Dynamically electrical/thermal-tunable perfect absorber for a high-performance terahertz modulation

Dongwen Zeng; Dongwen Zeng; Shu Zong; Shu Zong; Guiqiang Liu; Wen Yuan; Wen Yuan; Xiaoshan Liu; Zhengqi Liu

doi:10.1364/OE.474970

1. Introduction

Terahertz radiation is an electromagnetic wave between infrared and microwave, ranging from 0.1 THz to 10 THz. The artificial and effective manipulation of Terahertz radiation has wide application in biomedicine [1,2], detectors [3–5], terahertz switches [6], imaging [7–9] and wireless communications [10,11]. Due to the natural materials contributing little to THz technologies, which is not conducive to its development. Later, the emergence of metamaterials (MMs) provides researchers with a new approach. Metamaterials consist of periodic arrays of subwavelength metals or dielectric blocks which can produce electromagnetic responses that are not exist in natural materials. Therefore, metamaterials have found a wide range of applications in the field of optical, such as perfect lenses [12–14], polarization converter [15–17], negative refraction [18], vector light fields [19] and perfect metamaterial absorber [20]. Perfect metamaterial absorber is a significant branch of metamaterial application. Degeneracy critical coupling [21] and breaking parity-time (PT) symmetry [22] are used to break the 50% absorption limit of subwavelength thickness film. Coherent asymmetric absorbers can change the absorption from almost perfect to very small by changing the incident Angle of coherent waves [23]. Random metasurfaces are used to reduce light interactions and thus solve the light scattering problem [24]. Metal-insulator-metal (MIM) structured absorbers utilizing Fabry-Perot (FP) cavity resonances are classic approach to achieve near-unity absorption. The search for perfect metamaterial absorbers (PMA) has not quit since Landy et al. first introduced a single band perfect absorber in 2008 [25], and gradually developed into a full-spectrum range including ultraviolet [26], visible light [27], infrared [28], THz [29] and microwave [30,31]. In particular, PMA in THz band is often limited to very narrow bandwidth and constant intensity which cannot be adjusted once the structure design is completed. Therefore, achieving dynamic tunable PMA with high absorption intensity over a wide THz range is an arduous task.

Graphene is a 2D film composed of periodic arrays of carbon atoms in a hexagonal lattice, and its conductivity can be dynamically adjusted over a wide frequency range by adjusting chemical doping or gate voltages [32–34]. As a phase change material, VO₂ is another excellent dynamic tunable material that differs from graphene in that it can change from an insulating state to a metallic state at about 340 K [35], and the transition is reversible. This transition can be triggered by externally excited light and thermal radiation and can achieve conductivity changes of multiple orders of magnitude in the picosecond range. Nonetheless, previous graphene and VO₂-based PMA remained limited to narrow-band or multi-band dynamic tuning [36,37], while tuning with high modulation depths remained rare for perfect absorbers of broadband terahertz. The comparison of wideband THz absorbers based on graphene or VO₂ that have emerged in the past year are shown in Table 1.

Table 1. Comparison of wideband absorbers based on graphene or VO₂ in the past year.

View Table

Here, a broadband perfect absorber was proposed with dynamical tunability, which combines graphene and VO₂, consists of a golden mirror at the bottom, a layer of topas, and a helical VO₂ located on a layer of graphene. By adjusting the conductivity of VO₂ from 200 S/m to 200000 S/m, VO₂ can transform from an insulating phase to a metallic phase, and obtain the best broadband perfect absorption at a conductivity of 100000 S/m. When the conductivity of VO₂ is 100000 S/m (metallic phase), the absorption rate is greater than 90% in the range of 1.594 THz-3.272 THz (bandwidth 1.678 THz) and greater than 99% in the range of 1.834 THz-3.155 THz (bandwidth 1.321 THz), of which the absorption of 2.05 THz is 100%, and the absorption of 3.08 THz is 99.55%. When the conductivity of VO₂ is 200 S/m (insulator phase), the absorption rate of the absorber as a whole is close to 0. The maximum modulation depth (MD) is 99.98% and the minimum extinction ratio (ER) is -36.5 dB. In addition, by adjusting the Fermi energy level of graphene from 0.01 eV to 0.7 eV, the absorber can be changed from a wide-band absorber to an absorber with two resonant absorption peaks. Finally, a supplementary analysis of the chiral characteristic of the helical structure reveals that there is a circular dichroism response under the excitation of left-circularly polarized (LCP) and right-circularly polarized (RCP). The results show that the designed absorber not only has simple structure, but also shows a good prospect in imaging, optical switches, modulators.

2. Design and method

Full-wave simulations were implemented by using the finite element method (FEM). A unit cell of the absorber is equipped with periodic boundary conditions in the X and Y directions to simulate infinite arrays, and a perfect matching layer is created in the Z direction. Periodic ports are set as excitation sources and monitor wave transmission and reflection. Graphene layer with single atom thickness can be regarded as 2D infinite-thin layer, and transition boundary condition is set for it to improve computation efficiency. Fine mesh is used to ensure the convergence of the results. A 3D, side and top view of the absorber is shown in Fig. 1.

