangement with the incident wave, strong chiral responses will be observed. The reflection property of the achiral metasurface can be analyzed by the complex reflection matrix $r_{ij}$ that connects the reflected wave $E_j^{inc}$ and the incident wave $E_i^r$ by the formula $E_i^r=r_{ij}E_j^{inc}$ , where ‘$i$’ and ‘$j$’ denote RCP ($+$) and LCP ($-$) waves. $R_{ij} = |r_{ij}|^2$ represents the direct reflection and converted reflection for RCP and LCP incident waves. To be specific, $R_{++}$ and $R_{--}$ correspond to the reflection of right-to-right and left-to-left circularly polarized wave, respectively. $R_{-+}$ and $R_{+-}$ correspond to the reflection of right-to-left and left-to-right circularly polarized wave, respectively. It is worth noting that, in our case, the rotational direction of the reflected circularly polarized wave is determined by the wave vector of the reflected wave. In order to quantify the chiral response of the structure, we calculate the converted reflection $R_{-+}$ and $R_{+-}$ to detect the 2D extrinsic chirality which is linked to the CCD: CCD = $R_{-+}-R_{+-}$. The total absorption of the structure can be expressed as $A_j = 1-R_{jj}-R_{ij}$. Figure 2(a) shows the simulated absorption and reflection spectra of LCP (dashed curve) and RCP (solid curve) waves for the incident waves with fixed angle $\theta =80^{\circ }$, $\phi =49^{\circ }$. The blue, gray and orange curve represent the absorption, direct reflection and converted reflection, respectively. We can see that there exists a pronounced peak of absorption locating at $\lambda =6.3$ µm for RCP wave, which is induced by the surface plasmon modes of BP and the coupling of the localized surface plasmons (LSPs) modes between neighboring metal rings. Moreover, as a kind of periodic metallic nanostructure, the Ag ring array not only can generate LSPs modes, but also can provide additional wavevectors to excite the surface plasmon modes of BP for different grating orders based on the Bragg’s coupling equation [44,49,50], which leads to the other peaks. In addition, the direct reflection of RCP (gray dashed curve) and LCP (gray solid curve) waves are equal ($R_{++} = R_{--}$). The absorption differences (blue curve) and reflection differences (the gray curve and orange curve) of RCP and LCP waves are depicted in Fig. 2(b). Results show that CCD reaches a maximal value of 0.863 at $\lambda =6.3$ µm and the absorption difference of RCP and LCP waves is related to the CCD: $\Delta A=R_{+-}-R_{-+}=-$CCD. We note that the maximum absorbance difference of RCP and LCP waves occurs when the absorption of RCP wave is maximum.
Fig. 1. Schematic of the BP-integrated achiral metasurface at oblique incidence. The unit cell consists of monolayer BP sandwiched by a silver ring and dielectric spacer stacking on a silver substrate. The cyan arrow represents the wave vector of the incident wave $k$. The blue and red helix arrows represent left circularly polarized (LCP) and right circularly polarized (RCP) waves, respectively. $\theta$ is the incident angle denoting the angle between the wavevector $k$ and the plane normal vector n, and $\phi$ is the azimuth angle denoting the angle between the in-plane (to the $x$–$y$ plane) component of the wavevector and the $x$ axis. The geometry parameters are given as $h_0$ = 300 nm, $h_1$ =1500 nm, $h_2$ = 30 nm, $L_x=L_y$ = 700 nm, $w$ = 14 nm, $R$ = 326 nm. The blue and red helix arrows represent left circularly polarized (LCP) and right circularly polarized (RCP) waves, respectively.
Fig. 2. Giant 2D extrinsic chiral responses for the BP-integrated achiral metasurface at oblique incidence ($\theta =80^{\circ }$, $\phi =49^{\circ }$). The absorption and reflection spectra (a) and the absorption differences and reflection differences spectra (b) of right circularly polarized (RCP) and left circularly polarized (LCP) waves. (c) $E_z$ and (e) |$E$| for RCP wave impinging the metasurface at $\lambda =6.3$ µm. (d) $E_z$ and (f) |$E$| for LCP wave impinging the metasurface at $\lambda =6.3$ µm.
