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Abstract
We experimentally demonstrate polarization-controlled multifrequency coherent perfect absorption in stereometamaterials with twisted asymmetrically split rings. The coupling effects in stereometamaterials lead to the mode hybridization and thus multiple electric and magnetic resonances. The coherent perfect absorptions of electric and magnetic modes in stereometamaterials have been verified to be individually switched on/off by an interferometric effect of two counter-propagating coherent beams. The alternation of two orthogonal polarization states enables direct modulation of the operation frequencies of coherent perfect absorptions in both microwave and optical metamaterials. The work provides an opportunity to manipulate coherent perfect absorption and is helpful to design tunable multifrequency absorbers.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials are artificial electromagnetic media with spatially well-designed meta-molecules on the sub-wavelength scale. They exhibit attractive electromagnetic properties, such as super-resolution imaging [1], invisibility [2], perfect absorption [3], polarization manipulation [4], and lateral gradient phase [5]. As a promising application, metamaterial absorbers have been widely studied due to incomparable advantages to naturally existing materials. A number of absorbers have been demonstrated in microwave, THz and optical ranges [3,6–8]. Although metamaterial absorbers have been well developed, it’s not easy to flexibly control absorption in metamaterials and obtain tunable absorbers. At present, tunable metamaterial absorbers can be restrictedly accomplished by incorporation of active materials or elements such as vanadium dioxide [9], varactor diodes [10], liquid crystal [11] and graphene [12], however, another alternative scheme deserves to be explored for achieving a large modulation depth and spectral shift.
Coherent perfect absorption (CPA) is regarded as the time-reversed counterpart of laser emission and can be achieved via interferometric control of two or even more input waves incident upon two opposite sides of a slab [13,14]. The CPA was initially investigated in thick silicon slabs instead of gain media to obtain optically modulated absorption by varying the relative phase of the incident fields [13,14]. Compared to single beam illumination, the interference effect selectively allows complete and null absorption that refer to CPA and coherent perfect transparency (CPT). Following the pioneering work [13], the CPA has been received much attention in other thin materials and structures such as highly doped silicon slab [15], graphene [16–18], coupled resonators [19] and particularly metamaterials [20–43]. An ultrathin slot metamaterial has been experimentally demonstrated to exhibit CPA phenomenon [27], in which the perfect absorption occurs when all outgoing beams away from it completely vanish due to destructive interference. The flexible designs of metamaterials enrich and extend the scope of the CPA. On the one hand, many efforts have been devoted to the fundamental principles and related properties of CPAs in a variety of metamaterials from epsilon-near-zero [21], Fano or EIT-type [22–24], phase gradient [25–29], chiral [30], dielectric [31], anisotropic metamaterials [32] to PT-symmetric structures [33] and quantum regime [34,35]. On the other hand, beyond absorption, the coherent concept has been applied to achieve other important optical effects ranging from polarization effect [36], generalized Snell's refraction and reflection [25], coherent data processing [37], mode recognition [38], two-dimensional coherent control [39] and high-order mode excitation [24]. The CPA will be predicted to have potential applications in excitation of surface plasmons [40], perfect absorbers [13], CPA-lasers [33], all-optical coherent devices [41], coherent data processing [42] and coherent spectroscopy [43,44]. Further, we expect the incident polarization state will offer another route to design CPAs in metamaterials and manipulate their properties.
In this work, we have experimentally demonstrated polarization-controlled multifrequency CPAs in stereometamaterials with stacked twisted asymmetrically split rings (ASR). The subtle coupling effects in bilayered ASRs cause abundant electromagnetic responses that strongly depend on incident polarization states. The absorption at each resonance can be coherently modulated by interferometric effect of two counter-propagating coherent beams. The tunability of the operation frequencies of the CPAs has been accomplished by changing the polarization state of incident waves. The scheme of multiple CPAs can work in the optical frequency by scaling down the size of the ASR dimer, provided that appropriate nanostructures are designed and available materials are also considered. The polarization state offers a freedom to design coherent perfect absorbers and the proposed scheme is beneficial to realize tunable polarization-dependent multifrequency absorbers.