Fig. 1. (a) 3D schematic of the designed wideband absorber. (b) and (c) The side and top views of the absorber and descriptions of various parameters, respectively.

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The unit consists of a gold substrate, a waveguide layer of topas, a layer of graphene covered in the waveguide layer and a VO₂ helix. The parameters of the structure are set as follow. The helical VO₂ with a thickness of t₁ = 1 µm, graphene layer with a thickness of t₂ = 0.34 nm, topas layer with a thickness of t₃ = 20 µm and gold mirror with a thickness of t₄ = 0.5 µm as the substrate, respectively. In addition, the lattice constant is P = 65 µm, the minimum radius of the innermost turn of helical VO₂ is r = 1 µm, the width d₁ and interval d₂ of each turn of the helical VO₂ are 2 µm and 3 µm, respectively. Furthermore, the designed structure can be manufactured by chemical vapor deposition (CVD) in practical applications.

Regardless of material loss and dispersion, the dielectric permittivity of topas is 2.35. The dielectric permittivity of VO₂ in the range of THz can be described by Drude model [47–49], which can be expressed as

(1)$$\varepsilon ({\omega ,\sigma } )= {\varepsilon _\infty } - \frac{{\omega _p^2(\sigma )}}{{{\omega ^2} + i\gamma \omega }},$$

where ɛ_∞=12 is dielectric permittivity at the infinite frequency, ω_p(σ) is plasma frequency dependent on conductivity, and γ=5.75 × 10¹³rad/s is the collision frequency. In addition, ω_p²(σ) and σ are directly proportional to the density of the free carrier, and the functional relationship between ω_p and σ can be expressed as

(2)$$\omega _p^2(\sigma )= \frac{\sigma }{{{\sigma _0}}}\omega _p^2({{\sigma_0}} ),$$

where σ₀= 3 × 10⁵ S/m and ω_p(σ₀) = 1.4 × 10¹⁵rad/s. Besides, the relative permittivity of Au can also be described by Drude model [50,51], which can be expressed as

(3)$${\varepsilon _{Au}} = 1 - \frac{{\omega _p^2}}{{{\omega ^2} + i\omega \Gamma }},$$

where plasma frequency ω_p= 1.37 × 10¹⁶rad/s and collision frequency Γ=1.24 × 10¹⁴rad/s. The conductivity of graphene can be divided into the contribution of the intraband and interband by Kubo formula [52–54]

(4)$$\sigma = {\sigma _{{\mathop{\textrm {int}}} ra}} + {\sigma _{{\mathop{\textrm {int}}} er}},$$

(5)$${\sigma _{{\mathop{\textrm {int}}} ra}} = \frac{{2i{e^2}{k_B}T}}{{\pi {\hbar ^2}({\omega + i{\tau^{ - 1}}} )}}\ln \left[ {2\cosh \left( {\frac{{{E_f}}}{{2{k_B}T}}} \right)} \right],$$

(6)$${\sigma _{{\mathop{\textrm {int}}} er}} = \frac{{{e^2}}}{{4\hbar }}\left[ {\frac{1}{2} + \frac{1}{\pi }\arctan \left( {\frac{{\hbar \omega - 2{E_f}}}{{2{k_B}T}}} \right) - \frac{i}{{2\pi }}\ln \frac{{{{({\hbar \omega + 2{E_f}} )}^2}}}{{{{({\hbar \omega - 2{E_f}} )}^2} + {{({2{k_B}T} )}^2}}}} \right].$$

According to the Pauli Exclusion Principle, the contribution of the σ_inter in the THz frequency is negligible at room temperature (T = 300 K) and for Fermi level of interest (E_f/2k_BT>>1), the conductivity of graphene can be simplified to a Drude-like model [55]

(7)$$\sigma = \frac{{i{e^2}{E_f}}}{{\pi {\hbar ^2}({\omega + i{\tau^{ - 1}}} )}}.$$

Here, we set the initial Fermi energy of graphene as 0.01 eV, k_B is Boltzman constant, e is electron charge, $\hbar $ is Planck constant, ω is incident light frequency and τ=1 ps is relaxation time. In practical applications, the Fermi level of graphene can be adjusted by the bias voltage according to the condition [56]

(8)$$|{{E_f}} |= \hbar {V_f}\sqrt {\pi |{{a_0}{V_{bias}}} |} ,$$

where Fermi speed V_f= 1 × 10⁶ m/s, a₀ is the capacitance of the structure, and V_bias is the bias voltage.