Then, to clarify the underlying physics behind the strong optical chirality, the side views of electric field distributions $E_z$ and |$E$| for RCP and LCP waves impinging the BP-integrated achiral metasurface at oblique incidence are plotted in Fig. 2(c)-(f). The responses to RCP and LCP wave are displayed on the top and bottom in Fig. 2, respectively. From the side view of $E_z$ distributions in Fig. 2(c) and (d), we can clearly find the positive and negative dipoles, which indicates the excitation of BP surface plasmon modes. The electric distributions are concentrated at the interface of BP and between the metal rings. Moreover, as shown in Fig. 2(e) and (f), it is clear that LSPs resonance modes are excited in the edge of the silver ring. Both RCP and LCP waves have similar electric field distributions, but the intensities for LCP wave are obviously weaker, which demonstrates a significant chiral response. Therefore, the excitation of BP surface plasmon modes and the coupling of LSPs between metal rings greatly enhance the chiral response.
Since the formation of this extrinsic 2D chirality is stem from the mutual orientation between the BP-integrated achiral metasurface and the oblique incident wave, the incident angle and azimuth angle have an important influence on the CCD. Figure 3(a) shows the absorption and reflection spectra of RCP and LCP waves varying with the incident angles. We set $\phi =49^{\circ }$ and $\lambda =6.3$ µm. We can observe that there exists a pronounced peak of absorption locating at incident angle of $\theta =80^{\circ }$ for the RCP wave. The absorption and converted reflection response of RCP and LCP waves are equal when the incident waves are normal illumination ($\theta =0^{\circ }$). Figure 3(b) depicts the absorption difference and reflection difference spectra of RCP and LCP waves varying with the incident angles. As the incident angle increases from $0^{\circ }$ to $90^{\circ }$, the magnitude of CCD increases from 0 to a maximum (at $\theta =80^{\circ }$, |CCD| = 0.863) and then decreases to 0 again at $\theta =90^{\circ }$. Moreover, the absorption and reflection spectra of RCP and LCP waves for varied azimuth angle are plotted in Fig. 3(c). Here the incident angle is $\theta =80^{\circ }$, and the wavelength is fixed at $\lambda =6.3$ µm. It is observed that these absorption and reflection curves show obvious periodicity (the period is $180^{\circ }$) as the azimuth angle changes from $0^{\circ }$ to $360^{\circ }$. The periodicity occurs due to the fact that the BP-integrated achiral metasurface has twofold rotational symmetry. To see more clearly, we calculate the absorption difference and reflection difference of RCP and LCP waves, as shown in Fig. 3(d). The spectra also show obvious periodicity. When the incident plane (at $\phi =N\times 90^{\circ }$, N is an integer) parallel or perpendicular to the mirror symmetry line the extrinsic 2D chirality disappears (CCD = 0). The results show that extrinsic 2D chirality can be easily tuned by varying the incident angles.
Fig. 3. The angular dependence of the absorption and reflection for LCP and RCP. The absorption and reflection spectra (a) and the absorption differences and reflection differences spectra (b) varying with the incident angles with a fixed azimuth $\phi =49^{\circ }$ at $\lambda =6.3$ µm. The absorption and reflection spectra (c) and the absorption differences and reflection differences spectra (d) varying with the azimuths with a fixed incident angle $\theta =80^{\circ }$ at $\lambda =6.3$ µm.
To investigate the dynamical tunable properties of the proposed BP-integrated achiral metasurface, Fig. 4 presents the absorption differences and reflection differences spectra of RCP and LCP waves with $\theta =80^{\circ }$, $\phi =49^{\circ }$ for different doping concentration of BP and different thicknesses of the dielectric spacer. As shown in Fig. 4(a), when the doping concentration $n_s$ increases from $3\times 10^{13}$ cm$^{-2}$ to $9\times 10^{13}$ cm$^{-2}$, the spectra have blue shift, and the magnitude of the CCD also increases. The modification of the BP doping concentration can change the BP’s conductivity and thus lead to a spectral tuning of the CCD. In this structure, a Fabry-Pérot cavity between the BP sheet and the silver substrate is formed, which can result in a multiband resonant phenomenon. As we know, the spacer thickness has a significant effect on the wavelength of BP-silver reflector Fabry-Pérot resonances. Therefore, we change the spacer thickness $h_1$ to study the absorption differences and reflection differences spectra of RCP and LCP waves, as shown in Fig. 4(b). From the figure, we can know that with the increase of the spacer thickness, the number of peaks and dips in the difference spectra of RCP and LCP waves increases. We can use the interference theory to explain the multiband phenomenon. The maximum absorbances occur at the constructive interference with phase condition of $\Delta \varphi =2\widetilde {\beta }+\phi +\pi =2m\pi$ ($\widetilde {\beta }=n_dk_0h_1$ , m is an integer), where $\widetilde {\beta }$ is the transmission phase, $k_0$ is the free space wavenumber, $n_d$ and $h_1$ are the refractive index and thickness of spacer, respectively, $\varphi$ represents the reflection phase shift on the interface between BP and dielectric spacer. Therefore, by changing the doping concentration of BP or reasonably adjusting the thickness of the dielectric spacer, we can achieve multiband CCD spectra with giant chiral responses in the mid-infrared range.
