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Abstract
In this work, we propose a multi-band terahertz perfect absorber employing the topological photonic crystal combined with VO2 and graphene. The hybrid strong coupling among the topological photonic state, the Tamm plasmon polaritons excited around the interfaces of VO2 and graphene results in the three perfect absorption bands. Benefiting from the reversible insulator-metal phase transition of VO2 and the tunable Fermi level of graphene, it can actively switch among no absorption, single-band, dual-band and multi-band absorptions around 1THz, with the absorption frequencies tunable as well. Besides, the absorption bands are sensitive to the incident angle in almost the same dispersion rate, with high absorptions in a large angle range. Moreover, the splitting frequencies between the adjacent absorption peaks strongly depend on the pair number of the alternating multilayers. Apart from the three absorption bands, there are still many absorption peaks in the large frequency range resulting from the standing waves, including other 7 peaks above 0.9 between 0.83THz and 1.55THz. Such a tunable multi-band absorber with multiple modulation methods may find extended applications in active integrated terahertz devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz wave has attracted numerous attention due to the wide application prospects in spectroscopy and wireless communication [1,2]. However, few natural materials interact with THz radiation, resulting in the great demand for functional terahertz devices, such as switches, polarization converters and absorbers. Among them, perfect absorber with a near-unity absorption has become one of the most crucial components of sensors [3], modulators [4] cloaking [5] and imaging [6]. Benefitting from metamaterials [7,8], various terahertz perfect absorbers have been proposed, including narrow band [9,10], broadband [11–14], dual-band [15–19] and multi-band [20–22] absorbers. Multiband perfect absorbers have extensive applications in spectroscopic detection and phase imaging, as many kinds of drugs and explosives materials possess distinct fingerprints at multiple frequencies. General method to design dual- and multi-band terahertz perfect absorber is combing similar microstructures of different sizes horizontally or vertically, requiring precise microfabrication process to obtain the expected patterns. On the other hand, strong coupling system based on one-dimensional photonic crystals (PC) offers a convenient choice to design dual- and multi-band terahertz perfect absorbers [23–25], which is composed of alternating multilayers. The strong coupling systems support two or more optical modes with close frequencies, where the reversible energy exchange rate among them prevails their respective damping rates, giving rise to a set of splitting hybrid modes with perfect absorption. In these cases, the multiple absorption modes inherit the optical properties from those participating in the strong coupling process, integrating the characteristics of every single mode into the resulted hybrid modes, which improves the diversity and tunability of the multi-band perfect absorbers.
In recent years, tunable perfect absorber gradually becomes a research focus due to the consideration of developing active terahertz devices. Employing tunable elements, such as photoconductive silicon [26], liquid crystal [27,28], graphene [29–32], Dirac semimetal [33] and VO2 [34–36], the absorptance or the working frequency of the perfect absorbers can be actively controlled. Furthermore, bi-tunable perfect absorbers can be achieved by simultaneously taking the advantages of different active materials [37–39], enriching the modulation means and effects.
At the interface between one-dimensional PC and metal film, a unique electromagnetic surface state called Tamm plasmon polariton (TPP) can be excited [40], analogous to the electronic surface state predicted by Tamm [41]. On the other hand, the edge mode named topological photonic state (TPS) existing at the interface of a topological PC heterostructure is introduced by the analog between photonic systems and quantum systems [42,43], where the topological properties of the two semi-infinite systems on each side of the interface are different. In this work, we design a topological photonic crystal heterostructure combined with VO2 and graphene, in which one TPS and two kinds of TPPs are excited. The strong coupling among the three modes leads to the multi-band terahertz perfect absorption with multiple modulation pathways. Both the absorption strength and the band number can be modulated because of the reversible insulator-metal phase transition of VO2. The working frequencies and the bandwidths of the absorber can be controlled via the Fermi level of graphene. Besides, the working frequencies are sensitive to the incident angle as well. Moreover, there are also many high absorption peaks coming from the stand waves, expanding its potential applications in active terahertz switches, filters and detectors.