3. Results and discussion

The absorption of the designed absorber can be expressed by the formula A(ω) = 1-R(ω)-T(ω) = 1−|S₁₁|²−|S₂₁|², where R(ω) and T(ω) represent reflectance and transmittance respectively and the S-parameters can be obtained in the finite element method (FEM) simulation. Since the Au substrate with a thickness of 0.5 µm blocks the transmission of electromagnetic wave, T(ω) can be regarded as zero, the absorption can be simplified as A(ω) = 1-R(ω) = 1−|S₁₁|² [57].

As shown in Fig. 2(a), the absorptivity of proposed absorber can reach greater than 90% from 1.594 THz to 3.272 THz with bandwidth 1.678 THz when the fermi energy of graphene is 0.01 eV and the conductivity of VO₂ is 100000 S/m. The relative absorption bandwidth of the absorber can be calculated as 69% according to the calculation formula RAB = 2 × (f_h-f_l)/(f_h+ f_l), where f_h and f_l are the highest limit and lowest limit of frequencies with absorptivity above 90%, respectively [58]. In addition, a larger version of the spectrum with absorption greater than 90% are shown in Fig. 2(b), it can be seen that a high absorptivity of more than 99% is achieved in the range of 1.834 THz to 3.155 THz (bandwidth 1.321 THz). There are two resonance absorption peaks at 2.05 THz and 3.08 THz, which are 100% and 99.55%, respectively. In order to analyze the mechanism of broadband perfect absorption, we plotted the surface electric field distributions in the x-y plane of E_Z and surface current distributions at 2.05 THz, 2.5 THz, 3.08 THz and 3.155 THz frequencies, respectively, as shown in Figs. 2(c)–2(f). It can be seen from Figs. 2(c) and 2(e) that the obvious electric dipole resonance occurs at the positions of the two formants supported by the helical rings. The electric field is mainly concentrated on the helical rings and the positive and negative charges are distributed on both sides of the x-direction. However, the direction of the surface current at the second resonant frequency is opposite to that at the first resonant frequency. Therefore, we selected the surface electric field and current distribution at the intermediate frequency of 2.5 THz to help the analysis as shown in Fig. 2(d). It can be seen that the distribution of positive and negative charge positions at 2.5 THz is opposite to that at 2.05 THz. The change of the positions of positive and negative charges in the resonator is the main reason for the change of the direction of the surface current. In addition, it can be seen from Fig. 2(f) that the distribution of positive and negative charges in the innermost turn at 3.155 THz has a slight counterclockwise shift compared with that at 3.08 THz. From this we can deduce that the positive and negative charges will migrate counterclockwise along the helix as the frequency increases in the whole broadband perfect absorption frequency range. The combination of multiple modes of electric dipole resonance ensures the broadband perfect absorption characteristics of the absorber.

Fig. 2. (a) Absorption, reflection and transmission spectra of wideband absorption when the Fermi level of graphene is 0.01 eV and the conductivity of VO₂ is 100000S/m. (b) Local enlargement of absorption spectrum (absorptivity greater than 90%). The electric field distributions of E_Z and the surface current distributions in the top view at frequencies of (c) 2.05 THz, (d) 2.5 THz, (e) 3.08 THz and (f) 3.155 THz.

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Impedance matching theory is used to further explain the physical mechanism of broadband absorption [59,60], which can be expressed as

(9)$$A(\omega )= 1 - R(\omega )= 1 - {\left|{\frac{{Z - {Z_0}}}{{Z + {Z_0}}}} \right|^2} = 1 - {\left|{\frac{{{Z_r} - 1}}{{{Z_r} + 1}}} \right|^2},$$

(10)$${Z_r} ={\pm} \sqrt {\frac{{{{({1 + {S_{11}}} )}^2} - S_{21}^2}}{{{{({1 - {S_{11}}} )}^2} - S_{21}^2}}} ,$$

where Z is the effective impedance of the absorber, Z₀ is the free space impedance, and Z_r= Z/Z₀ is the relative impedance between the absorber and free space. S₁₁and S₂₁ are reflection and transmission coefficients, respectively. As shown in Fig. 3, the real part of the relative impedance of the absorber is close to 1 and the imaginary part is close to 0 in the range 1.594 THz to 3.272 THz, which means the impedance of the absorber and free space are matched perfectly in this range.

Fig. 3. The real and imaginary parts of the relative impedance of the absorber when the conductivity of VO₂ is 100000 S/m and the Fermi level of graphene is 0.01 eV.

