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Abstract
This paper proposes a vanadium dioxide metamaterial-based tunable, polarization-independent coherent perfect absorber (CPA) in the terahertz frequency range. The designed CPA demonstrates intelligent reconfigurable switch modulation from an ultra-broadband absorber mode to a dual-band absorber mode via the thermally controlled of VO2. The mode of ultra-broadband absorber is realized when the conductivity of VO2 reaches 11850 S/m via controlling its temperature around T = 328 K. In this mode, the CPA demonstrates more than 90% absorption efficiency within the ultra-wide frequency band that extends from 0.1 THz to 10.8 THz. As the conductivity of VO2 reaches 2×105 S/m (T = 340 K), the CPA switches to a dual-band absorber mode where a relatively high absorption efficiency of 98% and 99.7% is detected at frequencies of 4.5 THz and 9.8 THz, respectively. Additionally, using phase modulation of the incident light, the proposed CPA can regulate the absorption efficiency, which can be intelligently controlled from perfect absorption to high pass-through transmission. Owing to the ability of the proposed CPA to intelligently control the performance of light, this study can contribute towards enhancing the performance of stealth devices, all-optical switches and coherent photodetectors.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials, which artificial materials consisting of periodically arranged micro-nanoscale structures, have demonstrated extraordinary electromagnetic properties and have been applied in various promising applications, such as those requiring negative refractive index [1,2], phase modulation [3–5], amplitude modulation [6–9], and plasmonic waveguides [10,11]. Among these applications, absorbers have attracted extensive attention because of their significant performance in optical cloaking [12,13], optical switches [14], and optical sensing [15,16]. In 2008, Landy et al. proposed the first metamaterial absorber (MMA) and reported its perfect absorption characteristics, which were validated both theoretically and experimentally [17]. In terms of absorber applications for different frequencies, various types of metamaterial absorbers have been proposed and designed over a wide frequency band, in which includes the microwave [18], terahertz (THz) [19], infrared [20], visible [21] and ultraviolet (UV) ranges [22]. The narrowband absorbers, including single-band, dual-band and multi-band absorbers, in the THz range, have been reported either through theoretical or experimental validation with different applications [23–29]. However, all of them are limited by the narrow absorption bandwidth in practical applications, such as solar energy equipment, optoelectronic devices, and bolometers. Then, the broadband absorbers by integrating multiple resonant structures within one unit cell or the stacking of multilayer structures have been proposed to overcome such limitations [30–33]. The broadband absorbers can extend the working frequency band; however, they are not capable of post-tuning after fabrication, which limits their applications when intelligent control capabilities are required.
Active controlled materials are commonly used to achieve intelligent tunable MMA and have been validated for their ability in tunable absorber applications. These tunable absorbers can be classified into different categories based on tunable materials, such as graphene-based [34,35], liquid metal-based [36], liquid crystal-based [37], and vanadium dioxide (VO2)-based absorbers [38,39]. Vanadium dioxide (VO2) is a type of phase transition metal oxide that has the unique optical property of insulator-metal transition over a broad spectral range via temperature [40,41], light [42,43], or electric field [44,45] modulation. Owing to this unique optical property, VO2 has attracted increasing attention in the design and fabrication of metamaterial-based absorbers for terahertz and infrared frequencies [46–48].
The coherent perfect absorber (CPA), a new type of tunable MMA based on critical coupling, has been widely studied and reported for its characteristic of all-optical modulation [49,50]. Given the interference of the two incident beams and the relative phase change, CPA shows different modulations with absorption efficiency ranging from approximately 0% to 100%. The theoretical explanation and experimental validation of the first CPA [51] have promoted the practical application of CPA with different materials and structures in different fields, such as those involving nanoscale light manipulations, sensors, and data processing [52–54].
