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Abstract
Perfect absorbers are of great importance in various applications such as photodetectors, optical sensors and optical modulators. Recently, perfect absorption metasurface based on monolayer graphene has attracted lots of research interest. In this paper, a graphene-lithium niobate (LN) perfect absorption metasurface is constructed, where graphene works as a thin absorptive layer as well as a conductive electrode. The proposed device achieves 99.99% absorption at 798.42 nm and 1.14 nm redshift of the absorption peak is realized at 300 V(from -150 V to 150 V) external bias voltage through the electro-optical effect of LN, which enables the proposed device work as a electrically tunable absorber in the visible and near infrared range. The switching ratio of reflected light R/R0 could reach -44.08 dB with an applied voltage tuning from -150 V to 0 V at 798.42 nm. Our work demonstrates the potential of LN integrated high-Q resonant metasurface in realizing electro-optic tunable nanophotonic devices in the visible and near infrared band. It will promote the research of graphene integrated optoelectronic devices as well as LN based tunable nanophotonic devices which have widespread applications such as modulators and optical phase arrays.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical absorption plays a key role in light-matter interactions. Perfect absorbers, which absorb the entire incident light, have been widely studied in the past decade [1]. They are of great importance in various applications ranging from photodetectors [2], optical sensors [3] and optical modulators [4,5] to stealth technology [6]. Recently, perfect absorption metasurface based on monolayer graphene has attracted lots of research interest [7]. Graphene has full spectral response from UV to Terahertz [8], ultra-fast response to light and ultra-high carrier mobility, which has been the subject of intensive research for tunable optical devices through tunable conductivity [9–12]. Over the past few years, abundant progress has been done on tunable nanophotonic metasurfaces through graphene as well as other gate-tunable index-changing materials [4,13,14]. However, adjusting the conductivity of graphene requires a sufficiently high carrier concentration to change the Fermi level, especially in the visible to near infrared band [15]. This limits its application in the case of low electric field intensity and high photon energy.
Lithium niobate (LN) is another promising material for EO tunable metasurfaces. LN shows Pockels electro-optic (EO) effect and its refractive index could be tuned by an external electrical voltage, at femtosecond timescale. Bulk LN crystals have been used for decades as EO modulators due to its large second order EO coefficient and high transparency [16]. The recent progress in the fabrication technology of thin-film LN on insulator has further promoted the development of LN optical devices [17]. Thin-film LN on insulator preserves LN’s outstanding materials properties while enables the realization of more compact and efficient LN electro-optic devices [18]. So it has recently emerged as a versatile platform for compact tunable nanophotonic devices [19]. Intergrated LN modulators with modulation speed from tens to hundreds of GHz have been demonstrated [20,21]. Meanwhile, significant progresses have also been made in LN metasurfaces even though fabricating nanostructures in LN films is still challenging and the quality factor (Q-factor) of most demonstrated LN resonant metasurfaces are normally low (in the order of tens) [22,23].
In this work, we propose a type of electrically tunable absorber based on monolayer graphene integrated lithium niobate resonant metasurface. The graphene works as a thin absorptive layer as well as a conductive electrode [24,25]. By coupling graphene with a high-Q guided mode resonance grating, 99.99% absorption is achieved in the visible to near infrared range. Furthermore, increasing gate voltage to change the refractive index through the electro-optic effect of LN makes the absorption of the structure tunable, which is difficult to achieve the same modulation degree by adjusting the Fermi level of graphene.
2. Results and discussion
Figure 1(a) shows the schematic of the proposed structure with geometric parameters. We choose z-cut LN ($n_o = 2.286$, $n_e =2.203$) as the material of the waveguide layer and silicon dioxide ($n = 1.46$) as the material of the substrate. A monolayer graphene lies on the waveguide layer (LN) with periodic PMMA ($n = 1.49$) gratings on the top. The graphene works as a thin absorptive layer as well as the top electrode. At the bottom, the Au layer is placed under the substrate as a mirror and bottom electrode. Modulation of LN is realized through electric field generated between the grounded graphene and the Au layer. The proposed structure can be fabricated with similar methods in ref. [26]. We focus on the normally incident transverse electric (TE) wave (the electric field is along the y axis). As shown in Fig. 1(b), when adding gate voltage, the refractive index of LN can be described as [16]:
where $r_{13}=10~pm/V$ is the electro-optic coefficient of LN and $E_Z$ is the electric field intensity in LN, which is along the negative direction of the z-axis. Here the voltage is applied in the vertical direction and the tunable device can be scaled to larger sizes without sacrificing the gating ability, which is an advantage compared to gating in the horizontal direction [23].