2. Structure design and simulation results
The hybrid topological photonic crystal heterostructure is shown in Fig. 1(a), consisting of VO2, PC1, PC2 and monolayer graphene. The PC1 is composed of 6 pairs of alternating silica and TPX films, while the PC2 consists of 6 pairs of alternating silica and Zeonor films. In terahertz band, the TPX and Zeonor are low-loss polymers whose refractive indexes are nT = 1.46 and nZ = 1.53 [44], respectively, and the silica is also low-loss with the refractive index of nS = 1.95 [45]. The film thicknesses in PC1 and PC2 are dS1 = 40µm, dT = 48µm, dS2 = 35µm, dZ = 52µm, respectively. The thickness of the silica spacer between PC1 and VO2 is t1 = 40µm, and that between PC2 and graphene is t2 = 28µm. The thickness of VO2 is dV = 30µm.
Fig. 1. (a) The schematic of the V/PC1/PC2/G structure. (b) The absorption spectra in the ON (solid line), VON (blue dotted line), GON (yellow dotted line) and OFF (green dotted line) states.
In this system, the absorption spectra can be modulated by tuning the Fermi level EF of graphene and the conductivity σVO2 of VO2. We define the condition where EF = 0 eV and σVO2 = 10 S/m as the OFF state, EF = 0 eV and σVO2 = 2×105 S/m as the VON state, EF = 0.7 eV and σVO2 = 10 S/m as the GON state, EF = 0.7 eV and σVO2 = 2×105 S/m as the ON state. The absorption spectra in these states are shown in Fig. 1(b). In the OFF state, there is almost no absorption. In the VON and GON states, it behaves as a dual-band absorber. In the ON state, it acts as a multi-band perfect absorber, with three absorption peaks P1, P2 and P3 at the frequencies of f1 = 0.97 THz, f2 = 1.01 THz and f3 = 1.05 THz, respectively.
In simulation, the surface conductivity of graphene varies with the Fermi level EF is expressed as [46]
Fig. 2. The relative permittivity of (a) graphene and (b) VO2, with the solid and dashed lines indicating the real and imaginary parts, respectively.
The relative permittivity of VO2 in the terahertz band can be described by the Drude model as [48,49]
To explore the physical mechanism of the absorber, we calculate the spectra of the structures PC1/PC2, VO2/PC1 and PC2/graphene, as shown in Fig. 3(a). The band structures of the single PC1 and PC2 can be obtained from [42]
Fig. 3. (a) The reflection spectra of the PC1/PC2 (red dotted line), the absorption spectra of the V/PC1 (yellow solid line) and PC2/G (blue solid line) for VON and GON states, respectively. (b) Left and middle, the band structures of the PC1 and PC2, where the band gap and the Zak phase of every band are listed with blue and orange labels, respectively. Right, the DOS of the PC1/PC2 structure, where the blue shadows are in the same position with those indicating the band gaps in the band structures. (c)-(e) The electric field distributions at the frequencies of the dip and peaks in (a).
Furthermore, we calculate the field distributions at the absorption peaks P1-P3 of the ON state, as shown in Figs. 4(a)–4(c), where the fields are simultaneously localized around the boundaries of VO2/PC1, PC1/PC2 and PC2/graphene. Thus, the multi-band absorptions come from the hybrid strong coupling among the TPS, VTP and GTP modes, as schematically described in Fig. 4(d). For the VON state, the dual-band absorption comes from the strong coupling of TPS and VTP, as the GTP cannot be excited. For the GON state, the strong coupling between TPS and GTP results in the dual-band absorption, because of the absence of VTP.
Fig. 4. (a)-(c) The electric field distributions at the frequencies of the peaks P1-P3, respectively. The dashed lines indicate the boundaries between the structures. (d) Schematic of the strong coupling process leading to the three perfect absorption peaks.