In this study, we designed a polarization-independent, tunable CPA based on a vanadium dioxide metamaterial for terahertz frequencies. Theoretical analysis and simulation results show that the designed CPA has reconfigurable switch modulation to operate in the ultra-broadband absorption mode and dual-band absorption mode by temperature modulation. In the ultra-broadband absorber mode, the absorption efficiency of CPA can reach 90% and more in a wide frequency range extending from 0.1 THz to 10.8 THz. In the dual-band absorber mode, two absorption vertexes at 4.5 THz and 9.8 THz are observed with absorption efficiency of 98% and 99.7%. In addition, with the phase modulation of incident light, the absorption performance can be controlled from near-perfect absorption to high pass-through transmission. These optical performances can enable the future study of perfect absorbers and their potential applications in integrated optics such as all-optical switches and coherent photodetectors.
2. Architecture of coherent perfect absorber and theoretical analysis
The designed CPA, which is shown in Fig. 1(a), consists of three layers. The top layer is a transparent dielectric layer, VO2 based metamaterial is the middle layer, and the transparent dielectric substrate at the bottom is the same as the top layer. The thicknesses of the VO2 layer and transparent medium are h1 = 1.8 µm and h2 = 2 µm, respectively. An array of units with quad elliptical holes in the middle layer and quad VO2 cylinders deposited in the top and bottom layers is shown in Fig. 1(b). The period of the structural unit is P = 25 µm. The semi-major and semi-minor axes of the ellipse are a = 5 µm and b = 2 µm, respectively. The height and radius of the cylinder are h3 = 7 µm and r = 1 µm, respectively. The distance between the cylinder and unit centers is d = 4 µm.
Fig. 1. (a) The schematic of the proposed tunable dual-band and ultra-broadband CPA. (b) The surface of VO2 layer in the unit cell.
Light beams I1 and I2 are incident on the CPA either from the top or bottom layer, with outputs of O1 and O2, respectively. The transmission and reflection between the input and output beams can be demonstrated by the scattering matrix [55]:
Here, r1, r2, t1, and t2 are the reflection and transmission coefficients of each side, respectively. Owing to the symmetric environment (structure and material), the reflection and transmission coefficients in both the upper and lower directions are the same: r1 = r2 = r, t1 = t2 = t. With the assumption that r = −0.5, t = 0.5, and the wave function of the incident waves I1 = αI2exp(iβ+ikz) with z = 0, the coherent absorption Aco is expressed as [55]:
3. Results and discussion
The characteristics of the designed CPA were numerically simulated using the commercial software COMSOL Multiphysics, which is based on the finite element method (FEM) [56–59]. In the simulation, periodic boundary conditions are applied along the x and y directions, and perfectly matched layer is applied along the z-direction including both the top and bottom of the proposed device. And two ports are applied along the z-direction to input plane wave. In addition, the transmission, reflection and absorption of the CPA can be calculated by the S-parameters, which obtained from the ports. The relative permittivity of the transparent dielectric was set as εr = 2.1 with negligible loss in the terahertz range. The relative permittivity of VO2 in the terahertz range can be expressed using the Drude model [60]:
Figure 2(a) shows the absorption spectra of the designed CPA with different conductivity of VO2. It can be found as the conductivity of VO2 is σ = 11850 S/m, the designed CPA can achieve ultra-wide absorption which covers all the THz range (corresponds to the ultra-broadband absorber mode). As the conductivity of VO2 is σ = 2×105 S/m, the designed CPA can achieve near-perfect double narrowbands absorption (corresponds to the dual-band absorber mode). To further analyze the performance of these two absorbers modes, Fig. 2(b) shows the absorption and output spectra of the designed CPA as a function of frequency with the conductivity of VO2 is σ = 11850 S/m and σ = 2×105 S/m. It can be clearly seen that the designed CPA functions as an ultra-broadband absorber when the conductivity of VO2 is 11850 S/m, and an absorption of more than 90% is obtained in the frequency range from 0.1 THz to 10.8 THz (blue solid line). Based on this performance, the proposed CPA can have stealth applications at terahertz frequencies, which can prevent aircraft, missiles, and satellites from being detected by a THz radar. For the dual-band CPA, two perfect absorption peaks appear at p1 = 4.5 THz and p2 = 9.8 THz when the conductivity of VO2 is 2×105 S/m. The absorption efficiency can go up to 98% and 99.7%, respectively (red solid line). Thus, near-perfect ultra-broadband and dual-band absorbers can be successfully obtained in metamaterials by temperature modulation and have great application prospects in stealth technology, modulators, and optical switches.
