Tunable bidirectional perfect THz absorber realized by graphene-based one-dimensional photonic crystals

In this paper, a perfect absorption structure of graphene-based one-dimensional photonic crystals (1DPC) with tunable absorption channels and absorptivity is proposed. The proposed structure can achieve four perfect absorption peaks with the absorptivity of 99.31%, 99.88%, 99.74% and 99.32% at the same time, and the absorptivity of all absorption peaks is more than 95%. By adjusting the period number of 1DPC, the number of absorption peaks and absorption efficiency can be changed. By changing the chemical potential and relaxation rate of graphene, the absorption of the proposed structure can be dynamically tuned. And the influence of structural layer thickness on absorption property is also explored. In addition, we use this structure to design two different bidirectional absorbers. The designed bidirectional absorber can tailor the perfect absorption frequency with the absorptivity of more than 99.51%, and can change the absorption channel from single channel to double channel and double channel to multi-channel under the forward and backward incidence. This work not only fills the gap in the design of bidirectional perfect absorbers for 1DPC, but also provides a scheme for the design of multifunctional devices.


Introduction
Photonic crystal (Piper and Fan 2014;Zhang et al. 2013) is a periodic artificial microstructure that was proposed by John (1987) and Yablonovitch (1987) respectively in 1987. The most important characteristic of photonic crystals is the photonic band gap, and we can change the order of the dielectric layers to obtain the desired pass-band or gap band which can control the propagation behavior of light waves. When the dielectric material is inserted in the appropriate position of the photonic crystal, the original periodicity of the photonic crystal is broken and defects occur, the defect is photon localized. Benefit from these unique advantages, they are used to design filter (Ghimire et al. 2022;Gawali et al. 2019), sensor (Yao et al. 2021;Parandin et al. 2021), optical fiber (Pakarzadeh et al. 2021;Meshginqalam and Barvestani 2022), absorber (Nickpay et al. 2022;Zamzam et al. 2021), etc. Graphene is often used to design high-performance optical devices due to its excellent optical properties which were discovered by Andre K. Geim and Novoselov et al. (2004). Combining photonic crystals with graphene can achieve various optical properties, such as optical Tamm states (Wang et al. 2017;Ye et al. 2019) and surface plasmon (Islam et al. 2020;Li et al. 2021;He et al. 2022). The performance of graphene photonic crystal structure can be achieved not only by changing the carrier concentration of graphene, but also by different patterns and layers. Islam et al. (2020) proposed a surface plasmon structure with multiple absorption bands which has the characteristics of polarization insensitive. This structure used two layers of graphene and developed graphene pattern to achieve tunable multichannel perfect absorption. Zhu et al. (2020) designed a wideband absorber that perfectly absorbs waves in the range of 1-2.6 THz. And this structure can realize the conversion of broadband perfect absorption and multichannel perfect absorption.
One-dimensional photonic crystal (1DPC) is the simplest photonic crystal structure and is easy to manufacture, which can be used to design absorbers (Hu et al. 2022;Davoodi and Granpayeh 2018;Ahmed and Mehaney 2019;Acharyya et al. 2022), sensors (Elshahat et al. 2021;Jahani et al. 2020;Zaky et al. 2020) and so on (Zaky and Aly 2022;Chen et al. 2008;Qu et al. 2018). In this paper, we make full use of the local properties of photonic crystals and the excellent optical properties of graphene, and propose a structure based on 1DPC and graphene which can achieve tunable multichannel perfect absorption. This structure can be used to design bidirectional absorbers. Compared with Deng et al. (2014), our proposed structure can adjust the absorptivity of multiple absorption peaks with the absorptivity of more than 99.5%. Compared with Jahani et al. (2020), the proposed structure can produce more absorption peaks, and have four perfect absorptions at the same time. And we can change the number of absorption peaks by changing the photonic crystal period. Compared with Hu et al. (2022), the absorber designed by us can not only achieve perfect bidirectional absorption, but also achieve perfect multichannel absorption. And we can tailor the perfect absorption frequency and absorption channel by changing the number of periods of the photonic crystal.