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The influences of the insulator-to-metal transition (IMT) property of VO₂ on broadband absorption are also discussed. Figure 4(a) shows that when the Fermi level of graphene is fixed at 0.01 eV and the conductivity of VO₂ is adjusted from 200000 S/m (metal phase) to 200 S/m (insulator phase), the absorber can gradually change from broadband perfect absorption to perfect reflection. In this regard, we selected the x-y plane electric field diagram when the conductivities are 200S/m, 2000S/m, 20000S/m and 200000S/m as shown in Figs. 4(b)–4(e). It can be seen that the electric field in the whole helical region is weak when the conductivity of VO₂ is 200 S/m and 2000 S/m.The strong electric field is concentrated at the tip of the innermost turn ofthe helix when the conductivity is increased to 20000 S/m, and there is a strong electric field in the whole helical region when the conductivity is set to 200000 S/m, which is consistent with the description in Fig. 4(a). In addition, the IMT property of VO₂ can be achieved by changing temperature [61,62]. According to the relationship between dielectric function and conductivity of materials [63], the functional relationship between the conductivity of VO₂ corresponding to different temperatures in the phase transformation process can be obtained as

(11)$$\sigma = i{\varepsilon _0}\omega ({{\varepsilon_c} - 1} ),$$

where ɛ₀ is the vacuum permittivity and ɛ_c is the temperature dependent permittivity.

Fig. 4. (a) The change in absorption when the Fermi level of graphene was set to a fixed value of 0.01 eV and the conductivity of VO₂ was adjusted from 200000 S/m to 200 S/m. The electric field distribution in the x-y plane when the conductivity of VO₂ is (b) 200 S/m, (c) 2000 S/m, (d) 20000 S/m, and (e) 200000 S/m. (f) The curve of the conductivity of VO₂ as a function of temperature. The phase transition temperature at heating (red curve) is about 5 K higher than that at cooling (blue curve). (g) The reflectivity comparison of the absorber when the Fermi level of graphene is 0.01 eV and the conductivity of VO₂ is 200 S/m and 200000 S/m, respectively. (h) Modulation depth (MD) and extinction ratio (ER) as a function of frequency.

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Figure 4(f) shows the curve of VO₂ changing with temperature, and the change process is reversible. Nevertheless, there is obvious thermal hysteresis effect in the curve, and there is a certain temperature difference ΔT between the heating curve and the cooling curve. This dynamically adjustable property of the absorber can be applied to modulation techniques, the modulation depth (MD) and extinction ratio (ER) are important indicators of a modulator [64,65], which can be expressed as

(12)$$MD = \frac{{{P_{\max }} - {P_{\min }}}}{{{P_{inc}}}} = {R_i} - {R_m},$$

(13)$$ER ={-} 10{\log _{10}}\frac{{{P_{\max }}}}{{{P_{\min }}}} ={-} 10{\log _{10}}\frac{{{R_i}}}{{{R_m}}},$$

where P_max is the maximum reflected power, P_min is the minimum reflected power, and P_inc is the incident power. R_i and R_m are the reflection of the modulator when VO₂ in the insulator phase and the metal phase, respectively. As shown in Fig. 4(g), the blue curve is the reflection of the modulator when VO₂ is the insulator phase, and the red curve is the reflection of the modulator when VO₂ is the metal phase. The modulation depth (MD) and extinction ratio (ER) of the absorber are shown in Fig. 4(h). The maximum modulation depth is 99.98% at 3.165 THz and the bandwidth with a modulation depth greater than 90% covers 1.71 THz from 1.57 THz to 3.28 THz. The minimum ER of the modulator is -36.5 dB, which meets some practical applications that only require the ER of the modulator to be less than -7 dB, and the bandwidth with extinction ratio less than -7 dB covers 1.82 THz from 1.49 THz to 3.31 THz.

Furthermore, the simulated absorption spectra of the absorber as a function of the Fermi energy are presented in Fig. 5(a), as the Fermi level of graphene changes from 0.01 eV to 0.7 eV, the absorber gradually evolves from broadband absorption to dual-band absorption. Formant λ₁ and λ₂ have blue shift as the Fermi energy level of graphene increases is shown in Fig. 5(b), and the maximum adjustment range of absorption of λ₁ and λ₂ ranges from 21.8%-67% and 24.8%-95.5%, respectively. In order to analyze the reasons for the formation of the two formants, the three-dimensional surface electric field diagram of the formants λ₁ and λ₂ were selected at the Fermi level of 0.6 eV. The electric field distribution of λ₁ is mainly concentrated on the four diagonals of the graphene layer, and is strongly confined to the interface between the graphene layer and topas layer, indicating that localized surface plasmon-polaritons (LSPP) and propagating surface plasmon-polaritons (PSPP) are excited simultaneously. The resonance principle of λ₂ is basically similar to that of λ₁, but it has more resonance regions than that of λ₁, which is also consistent with the fact that the absorption strength of λ₂ is higher than that of λ₁.

Fig. 5. (a) The spectral variation of the absorber when the conductivity of VO₂ is fixed at 100000 S/m and then the Fermi level of graphene is adjusted from 0.01 eV to 0.7 eV. (b) The migration of the absorption of formant λ₁ and λ₂ with the increase of Fermi level and the three-dimensional surface electric field distributions of the two formants.