Fig. 2. (a) The absorption spectra of the CPA with different conductivity of VO2. (b) The absorption (A) and output (O1, O2) of dual-band CPA with the conductivity of VO2 σ= 2×105 S/m and ultra-broadband CPA with the conductivity of VO2 σ = 11850 S/m.
To better understand the physical mechanism of the designed CPA, we analyzed the electric-field distributions over the metamaterial structure of the proposed CPA. Figure 3(a) and 3(b) show the normalized electric field amplitude distribution of the metamaterial structure as a dual-band absorber at p1 = 4.5 THz and p2 = 9.8 THz where the electric field is concentrated at the corners and edges of the ellipse. For the corresponding z-component of the electric field (EZ) distributions in Fig. 3(e) and 3(f), we can see that the opposite charges gather at the corners and edges of the ellipse along the y direction. Based on the results shown in Fig. 3(a), 3(b), 3(e), and 3(f), the typical electric dipole resonance occurs at p1 and p2 [62,63]. For the ultra-broadband CPA, the distributions of the normalized electric field amplitude |E| at p3 and p4 and z-component of the electric field (EZ) at p3 and p4 are shown in Fig. 3(c), 3(d), 3(g), and 3(h), respectively. At p3, the electric field is concentrated at the corners and edges of the ellipse along the y-direction, and so also the opposite charges [Fig. 3(c) and Fig. 3(g)]. In contrast to the electric field distribution at p3, the electric field and opposite charges at p4 are mainly concentrated at the edge of the ellipse [Fig. 3(d)], whereas the weak charges accumulate at the bottom of the cylinder. Compared with the enhanced electric field at the edges of the ellipse, the electric field at the cylinder is too weak to have a significant effect on the electrical dipole resonance and absorption of the CPA at different frequencies. Therefore, the cylinder has no significant effect on the resonance, and broadband absorption is caused by the electric dipole resonance.
Fig. 3. The electric field distribution of the dual-band CPA at p1 = 4.5 THz (a) and p2 = 9.8 THz (b) and ultra-broadband CPA at p3 = 2.8 THz (c) and p4 = 8 THz (d). The EZ field distribution of the dual-band CPA at p1 = 4.5 THz (e) and p2 = 9.8 THz (f) and ultra-broadband CPA at p3 = 2.8 THz (g) and p4 = 8 THz (h).
To further analyze the effect of the cylinder, we simulated the performance of the designed metamaterial structure without the quad VO2 cylinders and the results for different states of VO2 are shown in Fig. 4. For the metallic state of VO2, the CPA shows dual-band absorption with two absorption peaks located at p1 = 5.6 THz and p2 = 11.9 THz. The corresponding distributions of the normalized electric field |E| and z-component EZ at p1 and p2 are shown in Fig. 4(c), 4(e), 4(d), and 4(f). Comparing Fig. 3(a), 3(e), and Fig. 4(c) and 4(e), it can be observed that the electric field distributions at p1 in these two structures are similar, and both correspond to the typical dipole resonance. However, there is a distinct difference at p2 in Fig. 2 and 4(a); the bandwidth at p2 in Fig. 4(a) is narrower than that in Fig. 2, which is due to the higher-order resonance mode. From the distributions of the electric field amplitude |E| and z-component EZ at p2 as shown in Fig. 4(d) and 4(f), we can see that the opposite charges not only gather at the corners of the quad ellipse but also at the tail of the ellipse along y direction, which corresponds to multipole resonance [64]. Thus, the quad-cylinder has nearly no effect on the absorption peak p1 but has a significant effect on the absorption peak p2 by inducing a change in the charge distribution and higher-order resonance mode. Figure 4(b) and 4(g)–4(j) show the plots of absorption of CPA and the corresponding |E| and EZ of CPA, where the array units have no quad-cylinder functions as an ultra-wide band absorber when VO2 is in its insulating state. Comparing with Fig. 3, it can be concluded that the quad-cylinder has less of an effect on the resonance of the broadband CPA.