The strong coupling process here can be described by the coupled oscillator model as [52]
3. Modulations and discussions
In the insulator-metal phase transition process of VO2, the conductivity σVO2 varies from 10 S/m to 2×105 S/m, which affects the strength and damping rate of the VTP, as indicated by the dashed lines in Fig. 5. As displayed in Fig. 5(a) for EF = 0, no absorption changes into single-band absorption when σVO2 increases to 2×103 S/m from the OFF state. The absorption of the TPS is enhanced because of the weak coupling between VTP and TPS. The VTP-TPS coupling strength increases with the σVO2, which turns into strong coupling regime when σVO2 exceeds 6×103 S/m, leading to the switch from single-band to dual-band absorption. As a result, the OFF state finally turns into VON state with two absorption bands, as shown in Fig. 5(a). The detune between the frequencies of TPS and VTP leads to the asymmetric profile of the two peaks in the VON state, even though both VTP and TPS in Fig. 3(a) behave symmetric profiles. Similarly, if the Fermi level of graphene is 0.7 eV, it switches from the GON state to ON state as the VO2 transits from insulator to metal phase. The absorptions of the two bands in the GON state are enhanced as σVO2 increasing to 2×103 S/m, due to the weak coupling between VTP and the other two modes. When σVO2 increases over 6×103 S/m, the two absorption bands gradually split into three bands because of the strong coupling. Therefore, σVO2 has a great impact on the coupling strength, result in the affection on the absorption strength and the band number.
Fig. 5. Tuning σVO2, the absorption spectra with offset when (a) EF = 0 eV and (b) EF = 0.7 eV, with those of the V/PC1 for comparison (dashed lines).
Besides, the Fermi level of graphene offers another means to control the multi-band absorption. Increasing the EF, the absorption spectra in the ON state are shown in Fig. 6(a). The working frequencies of the three absorption bands blue-shift with the Fermi level. The dispersion properties are inherited from the GTP, indicated by the blue dashed line. Seen from Fig. 6(b), the three peaks narrow down with the EF as well, due to the decrease of the GTP bandwidth. Employing Eq. (5), the frequencies of the absorption bands are calculated, as depicted by the black dashed lines, fitting well with the simulation results. Moreover, the mixing fractions of TPS, VTP and GTP in every absorption band are displayed in Figs. 6(c)–6(e). As EF increasing, the P1 turns from GTP-like into VTP-like, the P2 turns from more VTP-like into equal proportion mixing, and the P3 turns from TPS-like into GTP-like, leading to the deformation of the absorption bands. Accordingly, changing the Fermi level of graphene, both the absorption frequencies and the bandwidths of the absorption bands can be modified.
Fig. 6. (a) The variation of the absorption spectra related to the Fermi level EF. The black dashed lines show the fitting results and the blue dashed line indicates the GTP mode. (b) The absorption spectra with offset for different EF, with those of the PC2/graphene for comparison (dashed lines). (c)-(e) The mixing fractions of TPS (|αT|2), VTP (|αV|2) and GTP (|αG|2) in P1-P3, respectively.
Different from the σVO2 and EF, which control the absorption bands via influencing the VTP and GTP, respectively, the incident angle can simutaneously affect all the TPS, VTP, and GTP. Increasing the incident angle, the absorption spectra in the ON state under TM illumination are shown in Fig. 7(a). The three absorption peaks turns to higher frequencies altogether, with almost the same dispersion. Such a dispersion property can find explanations from Fig. 7(b). The three single modes, TPS, VTP and GTP, all shift to higher frequencies, with almost the same dispersion as well. Consequently, the coupling strengths VTV, VTG and VVG remain nearly unchanged as the incident angle varies, leading to the similar dispersion properties of the three absorption peaks. As this planer multilayer structure is isotropic in x-y plane, similar dispersion would occur under TE illumination. The three absorption peaks keep above 0.95 and distinguishable to each other even for the incident angle as large as 60°, with the frequencies varied about 0.11THz. Hence, this absorber is sensitive to the incident angle in a wide angle range, which helps it to find applications in sensors.
Fig. 7. (a) The variation of the absorption spectra related to the incident angle. (b) The frequencies of the TPS, VTP and GTP modes for different incident angles.
Apart from the active modulation elements, there is also an important passive parameter that impacts the multiple absorption peaks by influencing the TPS, VTP and GTP in the meanwhile, which is the pair number of the alternative multilayers in the PC1 and PC2. As shown in Figs. 8(a) and 8(b), the splitting between the two adjacent absorption peaks decreases with the pair number, for all the ON, VON and GON states, accompanied by the decrease of the damping rates of TPS, VTP and GTP in Figs. 8(c) and 8(d). Moreover, the absorption of the VTP gradually vanishes while the pair number increases to 13. As a result, the peak number in the ON state reduces to two and that in the VON state reduces to one. Define the damping factors of the adjacent absorption peaks in the ON state as Γij = (γi + γj)/2, and the splitting frequencies between them as Δfij = fj - fi, in which (i, j) is (1, 2) or (2, 3) for P1-P3. Thereby, the strong coupling regime can be expressed as Γij < Δfij, where the splitting is larger than the damping. Otherwise, it enters the weak coupling regime, where the neighbouring modes superimpose into one mode. As displayed in Fig. 8(d), the strong coupling enters to weak coupling as the pair number increase to above 10, with the three absorption peaks gradually reducing to two and even one. Therefore, the splitting of the three absorption peaks can be decided by the pair number, which is in the range from 3 to 10 to keep every peak distinguishable.