Theoretical model and calculation method
We propose the structure is (ABA) N -G-C-(AB) M plotted in Fig. 1, and A is SiC, B is SiO 2 , G is graphene, C is air, N and M represent the period numbers of the two 1DPC respectively. The permittivity of SiC and SiO 2 comes from references (Deng et al. 2014;Liu et al. 2021).
We use the characteristics matrix method (Deng et al. 2014;Zhan et al. 2013) based on permittivity to calculate the reflectivity, transmissivity and absorptivity of the structure. And the transmission matrix from medium a to medium b can be written as for TM case, with is frequency of the incident wave, k 0 is the wave vector in incident medium, a b is the permittivity of the medium a (b). The propagation matrix P a of the electromagnetic wave in the dielectric layer can be expressed by the following matrix.
With k az = k 0 √ a − 0 sin 2 . And when light travels from medium a through graphene to medium b, the transmission matrix can be written as is conductivity of graphene, a is permeability of medium a, J TE = 1 1 −1 −1 , and J TM = −1 1 −1 1 .
In the THz range graphene is well described by the Drude-like conductivity where c is chemical potential, Γ is relaxation rate, k B is Boltzmann constant, T 0 is absolute temperature. The transmission matrix of the entire structure can be written as (3) The transmittance T, reflectance R and absorption A can be obtained by T

Absorption principle and tunability
The proposed structure is composed of four materials, namely SiC, SiO 2 , graphene and air. In the following calculations, we ignore the wave loss caused by SiC, SiO 2 and air, and the permittivity of these media can be taken as the real value with SiC = 12.88 , SiO 2 = 3.90 and air = 1.00 . The conductivity of graphene can be determined by defining the chemical potential c and relaxation rate Γ , we take c = 0.9 eV and Γ = 8 ps − 1 . The thickness of the SiO 2 , SiC, air and graphene layers in the structure are given by d SiC = 130 In what follows, the absorption, transmission and reflection characteristics of the structure under normal incidence are illustrated in Fig. 2a. We can see that there are six absorption peaks at 1.872, 2.046, 2.237, 2.429, 2.613, and 2.769 THz with absorptivity of 95. 01, 99.31, 99.88, 99.74, 99.32, and 97.55%, respectively. All absorption peaks had absorptivity of more than 95%, and four of them were perfect absorptions. There is another point worth noting, in this frequency range almost all THz waves are reflected or absorbed. From Fig. 2b, we can see that at the frequency corresponding to the absorption peak, the reflectivity without graphene is much larger than that with graphene, which indicates that the introduction of graphene leads to defects in the structure and changes the photonic band gap.
In order to explore the cause of the formation of absorption peaks, we have depicted the electric field diagrams corresponding to the six absorption peaks in Fig. 3, and we define the initial value of all-electric field intensities as 1. From these electric field diagrams, we can know that the electric field is mainly distributed in 1DPC on the light side of graphene and the electric field on both sides of graphene is weak. According to the critical coupling conditions, we can derive the formula for calculating the absorptivity: ∕Idx , with is angular frequency, is the product of the refractive index and extinction coefficient of graphene, E g is the electric field at graphene, I is the incident light intensity. As we can see, absorptivity is not only related to the electric field of graphene, but also related to a variety of factors. From the electric field distribution, we can know that the absorption peaks are caused by Fabry-Perot resonance, and the Fabry-Perot resonator is composed of graphene and photonic crystal on the left. Besides, the electric field distribution of the air layer and the photonic crystal on the right is very small, it shows that they mainly act as Bragg mirror. Next, we research the effect of changing the period number N and M of 1DPC on the absorptivity and plot the absorption as a function of frequency in Fig. 4. As shown in Fig. 4a, when N = 2, although there is only one absorption peak, the absorption peak is wider. When N = 7, the absorption peak is the narrowest, but the number is the largest, this phenomenon shows that the surface plasma resonance effect in the multilayer increases. Generally, the design multichannel absorption structure is obtained by increasing the number of graphene layers or changing the graphene pattern. However, our proposed structure provides another important way to design THz multi-frequency absorbers. In Fig. 4b, we can see that, 1DPC on the right only changes the absorptivity of the structure and doesn't change the number of absorption peaks, and we can think of it as a Bragg mirror.