Fig. 4. (a) The absorption of dual-band CPA with no cylinder structure. (b) The absorption of ultra-broadband CPA with no cylinder structure. The |E| and EZ field distribution of the dual-band CPA at p1 = 5.6 THz (c), (e) and p2 = 11.9 THz (d), (f) and ultra-broadband CPA at p3 = 3 THz (g), (i) and p4 = 8.6 THz (h), (j) with no cylinder structure, respectively.
4. Effect of geometry on the absorption performance of CPA
Additionally, we analyzed the influence of different geometric parameters on the absorption spectra of the designed CPA. The simulation results, shown in Figs. 5(a), 5(b), 5(e), 5(f) and 5(g), demonstrate the absorption of dual-band CPA as a function of h1, h2, a, b and h3. Figure 5(a) shows that the effect of the thickness h1 on the two absorption peaks is not significant. This is because that the dimensions of the ellipse remain unchanged, the dipole resonances induced by structure not greatly affected under the change of h1. Figure 5(b) shows that the two absorption peaks exhibit a redshift with the increase in the thickness h2 of the transparent dielectric. The absorption peak at high frequency becomes lower, and its bandwidth becomes wider when h2 is greater than 3 µm. The physical reason for this can be explained by the following equation [65]:
where f, φp and c are the resonance frequency, propagation phase, and speed of light in free space, respectively. In our simulation, εr = 2.1 and the incident angle θ = 0◦ are fixed values, and φp is also considered to be a fixed value because the incident wave is a plane wave. Thus, an increase in the thickness h2 of the transparent dielectric results in a redshift of the resonance peaks. As shown in Fig. 5(e), when the semi-major axis of ellipse a is increased, the two absorption peaks also show a redshift, and the absorption peak at low frequency becomes higher with an increase in the semi-major axis a. In contrast, the two absorption peaks show a blueshift with the increase in the semi-minor axis of ellipse b, the results are shown in Fig. 5(f). The parameters of the ellipse have a significant influence on the resonance, which is attributed to the concentration of the electric field in the ellipse. The effective impedance Z of the absorber is determined by its effective permittivity ε(ω) and permeability µ(ω). Different resonance modes or charge distributions lead to variations in the permeability µ(ω). According to the equations Z = $\sqrt {\mu (\omega )/\varepsilon (\omega )} $ [66] and Zr = Z/Z0, the excellent impedance matching between the absorber and free space is destroyed, which results in a different absorption spectrum. We also investigated the relationship between cylinder height h3 and the absorption of the dual-band CPA, and the results are shown in Fig. 5(g), demonstrating that the two absorption peaks redshift with the increase in cylinder height h3. It is noted that the absorption peak at high frequency exhibits a nonlinear decrease with an increase in h3. Specifically, when h3 increased from 4 µm to 6 µm, the absorption peak decreased significantly owing to the change in the charge distribution and transition of the resonance mode. Correspondingly, Fig. 5(c), 5(d), 5(h), 5(i) and 5(j) show the influence of different geometric parameters on the broadband CPA. The above results show that the selected geometric parameters influence the performance of both dual-band and ultra-broadband CPAs. By changing the geometric parameters of the structure, the dual-band and ultra-broadband CPAs can actively satisfy the performance specifications of the user.Fig. 5. Effect of geometry on absorption performance: dual-band CPA: (a) h1, (b) h2, (e) a, (f) b and (g) h3, ultra-broadband CPA: (c) h1, (d) h2, (h) a, (i) b and (j) h3.