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In addition, it is necessary to analyze the chiral characteristics of the designed absorber due to the asymmetry of the helical structure. Circular dichroism (CD) spectroscopy is a common method to characterize chirality by measuring the differential absorption of LCP light and RCP light. In this paper, the extinction cross-section of the structure was calculated to obtain the CD spectrum. The extinction cross-section excited by LCP and RCP is shown in Fig. 6(a), while the CD spectrum is defined as the difference between the extinction cross section excited by LCP and RCP, as shown in Fig. 6(b). Nevertheless, the extinction cross-section σ_ext is composed of two parts, the first is absorption cross section σ_abs and the second is scattering cross section σ_sc [66], which can be expressed as

(14)$${\sigma _{ext}} = {\sigma _{abs}} + {\sigma _{sc}} = \frac{1}{{{I_0}}}\int\!\!\!\int\!\!\!\int {QdV} + \frac{1}{{{I_0}}}\int\!\!\!\int {({\overrightarrow n \cdot \overrightarrow {{S_{sc}}} } )} dS,$$

where I₀ represents the incident light intensity, Q corresponds to the power loss density in the helical VO₂ molecule, $\vec{n}$ is the normal vector that points outwards from the helical VO₂, and ${\vec{S}_{sc}}$ corresponds to the scattering intensity (Poynting) vector. It can be seen from Fig. 6(b) that the excitation of the extinction cross section of the structure by LCP at low frequencies is slightly stronger than that of RCP, while the excitation of the extinction cross section of the structure by RCP at high frequencies is slightly stronger than that of LCP. In this regard, in order to understand the mechanism of interaction between this structure and two kinds of circularly polarized light, we selected the distribution of electric fields incident by LCP and RCP at frequencies 1.75 THz and 3 THz, as shown in Figs. 6(c)–6(f). From the Figs. 6(c) and 6(d), when the LCP light is incident at low frequency, the monopole resonance occurs at the tip of the first turn of the helix. The coupling effect is obvious in the outer three-turn helical resonator. However, when the RCP light is incident at low frequency, only the third and fourth turns of the helix have strong ring dipole resonance. Figures 6(e) and 6(f) show that when the LCP light is incident at high frequency, dipole resonance occurs between the first and second turns of the helix and the coupling effect is strong. Meanwhile, when the RCP light is incident at high frequency, the strong ring dipole resonance is trapped between the second turn and the third turn of the helix. In this regard, we believe that the difference of resonance mode caused by two different circularly polarized light at low frequency and high frequency is an essential reason for the CD value.

Fig. 6. (a) The extinction cross-section spectrum for LCP and RCP excitation. (b) The CD spectrum which defined as the difference of the extinction cross-section for LCP and RCP excitation. The electric field distributions at 1.75 THz excited by (c) LCP and (d) RCP light. The electric field distributions at 3 THz excited by (e) LCP and (f) RCP light.

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4. Conclusions

In conclusion, we present a high-performance broadband terahertz wave absorber platform with dynamically electrical and thermal tunable absorption due to the management on the resonant properties via the external surroundings. We then numerically demonstrate the realization of multifunctional manipulations on such absorber. A wide-frequency terahertz perfect absorber with the operation frequency ranges from 1.594 THz to 3.272 THz with absorption intensity over 90% is achieved. The spectral frequency bandwidth exceeding of 1.321 THz with the absorption over 99% is also obtained when the conductivity of VO₂ is set to 100000 S/m (metal phase) and the Fermi level of graphene is 0.01 eV. Moreover, the absorption can be artificially changed from 0 to 99.98% and in verse by adjusting the conductivity of VO₂. In addition, the spectral absorption is feasible to be changed from wideband absorption to dual-band absorption by adjusting the Fermi level of graphene. Besides, the analysis of the chiral characteristics of the helical structure suggests that the extinction cross-section has a circular dichroic response. During the study, the impedance matching theory is introduced to analyze and elucidate the wideband absorption rate. Our results may introduce approaches to manipulate the wide-band terahertz wave with multiple ways and pave the way towards the development of advanced technologies in the fields of switches, modulators, and imaging devices.

Funding

National Natural Science Foundation of China (11804134, 62065007, 62275112); Natural Science Foundation of Jiangxi Province (JXSQ2019201058).

Disclosures

The authors declare no conflicts of interest.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

References

1. N. Picqué and T. W. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13(3), 146–157 (2019). [CrossRef]

2. A. Ahmadivand, B. Gerislioglu, Z. Ramezani, A. Kaushik, P. Manickam, and S. A. Ghoreishi, “Functionalized terahertz plasmonic metasensors: Femtomolar-level detection of SARS-CoV-2 spike proteins,” Biosens. Bioelectron. 177, 112971 (2021). [CrossRef]

3. C. W. Berry, N. Wang, M. R. Hashemi, M. Unlu, and M. Jarrahi, “Significant performance enhancement in photoconductive terahertz optoelectronics by incorporating plasmonic contact electrodes,” Nat. Commun. 4(1), 1622 (2013). [CrossRef]