Fig. 4. The tunable extrinsic chirality of the proposed structure. (a) The absorption differences and reflection differences spectra of RCP and LCP waves with $\theta =80^{\circ }$, $\phi =49^{\circ }$ for different doping concentration of BP ($n_s=3\times 10^{13}$ cm$^{-2}$, $6\times 10^{13}$ cm$^{-2}$, $9\times 10^{13}$ cm$^{-2}$). (b) The absorption differences and reflection differences spectra of RCP and LCP waves with $\theta =80^{\circ }$, $\phi =49^{\circ }$ for different thicknesses of the dielectric spacer ($h_1$ = 1.5 µm, 5 µm, 10 µm).
Finally, to intuitively elucidate the FP resonance mechanism of multiband phenomenon, we simulate electric field distributions |$E$| at resonant wavelengths for the proposed BP-integrated achiral metasurface with different thickness when the RCP wave incidents at an oblique angle. Since the peak and dip of RCP waves almost correspond to the peak and dip of the differences spectra of RCP and LCP waves, the CCD spectra in Fig. 4(b) can well reflect the spectral characteristics of RCP wave. Figure 5(a) and (b) show the side views of |E| distributions of the proposed structure with a spacer thickness $h_1$ = 5 µm at first and second peak resonance wavelength of 6.75 µm and 13.5 µm in the middle subgraph of Fig. 4(b), respectively, where the second- and first-order Fabry-Pérot resonances are clearly excited between the BP and silver reflector. Similarly, when we change the thickness of spacer to $h_1$ = 10 µm, the fourth-, third- and second-order Fabry-Pérot resonances are also excited between the BP and silver reflector in Fig. 5(c), (d) and (e), which correspond to the resonant wavelengths of 6.2 µm, 8.25 µm and 12.1 µm in the bottom subgraph of Fig. 4(b), respectively. Therefore, it is demonstrated that multiband phenomenon for CCD spectra arises from the Fabry-Pérot resonance by adjusting the thickness of spacer.
Fig. 5. The side view of electric field distributions |E| for the structure with different thicknesses of the dielectric spacer and resonant wavelengths at $\theta =80^{\circ }$, $\phi =49^{\circ }$. (a) $h_1$ = 5 µm, $\lambda$ = 6.75 µm. (b) $h_1$ = 5 µm, $\lambda$ = 13.5 µm. (c) $h_1$ = 10 µm, $\lambda$ = 6.2 µm. (d) $h_1$ = 10 µm, $\lambda$ = 8.25 µm. (e) $h_1$ = 10 µm, $\lambda$ = 12.1 µm.
4. Conclusion
In conclusion, we have demonstrated that a giant extrinsically 2D chiral response (CCD) in the IR region can be achieved in a BP-integrated achiral metasurface. At oblique incidence, the giant extrinsically chiroptical responses of the achiral metasurface can be dynamically modulated by controlling the doping concentration of BP. Moreover, due to the Fabry-Pérot resonance between the BP sheet and the silver substrate, a multiband phenomenon for CCD response can be observed when we adjust the thickness of spacer. In contrast to intrinsic chirality in metamaterials, extrinsic 2D chirality is readily tunable by controlling the angle of incidence, the doping concentration of BP, and the structural parameters. Therefore, the tunable giant extrinsically 2D chiral responses for the proposed BP-integrated achiral metasurface are expected to be applied in circular polarizers, polarization modulators and polarization selective detectors designs in the IR region.
Funding
National Natural Science Foundation of China (11504306, 11874311, 92050102); National Key Research and Development Program of China (2020YFA0710100); Fundamental Research Funds for the Central Universities (20720200074); Natural Science Foundation of Fujian Province (2021J01055, 2021J01584); China Scholarship Council (202006310049).
Acknowledgments
Y. L. Zeng acknowledges the support from the China Scholarship Council (202006310049).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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