Fig. 8. (a) The absorption spectra in the ON state related to the pair number in the PC1 and PC2. (b) The absorption spectra with offset in the ON (solid lines), VON (dotted lines) and GON (dashed lines) states. (c) The reflection spectra with offset for the PC1/PC2 (solid lines), and the absorption spectra of the V/PC1 (dotted lines) and PC2/G (dashed lines). (d) The damping rates of the TPS (γT), VTP (γV) and GTP (γG), the damping factors of the adjacent absorption peaks (Γ12 and Γ23), and the frequency differences between the adjacent peaks (Δf12 and Δf23).
As the pair number increasing, more perfect absorption peaks appear in both sides of the multi-peaks we are interested. Thus, we expand the frequency range in simulation to explore the existence of the other absorptions for the pair number of 6. As shown in Fig. 9(a), multiple absorption peaks appear besides the peaks around 1THz. There are altogether 10 peaks whose absorptions are above 0.9 in the range between 0.83THz and 1.55THz, and 16 peaks above 0.8 in the range from 0.69THz to 1.86THz. At the frequencies around 1THz and 3THz, hybrid strong couplings among TPS, VTP and GTP occur, leading to the three splitting absorption peaks. At the frequencies around 2THz, weak coupling results in the enhancement of the original low absorptions in the VO2/PC1/PC2 structure, without frequency shift and mode splitting. Apart from these, the other absorption peaks decrease for the frequencies away from 1THz.
Fig. 9. (a) The reflection/absorption spectra with offset for different structures in the large frequency range, where the green and gray shadows indicate the absorptions above 0.9 and 0.8, the blue and red shadows indicate the weak and strong couplings, respectively. (b) The frequencies and amplitudes of the absorption peaks, with the fitted results (solid line).
Extracting the frequencies and absorptance of the peaks, the results are displayed in Fig. 9(b). Except the peaks around 1THz, 2THz and 3THz that comes from strong and weak couplings, the frequency differences between the adjacent absorption peaks are almost the same, because they all come from the standing waves, which are absence in the other structures in Fig. 9(a). Thus, the frequencies of the absorption peaks should following
where Σ(nidi) is the optical distance between graphene and VO2, m is a positive integer, and c is the light speed in vacuum. The peak frequencies calculated via Eq. (6) are shown by the solid line in Fig. 9(b), where the first peak is related to m = 4 and the gradient is about 78.6 GHz, fitting well with the simulation results. Therefore, this system can actually support multiple absorption peaks due to different mechanisms, including strong coupling, weak coupling and standing wave.4. Summary
In summary, we propose a multi-band perfect absorber with multiple active control means, whose absorption peaks around 1THz come from the hybrid strong coupling among the TPS, VTP and GTP. The properties of the absorber can be actively tuned by the σVO2 and EF. The σVO2 mainly affects the absorption band number, while the EF mainly impacts the frequencies of the absorption bands. Consequently, the absorber can turn from no absorption to single-band, dual-band and even multi-band absorption, with the absorption frequencies controllable. Besides, the absorber is sensitive to the incident angle and keeps high absorptions in a wide angle range. Apart from the active modulation, the pair number of the multilayers affect the coupling strength as well, resulting in the variation of the splitting frequencies between the adjacent absorption peaks. Moreover, the multilayered system also supports a lot of absorption peaks in the large frequency range, which result from the standing wave. Such an active multi-band absorber with multiple modulation methods may achieve potential applications in active integrated terahertz devices, such as switches, filters, detectors and sensors.
Funding
National Natural Science Foundation of China (11804178); Natural Science Foundation of Shandong Province (ZR2018BA027); National Laboratory of Solid State Microstructures, Nanjing University (M34009).
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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