2. Design of stereometamterials and absorption
The electromagnetic responses of metamaterials are governed by their structural designs and spatial arrangements. In stereometamaterials the structural designs are identical in the ensemble, the involved coupling effects vary with spatial arrangements such as twist angle, therefore metamaterials will exhibit various electromagnetic responses. Here we investigate stereometamaterials consisting of an array of stacked asymmetrically split rings (ASR) dimers with different twist angles of θ = 0° and 180° around the z-axis in Fig. 1. In one square dimer with a size of d = 15 mm, two twist copper ASRs are separated by a 1.6mm-thick FR4 dielectric layer with a permittivity ε = 4.05-i0.05. Each ASR is constructed by two unequal wire arcs corresponding to different angles α = 160° and β = 140° in Fig. 1(b). The inner radius of the ASR is r = 5.6 mm and the metal line width is w = 0.8 mm. Based on full-wave simulations using a three-dimensional Maxwell finite element method solver (COMSOL Multiphysics), we firstly investigate polarization-dependent absorption of single layer ASR metamaterial in Fig. 1(c). In all the simulations, 35μm-thick copper layer of commercial FR4 PCB was simulated as a perfect electric conductor. Absorption of single layer anisotropic metamaterial depends strongly on the polarization state of incident electromagnetic waves. Fano resonance is allowed for x-polarized wave and strong antiparallel currents excitation along symmetry-broken ASRs leads to large absorption up to 50% at about 5.6GHz. For y-polarized wave, Fano resonance disappears, while at high frequencies there are two pronounced absorption peaks corresponding to a bright dipolar-like mode and a dark quadrupole-like mode, which is verified by excited surface current modes in the insets in Fig. 1(c).
Fig. 1 Schematic of coherent interaction of light with ASR stereometamaterials and absorption in the single layer ASR. (a) Schematic of coherent interaction of stereometamaterials. The insets indicate two types of stereometamaterials with twist angles of θ = 0° and θ = 180° as well as the fabricated sample picture. (b) The structure design of the ASR. The geometry parameters are d = 15 mm, w = 0.8 mm, and r = 5.6 mm, t = 1.6 mm, α = 140°, β = 160°. (c) Simulated absorption spectra of the single layer ASR metamaterial. The black solid and red dotted lines correspond to absorption for incident x- and y-polarized waves, respectively. The insets show resonant surface current modes at the frequencies marked by black arrows.
In the stereometamaterials, symmetric and antisymmetric excitations of two stacked ASRs leads to the mode hybridization, thus multiple resonant absorption peaks occurs for single x- and y-polarized beam illumination as the simulated and measured results are shown in Fig. 2. Although the meta-molecules in each layer are structurally identical, the twist angles can tailor the near-field coupling between two adjacent metallic arcs and therefore two stereometamaterials exhibit distinct absorption spectra from each other. Obviously, both stereometamateirals with θ = 0° and 180° exhibit polarization-dependent absorption. Multiple peaks with 50% absorption occur in the low frequency range from 4 to 6 GHz for x-polarized wave, while strong absorption peaks of y-polarized wave are observed in the high frequency range from 9 to 11 GHz. The phenomenon can be easily understood according to the polarization-sensitive resonant modes in the single ASR metamaterial in Fig. 1(c). Due to the coupling effect between two layers and mode overlap, there are absorptions larger than 50% at some frequencies. In order to verify the simulated results, two stereometamateirals samples with θ = 0° and 180° were fabricated with an overall size of 300 × 300 mm2 using photolithography techniques illustrated in Fig. 1. The experiments were carried out in an anechoic chamber using two broadband horn antennas (SCHWARZBECK BBHA9120D) and a vector network analyzer (Anritsu MS4644A). The measured absorption spectra agree well with the simulated ones in the considered frequency range. The polarization-sensitive multiband half absorption properties of the stereometamaterials provide an essential prerequisite to realize polarization-controlled multifrequency CPAs, in which they may reveal completely annihilated outgoing waves [16, 20, 33, 34].
Fig. 2 Simulated and experimental absorption spectra of two stereometamaterials with twist angles of (a) θ = 0° and (b) θ = 180° for single beam illumination. The black solid and red dotted lines correspond to the simulated results for x- and y-polarized incident waves. The green asteroid and blue triangle marks correspond to the measured results for x- and y-polarized incident waves. The insets illustrate the structural unit cells of two stereometamaterials.