Fig. 1. (a)Schematic of vertical incidence at a guided mode resonant (GMR) structure with linearly polarized waves in a Cartesian coordinate system. The gate voltage is connected to the gold layer. $P$, $f$, $h_g$, $h_{wg}$, $h_s$ and $h_m$ denote the grating period, duty cycle, the thickness of PMMA, LN, $\rm {SiO_2}$ and Au, respectively. (b)The refractive index of LN varying with the external electric field. For every 50 $V$ increase in gate voltage, the refractive index decreases by nearly 0.0018. The monolayer graphene based perfect absorption structures were fabricated on a silicon substrate.
The monolayer graphene based perfect absorption structures are integrated with GMR gratings [27]. A suspended monolayer graphene has the absorption of 2.3% toward the normal incidence [8]. In order to effectively enhance the optical absorption of graphene, it is usually integrated with resonant structures. Under phase matching conditions, resonant modes supported by the GMR structure could be excited by outside incident waves. The absorption of graphene is significantly enhanced due to local field enhancement at the resonant wavelength. The transmission channel is blocked by the bottom mirror and the reflection wave can be eliminated due to the interference. Perfect absorption can be achieved if the critical coupling condition is met [28,29].Here, graphene is defined by a conductivity model [30]:
A fully three-dimensional finite element technique (in COMSOL Multiphysics) is used to conduct the numerical simulations. A periodic unit is constructed and expanded periodically in the x direction. The transition boundary condition is used to define graphene with a thickness of 0.34 $nm$ and its conductivity is obtained from Formula 2. In order to ensure the accuracy of the simulation results, the maximum cell size of the grid is 1 $nm$. The absorption spectra of Au, graphene and the whole structure are shown in Fig. 2. A guided mode resonance, resulting in up to 21.0 times amplification of electric field mode (see the inset in Fig. 2), is generated within the LN metasurface to provide favorable conditions for perfect absorption. The full width at half maximum (FWHM) of the resonance is about 0.9 $nm$, giving a Q-factor of about 890. The peak absorption at 798.42 $nm$ is over 99.99%, in which graphene contributed 98.2% of the total absorption. As the refractive index of LN is higher than $\rm {SiO_2}$, the LN layer works as a waveguide layer and most of the electromagnetic field locates inside the LN layer. The existence of silicon dioxide keeps the enhanced electric field away from the Au layer to reduce the absorption in Au, making it possible to achieve high Q resonance of the structure and nearly total absorption in the graphene. The reflective Au and the top LN layer forms an F-P cavity here and the thickness of it affects the phase of reflected light. Thus it plays an important role in the proposed device. For example, the resonant absorption of graphene decreases significantly to 57.6% when the thickness of silicon dioxide reduces from 690 nm to 500 nm. The high absorption of graphene gives it great potential in light modulation, photodetection and other applications [31]. The wavelength and bandwidth of the resonance can be engineered by varying the geometric parameters of the structure [7]. For example, if we change the parameters of the structure to be $P = 800~nm$, $f = 0.5$, $h_g = 200~nm$, $h_wg = 300~nm$, $h_s = 570~nm$, nearly perfect absorption can be realized at the resonant wavelength of 1515.72 nm.
Electrical doping is normally used to adjust the Fermi level of graphene in order to achieve the graphene based tunable devices. According to Formula 2, Fermi level can affects the conductivity of graphene to change the absorption. In Fig. 3(a), the spectra with graphene Fermi levels of $0.1~eV$, $0.4~eV$, $0.7~eV$ are shown. As it is shown, the Fermi levels had little effect on the absorption spectrum in the studied spectra range. When the photon energy $hv>2E_f$, $E_f$ has little influence on the absorption of graphene. The photon energy is 1.55 $eV$ at 800 $nm$, so when the Fermi level $E_f >0.775~eV$, the graphene absorption significantly decreases. In this structure, graphene and Au constitute a parallel plate capacitor, where the filler make up of LN layer and $SiO_2$ layer. Induced charges are formed on the surface of graphene under external bias voltage and changes the Fermi level of graphene. The relationship between $E_f$ and $V_0$ can be expressed as [32]:
where $n_e$ is the surface charge density, $C = \epsilon {\epsilon _0}/t$ is the capacitance of the graphene-Au parallel-plate capacitor and $V_f$ is the Fermi velocity.As shown in Fig. 3(b), to achieve the needed Fermi level of graphene in the structure for effective absorption modulation, an external bias voltage of more than 2500 $V$ is required, which is obviously hard to realize under experimental conditions.
Fig. 2. Absorption spectra and the field distribution of the structure. The absorbance by Au and graphene is calculated by an integration of resistive losses in the respective areas in the numerical simulations. The results show that only 1.7% of light is absorbed in gold layer while 98.2% of light is absorbed in graphene. Perfect absorption is realized due to the GMR, which leads to the nearly perfect absorption in graphene. The electric field distributions at the resonant wavelength of 798.42 $nm$ are shown in the inset and the parameters of the structure are $P = 760~nm$, $f = 0.25$, $h_g = 130~nm$, $h_wg = 300~nm$, $h_s = 690~nm$.