In Fig. 5, we represent the effect of the angle of incidence on the light absorption in the structure. we can clearly see that when incident angle increases absorption peak blueshift for both TE and TM polarizations. And when the incident angle is in the range of 0-20 • , the absorption peak blueshift can be ignored, but when the incident angle ⩾ 20 • , the absorption peak blueshift obviously. Furthermore, the structure maintains absorption up to 90% even at an incident angle of 60 0 for TE polarization and 45 0 for TM polarization. According to the relationship between propagation angle and frequency ( ∝ 1∕ cos ) (Deng et al. 2014), we can know that when propagation angle increases, 1∕ cos also increase, leading to an increase in frequency . And it can be observed in Fig. 5b that some higher-order modes appear at high incident angles for TM polarization, which cause the absorption band to break (Feng et al. 2021;Huang et al. 2020).
To analyze the tunable properties of light trapping, the absorption in the absorbing layer with various chemical potential c and relaxation rate Γ of graphene have been simulated in Fig. 6 (Zhou et al. 2014;Wang et al. 2010;Fang et al. 2014). And Fig. 6a shows that with the decrease of chemical potential, the absorption decreases and the absorption peak is slightly redshifted. When the chemical potential is in the range of 1-0.5 eV, the absorption is more than 80%. When the chemical potential drops from 0.5-0 eV, the absorption decreasing rapidly. The chemical potential of graphene can be adjusted by changing the gate voltage, and then the absorption can be tuned from 0 to 99%. And Fig. 6b shows that with the relaxation rate decreases from 10 to 0 ps − 1 , the absorption decreases from 99 to 0%, and the frequency corresponding to the absorption peak is basically unchanged. Due to the dynamic tunability of absorption, the proposed structure has great potential in modulator design. As mentioned earlier, we calculate and discuss the absorption performance of the absorber in the ideal case, but in the actual production process, the structural layer thickness will cause errors. Therefore, as shown in Fig. 7, we explored the influence of structural layer thickness on absorption performance. And with the increase of the thickness of the structure layer, the absorption is almost unchanged, but the absorption peak has an obvious redshift. According to the principle of scale invariance, when the scale of the unit increases, the wavelength of the absorption peak increases and the corresponding resonant frequency will move towards low frequency. In order to make the results more intuitive, we calculated the sensitivity of frequency to the thickness of the structural layer by S = Δf ∕ Δd . For d A , from high frequency to low frequency, the corresponding sensitivities of absorption peaks are 0.22 THz∕um , 0.21 THz∕um , 0.19 THz∕um , 0.17 THz∕um , 0.16 THz∕um , and 0.15 THz∕um , respectively. And for d B , the corresponding sensitivities of absorption peaks are 0.06 THz∕um , 0.05 THz∕um , 0.05 THz∕um , 0.04 THz∕um , 0.04 THz∕um , and 0.03 THz∕um , respectively.

Application of bidirectional absorber
Next, we optimize the structure and design two bidirectional absorbers, and the new structure is shown in Fig. 8. We define the direction of ⃗ k 0 as a positive direction and− ⃗ k 0 as a negative direction. The thickness of the two air layers in the structure is the same d air = 20 m . Two graphene films are given the same chemical potential and relaxation rate with (4 √ SiO 2 )μm, Δd = 0.5 or 1 μm c = 0.9 eV and Γ = 8 ps − 1 . N 1 and N 2 are set as needed. All other parameters remain unchanged.