3. Coherent absorption of stereometamaterials
The realization of CPA-type metamaterials can be accomplished by their interaction with a standing wave formed by two counter-propagating coherent beams with equal intensity and the same polarization state in Fig. 1(a). The controllable properties of metamaterials are dictated by the phase difference φ between two input beams, equivalently different spatial positions located in the standing wave. When the phase difference φ alters in the range of 0°-180°, the strengths of electric and magnetic responses in the stereometamaterials correspondingly vary. Providing that the stereometamaterials are ultrathin, the coherent interaction of the standing wave on them can be described by Jones transmission and scattering matrices [36]. Two specific cases are φ = 0° and 180°, corresponding to electrical antinodes and nodes respectively. The metamaterials at electrical antinodes are in in-phase excitation and reveal double enhanced electric responses and completely suppressed magnetic responses, while the metamaterials at electrical nodes are in out-of-phase excitation and reveal completely suppressed electric responses and double enhanced magnetic responses. In the coherent case, the total intensity of two input beams is unitary and the intensities of the signal and control input beams are equally divided (i.e., defined as 0.5 each). The absorption is normalized to the input energy and thus A = 1 means complete absorption of two input beams. The coherent absorption spectra of two stereometamaterials are shown at two specific cases in Figs. 3(a) and 3(b). All absorption bands can be nearly switched on/off by changing the phase difference. Regardless of the twist angles, the stereometamaterials exhibit three and two CPAs for x- and y-polarized standing waves, respectively. Importantly, the operation of CPAs can be switched from low to high frequencies by changing the polarization state. According to the coherent absorption spectra, the electric or magnetic modes can be distinguished even in their overlapped regions, for instance, x-polarization excited modes in the 0°-twisted stereometamaterial in the vicinity of 5.5GHz and y-polarization excited modes in the 180°-twisted stereometamaterial in the vicinity of 10 GHz. For incident x-polarized wave, both two stereometamaterials show one electric mode and two magnetic modes. However, when two stereometamaterials are in the y-polarized standing wave, they have different electromagnetic modes. In the 0°-twisted stereometamaterial, the y-polarized input beams lead to two magnetic modes while one is an electric mode and the other one is a magnetic mode in the 180°-twisted stereometamaterial. Therefore, the electromagnetic modes in the stereometamaterials can be recognized by the coherent absorption and the polarization state can modulate the operation frequencies of CPAs.
Fig. 3 Coherent absorption spectra of the stereometamaterials with (a) θ = 0° and (b) θ = 180° twisted stereo-ASRs switched by incident polarization state. The green dashed and blue solid lines refer to the phase differences φ = 0° and φ = 180° for x-polarized wave, respectively. The magenta dotted-dashed and red dotted lines refer to the phase differences φ = 0° and φ = 180° for y-polarized wave, respectively.
In order to fully understand the polarization-controlled CPAs in two stereometamaterials, we numerically and experimentally studied their coherent absorption as a function of frequency and phase difference in the full phase range of 2π instead of two limiting cases of θ = 0° and 180°. In the simulations in Figs. 4(a) and 4(c), the absorbance in each narrow absorption band can change continuously in the range of 0-1 when the phase difference varies from 0 to 2π. More importantly, the incident polarization state remarkably affects the properties of multiple CPAs. For both stereometamaterials, three CPAs occur in the low frequency range of 4.8-5.8GHz under x-polarization illumination in the bottom panels in Figs. 4a and 4c while the y-polarized wave leads to two CPAs in the high frequency range of 9-11GHz in the upper panels in Figs. 4(a) and 4(c). The orthogonal polarization alternation can switch the operation frequencies of CPAs. Next we present the measured coherent absorption spectra of two stereometamaterials shown in Figs. 4(b) and 4(d). The experiments were carried out using three broadband horn antennas and a vector network analyzer. Two antennas as signal and control wave sources were connected by a powder divider and equally fed with the same signal through identical cables [36]. Moving the control antenna corresponds to place the stereometamaterials at different spatial positions of the standing wave generating by the counter-propagating signal and control beams. The relative phase difference between two coherent beams was achieved by moving the control antenna along the beam direction, selectively generating constructive and destructive interference. Another receiving antenna was used to measure the intensities of the output beams along two propagating directions for obtaining the coherent absorption. Due to practical volumes of microwave antennas, it is impossible to perform experiments under the normal incidence. Therefore, measurements were carried out with a small angle of incidence (~13°) to ensure the signal/control antenna and the receiving antenna as close as possible, which does not cause an obvious difference compared with simulations under normal incidence [36]. For x- and y-polarized waves, the coherent absorption measurements were completed within the displacement ranges of 150 and 60mm, with 5mm and 1mm moving steps of the control antenna respectively. Both the moving steps are much less than the incident wavelength. Apparently, the properties of CPAs can be well modulated via moving the control antenna. The coherent absorption properties of both two stereometamaterials periodically change with increasing the antenna displacement. The coherent absorption spectra of two stereometamaterials are plotted in the phase range of 0-2π in Figs. 4(b) and 4(d). The stereometamaterials experience an alternation from zero to unit coherent absorption when the displacement change is equal to half the wavelength (i.e. π phase difference). The frequencies of CPAs in the experiment results exactly agree with ones in the simulations. The modes at the central frequency of each CPA are marked by X1-X3 and Y1, Y2, which are observed for x- and y-polarized wave illumination, respectively. The fundamental electromagnetic features of the measured resonant modes are consistent with the simulated ones in Figs. 4(a) and 4(c). The simulated and measured coherent absorption agree with each other in Fig. 4. Coherent absorption peaks of x-polarized wave in 0°-twisted stereometamaterial are observed at frequencies of 4.8 (X1), 5.5 (X2) and 5.6 (X3) GHz in the bottom panel of Fig. 4(b), while two CPAs of y-polarized wave occurs at 9.5 (Y1) and 10.8 (Y2) GHz in the upper panel of Fig. 4(b). Figure 4(d) shows the experiment results of the coherent absorption of the 180°-twisted stereometamaterial, having coherent absorption at frequencies of 4.9 (X1), 5. 3 (X2) and 5.75 (X3) GHz for x-polarized wave and 10 (Y1) and 10.3 (Y2) GHz for y-polarized wave. According the simulated and measured results, it can be readily concluded that both two bilayered ASR stereometamaterials can exhibit polarization-controlled multiple frequency CPAs and are beneficial to realize tunable multiband absorption, even for absorbers in the THz and optical frequencies.