4. H. A. Hafez, S. Kovalev, J. C. Deinert, Z. Mics, B. Green, N. Awari, M. Chen, S. Germanskiy, U. Lehnert, J. Teichert, Z. Wang, K. J. Tielrooij, Z. Liu, Z. Chen, A. Narita, K. Mullen, M. Bonn, M. Gensch, and D. Turchinovich, “Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions,” Nature 561(7724), 507–511 (2018). [CrossRef]

5. X. Cai, A. B. Sushkov, R. J. Suess, M. M. Jadidi, G. S. Jenkins, L. O. Nyakiti, R. L. Myers-Ward, S. Li, J. Yan, D. K. Gaskill, T. E. Murphy, H. D. Drew, and M. S. Fuhrer, “Sensitive room-temperature terahertz detection via the photothermoelectric effect in graphene,” Nat. Nanotechnol. 9(10), 814–819 (2014). [CrossRef]

6. X. L. Zhang, X. B. Wang, and C. T. Chan, “Switching terahertz waves using exceptional points,” Phys. Rev. Appl. 10(3), 034045 (2018). [CrossRef]

7. R. Al Hadi, H. Sherry, J. Grzyb, Y. Zhao, W. Forster, H. M. Keller, A. Cathelin, A. Kaiser, and U. R. Pfeiffer, “A 1 k-Pixel video camera for 0.7–1.1 terahertz imaging applications in 65-nm CMOS,” IEEE J. Solid-State Circuits 47(12), 2999–3012 (2012). [CrossRef]

8. R. I. Stantchev, X. Yu, T. Blu, and E. Pickwell-MacPherson, “Real-time terahertz imaging with a single-pixel detector,” Nat. Commun. 11(1), 2535 (2020). [CrossRef]

9. C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014). [CrossRef]

10. T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10(6), 371–379 (2016). [CrossRef]

11. Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020). [CrossRef]

12. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef]

13. M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008). [CrossRef]

14. F. Yang, Z. L. Mei, and T. J. Cui, “Design and experiment of perfect relay lens based on the Schwarz-Christoffel mapping,” Appl. Phys. Lett. 104(7), 073510 (2014). [CrossRef]

15. X. Gao, X. Han, W.-P. Cao, H. O. Li, H. F. Ma, and T. J. Cui, “Ultrawideband and high-efficiency linear polarization converter based on double v-shaped metasurface,” IEEE Trans. Antennas Propag. 63(8), 3522–3530 (2015). [CrossRef]

16. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013). [CrossRef]

17. H. Li, C. Zheng, H. Xu, J. Li, C. Song, J. Li, L. Wu, F. Yang, Y. Zhang, W. Shi, and J. Yao, “Diatomic terahertz metasurfaces for arbitrary-to-circular polarization conversion,” Nanoscale 14(35), 12856–12865 (2022). [CrossRef]

18. R. Zhu, X. N. Liu, G. K. Hu, C. T. Sun, and G. L. Huang, “Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial,” Nat. Commun. 5(1), 5510 (2014). [CrossRef]

19. J. Li, J. Li, Z. Yue, C. Zheng, G. Wang, J. Liu, H. Xu, C. Song, F. Yang, H. Li, F. Li, T. Tang, Y. Zhang, Y. Zhang, and J. Yao, “Structured vector field manipulation of terahertz wave along the propagation direction based on dielectric metasurfaces,” Laser Photonics Rev. 2200325 (2022).

20. C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98–OP120 (2012). [CrossRef]

21. H. Li, G. Wei, H. Zhou, H. Xiao, M. Qin, S. Xia, and F. Wu, “Polarization-independent near-infrared superabsorption in transition metal dichalcogenide Huygens metasurfaces by degenerate critical coupling,” Phys. Rev. B 105(16), 165305 (2022). [CrossRef]

22. J. Yu, B. Ma, A. Ouyang, P. Ghosh, H. Luo, A. Pattanayak, S. Kaur, M. Qiu, P. Belov, and Q. Li, “Dielectric super-absorbing metasurfaces via PT symmetry breaking,” Optica 8(10), 1290–1295 (2021). [CrossRef]

23. F. S. Cuesta, A. D. Kuznetsov, G. A. Ptitcyn, X. Wang, and S. A. Tretyakov, “Coherent asymmetric absorbers,” Phys. Rev. Appl. 17(2), 024066 (2022). [CrossRef]

24. A. Novitsky, A. Paddubskaya, I. A. Otoo, M. Pekkarinen, Y. Svirko, and P. Kuzhir, “Random graphene metasurfaces: diffraction theory and giant broadband absorptivity,” Phys. Rev. Appl. 17(4), 044041 (2022). [CrossRef]

25. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef]

26. M. K. Hedayati, A. U. Zillohu, T. Strunskus, F. Faupel, and M. Elbahri, “Plasmonic tunable metamaterial absorber as ultraviolet protection film,” Appl. Phys. Lett. 104(4), 041103 (2014). [CrossRef]