5. All-optical modulation of CPA
To investigate the all-optical modulation characteristics of the proposed CPA, we discuss the influence of the phase difference between two counter-propagating incident beams on coherent absorption. In the dual-band absorber mode, the coherent absorption as a function of the phase difference at p1 = 4.5 THz and p2 = 9.8 THz are shown as solid, blue and red lines in Fig. 6(a), respectively. The results show that the absorption efficiency changed from 10% to 98% and from 14% to 99.7% as the phase difference varied from π to 0. Similarly, as shown in Fig. 6(b), in the ultra-broadband absorber mode, the ultra-broadband absorption can be changed from less than 10% to greater than 90% by changing the phase difference. The results in Fig. 6(a) and 6(b) imply that our proposed CPA has a higher absorption reconfigurability which was achieved by modulating the phase difference between the incident beams. With this characteristic, the designed CPA can be applied to all-optical switches and phase detectors. Usually, the performance of optical switch can be described by the modulation depth (MD), which is expressed as: MD = (Amax-Amin)/Amax [67]. Where Amax and Amin are the maximum and minimum of absorption from phase modulation. For the all-optical switch in dual-band mode, the MD at 4.5 THz and 9.8 THz are 89.7% and 85.9%, respectively. And for the all-optical switch in ultra-broadband mode, the MD in the THz range can reach up to 99.8%. Therefore, this work is of great significance to the development of all-optical switches.
Fig. 6. (a) The absorption of dual-band CPA with the phase difference between two incident beams at 4.5 THz and 9.8 THz. (b) The color map of absorption spectra of ultra-broadband CPA with the phase difference between two incident beams.
Next, we plot the functional relation between the absorption and polarization angle in Fig. 7(a) and 7(b). The simulation results indicate that the performance of the designed CPA is independent of the polarization angle of the incident wave, which benefits from the rotational symmetry of the metamaterial structure. We also study the influences of different incident angles on the absorption performance. Figure 8(a) and 8(b) show the dual-band and ultra-broadband absorption spectra as a function of the incidence angle. It is obvious that the absorption of both modes maintain well until the incident angle increases to 15°, which means the resonance is insensitive to small incident angle. The splitting of the absorption spectra, which is similar to Rabi splitting for the case of many atoms in an optical cavity [29,68,69], shows a clearly red shift with the increase of the incident angle.
Fig. 7. The absorption spectra of (a) dual-band and (b) ultra-broadband CPA for different polarization angles.
Fig. 8. The absorption spectra of (a) dual-band and (b) ultra-broadband CPA for different incident angles.
Finally, the performance parameters of the designed CPA, namely bandwidth, absorptance, tuning method, and tuning range are summarized in Table 1, and compared with the results of latest reported works. The comparison shows that the performance of the proposed broadband CPA is better than that of the others in the wider THz and wider tuning ranges.
Table 1. Comparison of broadband absorption between our work and previous reports
6. Conclusion
In conclusion, a polarization-independent CPA based on a vanadium dioxide metamaterial is proposed for applications in the THz range. From the full-wave FEM simulation, it can be seen that the proposed CPA can be switched from the ultra-broadband absorber mode to the dual-band absorber mode with different conductivity of VO2 controlled by temperature. For the ultra-broadband CPA, the absorption bandwidth covers almost the entire THz range from 0.1 THz to 10.8 THz with absorption efficiency exceeding 90%. For the dual-band CPA, the two absorption peaks appear at 4.5 THz and 9.8 THz and the corresponding absorptance are 98% and 99.7%, respectively. With centrosymmetric nanostructures, the proposed CPA exhibited polarization-independent properties. Additionally, the absorption efficiency of the designed CPA can be dynamically tuned by controlling the phase difference between the two incident beams. Therefore, our CPA has potential for application in stealth technology, all-optical switches, and coherent photodetectors.
Funding
National Natural Science Foundation of China (11144007, 11274188, 51472174); Natural Science Foundation of Shandong Province (ZR2017MF059); Optoelectronics Think Tank Foundation of Qingdao (501100013144).
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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