First, we define N 1 = 2 and N 2 = 3 to design a perfect absorber that can achieve bidirectional absorption. As we can see in Fig. 9a, there is one absorption peak at 2.393 THz with an absorptivity of 99.84%. In Fig. 9b, there are two absorption peaks at 2.144 THz and 2.578 THz with absorptivity of 99.89 and 99.51%, respectively. It's worth noting that these three perfect absorption peaks correspond to different frequency. When f = 1.786 THz and 2.893 THz, the absorber produces two asymmetric absorption peaks which caused by the Fano resonance.
To investigate whether the absorber can be used for wide-angle absorption, we calculate the absorptivity at different angles of the incident in Fig. 10. As we can see from the absorption spectra, when the incident angle increases the absorption peak blueshift. However, when the incident angle ⩽ 20 • , the frequency corresponding to the absorption peak basically doesn't change. Besides, For TM polarization, the absorption peak breaks at incidence angles ranging from 60 • to 80 • due to the appearance of higher order modes (Feng et al. 2021;Huang et al. 2020).
We design a multi-frequency absorber by changing the period of 1DPC with N 1 = 6 and N 2 = 7 , and other conditions are the same. We can see from Fig. 11 that there are four perfect absorption peaks for the forward propagation of light and five perfect absorption peaks for the backward propagation of light. It's also worth noting that the absorptivity of the remaining absorption peaks exceeds 95%, and all the absorption peaks correspond to different frequencies. When f = 1.776 THz and 2.850 THz, the absorber produces two asymmetric absorption peaks which caused by the Fano resonance too. In order to explore the effect of different angle incidence on absorption properties, we calculate the absorptivity at different angles of the incident in Fig. 12. We find that the absorptivity of the absorber is still very high when the incident angle ⩽ 70 • . But when the incident angle ⩾ 20 • the absorption peak obviously blueshift. And in contrast to TE polarization, the absorption peak of TM polarization is broken when the incidence Angle is large, which is caused by higher order modes (Feng et al. 2021;Huang et al. 2020).

Conclusion
In summary, a perfect absorption structure of 1DPC with a tunable absorption channel and absorptivity is designed and studied. When the period of 1DPC on the left of graphene of the proposed structure changes from 2 to 7, the absorption peak number changes from 1 to 6. For the structure (ABA) 7 -G-C-(AB) 6 , when the incident angle =0 • , there are six absorption peaks at 1.872 THz, 2.046 THz, 2.237 THz, 2.429 THz, 2.613 THz and 2.769 THz with the absorptivity of 95. 01, 99.31, 99.88, 99.74, 99.32 and 97.55% respectively, and all absorption peaks have absorptivity of more than 95%. When the incident angle increases, the absorption peak blueshifts, and the structure still maintains a high absorption of 90% even at an incident angle of 60 0 for TE polarization and 45 0 for TM polarization. Moreover, the absorption can be tuned from 0 to 99% by varying the chemical potential and relaxation rate of graphene. And by increasing the thickness of the structure layer, the absorption peak is redshifted. For the bidirectional absorption structure (ABA) 2 -G-C-(AB) 6 -C-G-(ABA) 3 , when the incident angle = 0 , there is one perfect absorption peak at 2.393 THz with the absorptivity of 99.84% for the forward incidence, and two perfect absorption peaks at 2.144 THz and 2.578 THz with the absorptivity of 99.89% and 99.51% for the backward incidence. For the bidirectional absorption structure (ABA) 6 -G-C-(AB) 6 -C-G-(ABA) 7 , when the incident angle = 0 , there are four perfect absorption peaks for the forward incidence and five perfect absorption peaks for the backward incidence. We can tailor the perfect absorption frequency and absorption channel by changing the period of photonic crystals.