27. M. ElKabbash, S. Iram, T. Letsou, M. Hinczewski, and G. Strangi, “Designer perfect light absorption using ultrathin lossless dielectrics on absorptive substrates,” Adv. Opt. Mater. 6(22), 1800672 (2018). [CrossRef]

28. H. Zhang, Z. Liu, G. Liu, X. Zhan, G. Fu, X. Liu, and J. Wang, “DVD assisted titanium metasurface for solar energy perfect absorption and potential applications for local thermal antibacterial treatment,” J. Phys. D: Appl. Phys. 54(11), 115106 (2021). [CrossRef]

29. X. Li, S. Tang, F. Ding, S. Zhong, Y. Yang, T. Jiang, and J. Zhou, “Switchable multifunctional terahertz metasurfaces employing vanadium dioxide,” Sci. Rep. 9(1), 5454 (2019). [CrossRef]

30. S. Qu and P. Sheng, “Microwave and acoustic absorption metamaterials,” Phys. Rev. Appl. 17(4), 047001 (2022). [CrossRef]

31. Y. J. Kim, J. S. Hwang, Y. J. Yoo, B. X. Khuyen, J. Y. Rhee, X. Chen, and Y. Lee, “Ultrathin microwave metamaterial absorber utilizing embedded resistors,” J. Phys. D: Appl. Phys. 50(40), 405110 (2017). [CrossRef]

32. A. H. Castro 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]

33. Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry's phase in graphene,” Nature 438(7065), 201–204 (2005). [CrossRef]

34. Z. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. An, Y. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015). [CrossRef]

35. Y. Kim, P. C. Wu, R. Sokhoyan, K. Mauser, R. Glaudell, G. Kafaie Shirmanesh, and H. A. Atwater, “Phase modulation with electrically tunable vanadium dioxide phase-change metasurfaces,” Nano Lett. 19(6), 3961–3968 (2019). [CrossRef]

36. Z. Song, A. Chen, and J. Zhang, “Terahertz switching between broadband absorption and narrowband absorption,” Opt. Express 28(2), 2037–2044 (2020). [CrossRef]

37. M. Zhang and Z. Song, “Switchable terahertz metamaterial absorber with broadband absorption and multiband absorption,” Opt. Express 29(14), 21551–21561 (2021). [CrossRef]

38. W. Liu and Z. Song, “Terahertz absorption modulator with largely tunable bandwidth and intensity,” Carbon 174, 617–624 (2021). [CrossRef]

39. N. Yi, R. Zong, J. Gong, and R. Qian, “Dynamically tunable broadband absorber with a single ultra-thin layer of graphene in the terahertz regime,” Mater. Sci. Semicond. Process. 136, 106161 (2021). [CrossRef]

40. G. Wu, X. Jiao, Y. Wang, Z. Zhao, Y. Wang, and J. Liu, “Ultra-wideband tunable metamaterial perfect absorber based on vanadium dioxide,” Opt. Express 29(2), 2703–2711 (2021). [CrossRef]

41. H. Feng, Z. Xu, K. Li, M. Wang, W. Xie, Q. Luo, B. Chen, W. Kong, and M. Yun, “Tunable polarization-independent and angle-insensitive broadband terahertz absorber with graphene metamaterials,” Opt. Express 29(5), 7158–7167 (2021). [CrossRef]

42. Y. Liu, R. Huang, and Z. Ouyang, “Terahertz absorber with dynamically switchable dual-broadband based on a hybrid metamaterial with vanadium dioxide and graphene,” Opt. Express 29(13), 20839–20850 (2021). [CrossRef]

43. J. Xu, Z. Qin, M. Chen, Y. Cheng, H. Liu, R. Xu, C. Teng, S. Deng, H. Deng, H. Yang, S. Qu, and L. Yuan, “Broadband tunable perfect absorber with high absorptivity based on double layer graphene,” Opt. Mater. Express 11(10), 3398–3410 (2021). [CrossRef]

44. N. Mou, B. Tang, J. Li, H. Dong, and L. Zhang, “Switchable ultra-broadband terahertz wave absorption with VO₂-based metasurface,” Sci. Rep. 12(1), 2501 (2022). [CrossRef]

45. Z. Xu and Z. Song, “VO₂-based switchable metasurface with broadband photonic spin hall effect and absorption,” IEEE Photonics J. 13(4), 4600305 (2021). [CrossRef]

46. W. Liu, J. Xu, and Z. Song, “Bifunctional terahertz modulator for beam steering and broadband absorption based on a hybrid structure of graphene and vanadium dioxide,” Opt. Express 29(15), 23331–23340 (2021). [CrossRef]