Fig. 3. (a) Absorption spectra at different Fermi levels of graphene.The structure and geometric parameters here is the same as in Fig. 2. (b) The Fermi levels of graphene at different external bias voltage.
Instead, here we change the refractive index of LN waveguide layer through electro-optical effect to tune the spectra. Such a strategy can be applied to other nanophotonic devices when the photon energy is relatively high in the visible and near infrared band. As shown in Fig. 4, the resonance wavelength has a shift about 0.57 $nm$ for every 150 $V$ increase in gate voltage $V_0$ with the FWHM of about 0.98 $nm$. The electric field reaches the level of $10^{7} V/m$ with a biased voltage of 150 $V$ in LN. According to previous experiments, it is possible to apply this type of voltage without leading to breakdown in the nanoscale LN film [23]. And many of other experiments have demonstrated that both graphene and the silicon dioxide layer can survive such an level of electric field as well [33]. When $V_0$ changes from $-150~V$ to $150~V$, the formant significantly shifts by 1.14 $nm$, which is large enough to change the optical reflection and absorption spectra around the resonance. At the same voltage, the Fermi level of graphene can only be raised to about 0.18 $eV$, which has almost no effect on the absorption spectrum. By the way, a shift of the optical spectra by 1 $nm$ corresponds to a bandwidth of about 470 $GHz$ around the wavelength of 800 $nm$. Thus this modulation shift may be explored for optical communications, spatial light modulation or other applications.
Fig. 4. Absorption spectra at different gate voltages. The variation of refractive index caused by EO effect makes the optical spectra of resonant metasurface shift. For every 150 $V$ increase in $V_0$, the resonant wavelength redshifts by 0.57 $nm$ and it redshifts from 797.85 $nm$ to 798.99 $nm$ when $V_0$ changes from $-150~V$ to $150~V$.
This method achieves the modulation of the structure absorption at relatively low voltage in near infrared band. The perfect absorption spectra modulated by LN electro-optic has a significant switching ratio as shown in Fig. 5. At 798.42 $nm$, the switching ratio $R/R_0$ reaches -44.08 $dB$ when the applied voltage changes from $V_0 =-150~V$ to $V_0 = 0~V$ (As nearly perfect absorption is realized at $V_0 = 0~V$, the reflection is normalized by that at $V_0=-150~V$ with $R_0=57.50\%$ in Fig. 5). This result demonstrates the superiority of the modulation ability of the structure at lower voltage in near infrared band.
Fig. 5. The curve of the reflectivity ($dB$) varying with the gate voltage $V_0$ at 798.42 $nm$. The reflection is normalized by that at $V_0=-150~V$ with $R_0=57.50\%$. The reflection drops to only $R_0 = 0.0022\%$ at $V_0 = 0~V$ corresponding to the perfect absorption. When $V_0=0~V$, $R/R_0$ has a minimal value of -44.08 $dB$.
Even though we have only studied the TE mode here, the proposed device can display similar resonances for TM mode (the magnetic field is along the y direction), but the resonant wavelength is different from that of TE mode. The electro-optical modulation of TM mode with LN will be similar to that of TE. It is well known that the resonant wavelength of guided mode resonances depend on the incidence angle [26,34], which may make requirement for alignment but it is not a fundamental problem. To reduce the angular dependence, one can also develop LN integrated dielectric metasurfaces with high refractive indices and local resonances [35].
3. Conclusion
In summary, an electrically tunable perfect absorber based on LN-Graphene integrated resonance metasurface has been numerically demonstrated. The graphene works as a thin absorptive layer as well as a conductive electrode. Through the guided mode resonance between the PMMA grating and the LN waveguide, a strong local field enhancement is generated, which greatly improves the absorption of graphene. The perfect absorption of 99.9% of the whole structure was achieved at 798.42 $nm$ with an absorption of 98.2% by graphene. Furthermore, through the linear electro-optic effect, the refractive index of LN could be adjusted through the applied voltage to control the absorption of the whole structure. At 798.42 $nm$, the switching ratio $R/R_0$ could reach -44.08 $dB$ by increasing $V_0$ from -150 $V$ to 0 $V$. On the constrast, to achieve the needed Fermi level of graphene in the structure for effective absorption modulation, an external bias voltage of more than 2500 $V$ is required. This result fully demonstrates the application prospect of LN integrated high-Q resonant metasurface in realizing electro-optic tunable nanophotonic devices in the visible and near infrared band. It also shows the excellent properties of graphene as an optical material as well as electric material (i.e., an electrode). Our work will promote the research of graphene integrated optoelectronic devices as well as LN based tunable nanophotonic devices which have widespread applications such as modulators and optical phase arrays.
Funding
Hunan Provincial Science and Technology Department (2017RS3039, 2018JJ1033); National Natural Science Foundation of China (11674396); NAtional University of Defense Technology (Postgraduate Scientific Research Innovation Project).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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