47. J. Li, Y. Yang, J. Li, Y. Zhang, Z. Zhang, H. Zhao, F. Li, T. Tang, H. Dai, and J. Yao, “All-optical switchable vanadium dioxide integrated coding metasurfaces for wavefront and polarization manipulation of terahertz beams,” Adv. Theory Simul. 3(1), 1900183 (2020). [CrossRef]

48. H. Liu, Z. H. Wang, L. Li, Y. X. Fan, and Z. Y. Tao, “Vanadium dioxide-assisted broadband tunable terahertz metamaterial absorber,” Sci. Rep. 9(1), 5751 (2019). [CrossRef]

49. S. Wang, L. Kang, and D. H. Werner, “Hybrid resonators and highly tunable terahertz metamaterials enabled by vanadium dioxide (VO₂),” Sci. Rep. 7(1), 4326 (2017). [CrossRef]

50. N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009). [CrossRef]

51. Y. Ren, T. Zhou, C. Jiang, and B. Tang, “Thermally switching between perfect absorber and asymmetric transmission in vanadium dioxide-assisted metamaterials,” Opt. Express 29(5), 7666–7679 (2021). [CrossRef]

52. J. Horng, C.-F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B 83(16), 165113 (2011). [CrossRef]

53. 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]

54. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011). [CrossRef]

55. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). [CrossRef]

56. H. Li, J. Li, C. Zheng, H. Xu, F. Yang, J. Li, Z. Yue, W. Shi, Y. Zhang, and J. Yao, “Dual-band giant spin-selective full-dimensional manipulation of graphene-based chiral meta-mirrors for terahertz waves,” Opt. Express 30(12), 22292–22305 (2022). [CrossRef]

57. M. S. Islam, J. Sultana, M. Biabanifard, Z. Vafapour, M. J. Nine, A. Dinovitser, C. M. B. Cordeiro, B. W. H. Ng, and D. Abbott, “Tunable localized surface plasmon graphene metasurface for multiband superabsorption and terahertz sensing,” Carbon 158, 559–567 (2020). [CrossRef]

58. F. Ding, S. Zhong, and S. I. Bozhevolnyi, “Vanadium dioxide integrated metasurfaces with switchable functionalities at terahertz frequencies,” Adv. Opt. Mater. 6(9), 1701204 (2018). [CrossRef]

59. F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016). [CrossRef]

60. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005). [CrossRef]

61. M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012). [CrossRef]

62. J. Ordonez-Miranda, Y. Ezzahri, K. Joulain, J. Drevillon, and J. J. Alvarado-Gil, “Modeling of the electrical conductivity, thermal conductivity, and specific heat capacity of VO₂,” Phys. Rev. B 98(7), 075144 (2018). [CrossRef]

63. M. Walther, D. G. Cooke, C. Sherstan, M. Hajar, M. R. Freeman, and F. A. Hegmann, “Terahertz conductivity of thin gold films at the metal-insulator percolation transition,” Phys. Rev. B 76(12), 125408 (2007). [CrossRef]

64. S. G. Carrillo, G. R. Nash, H. Hayat, M. J. Cryan, M. Klemm, H. Bhaskaran, and C. D. Wright, “Design of practicable phase-change metadevices for near-infrared absorber and modulator applications,” Opt. Express 24(12), 13563–13573 (2016). [CrossRef]

65. C. Li, W. Zhu, Z. Liu, S. Yan, R. Pan, S. Du, J. Li, and C. Gu, “Tunable near-infrared perfect absorber based on the hybridization of phase-change material and nanocross-shaped resonators,” Appl. Phys. Lett. 113(23), 231103 (2018). [CrossRef]

66. J. Ren, W. Qiu, H. Chen, P. Qiu, Z. Lin, J. X. Wang, Q. Kan, and J. Q. Pan, “Electromagnetic field coupling characteristics in graphene plasmonic oligomers: from isolated to collective modes,” Phys. Chem. Chem. Phys. 19(22), 14671–14679 (2017). [CrossRef]

Ref.	Bandwidth (>90%)	Bandwidth (>99%)	Tunable Range	Modulation Depth
[38]	0.94 THz	0	14.2%-96.3%	82.1%
[39]	1.74 THz	About 0.5 THz	11%-100%	89%
[40]	3.3 THz	About 0.02 THz	4%-100%	96%
[41]	0.76 THz	0.45 THz	1%-99%	98%
[42]	1.3 THz	0.55 THz	5.2%-99.8%	94.6%
[43]	1.96 THz	1.16 THz	52%-100%	48%
[44]	0.985 THz	About 0.02 THz	7%-100%	93%
[45]	1.4 THz	About 0.02 THz	11%-100%	89%
[46]	0.83 THz	About 0.45 THz	7%-90%	83%
This paper	1.678 THz	1.321 THz	0-99.98%	99.98%

Dynamically electrical/thermal-tunable perfect absorber for a high-performance terahertz modulation

Abstract

1. Introduction

2. Design and method

3. Results and discussion

4. Conclusions

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (6)

Tables (1)

Equations (14)

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