Fig. 4 Polarization-controlled multifrequency coherent perfect absorption (CPA) of two stereometamaterials as a function of frequency and phase difference. (a) and (b) Simulated and measured coherent absorption spectra of the 0°-twisted stereometamaterial. (c) and (d) Simulated and measured coherent absorption spectra of the 180°-twisted stereometamaterial. The simulation and experiment results are shown in the left and right columns. The x- and y-polarized coherent absorption spectra are illustrated in the bottom and top panels of each figure, respectively. The labels X1, X2, X3, Y1 and Y2 refer to resonant modes at the central frequencies of each CPAs.
Figure 5 shows coherent absorption in two stereometamaterials at the central frequencies of CPAs. All absorption spectra show sinusoidal dependence on the phase difference between the control and signal beams. In the simulations, the electric resonant modes exhibit nearly 100% absorption at the phase difference of φ = 0° and nearly zero absorption at the phase difference of φ = 180°, while the magnetic resonant modes exhibit nearly 100% absorption at the phase difference of φ = 180° and nearly zero absorption at the phase difference of φ = 0°. For the 0°- and 180°- twisted stereometamaterials, with x-polarization illumination, the measured and simulated results basically agree with each other at modes X1, X2 and X3 in Figs. 5(a) and 5(b). At modes Y1 and Y2 of y-polarized wave, the measured results are slightly worse compared with those in Figs. 5(a) and 5(b), but they are typically consistent with the simulated results. The discrepancies may result from the oblique incidence in the experiments, improper central frequencies selection, imperfect experiment system with slightly large background noises and insufficient simulated and measured data sampling. For instance, modes Y1 and Y2 in the 180°- twisted stereometamaterials are too close to each other to be easily distinguished. Based on the results in Fig. 5, it is easily found that CPAs can be selectively switched on/off with the change of phase difference and incident polarization states and the twist angles of the ASR dimers can tailor the electric or magnetic responses of the metamaterials.
Fig. 5 Coherent absorption spectra of two stereometamaterials as a function of the phase difference at the central frequencies of CPAs marked by X1-X3 in Fig. 4a and 4c and Y1, Y2 in Fig. 4b and 4d. (a) and (c) Simulated and measured coherent absorption spectra of the 0°-twisted stereometamaterial. (b) and (d) Simulated and measured coherent absorption spectra of the 180°-twisted stereometamaterial. The simulated results are illustrated by solid, dashed and dotted lines. The asteroid, diamond, circle and cross marks refer to the measured results.
4. Coherent absorption of optical stereometamaterial
The spatially engineered stereometamaterials also offer a flexible way to tailor electromagnetic responses of optical nanostructures [45]. Next, an optical ASR stereometamaterial is preliminarily proposed for demonstrating polarization-controlled mulitifrequency CPAs. The bilayered gold ASRs are patterned on both sides of a SiO2 dielectric layer, respectively. The unit cell of the optical stereometamaterial is shown in Fig. 6(a). The geometry parameters are d́ = 520 nm, ẃ = 40 nm, and ŕ = 185 nm, t́ = 120 nm, ά = 148°, β́ = 180°. The refractive index of SiO2 dielectric layer is 1.5. A Drude model is used for the dielectric constant of gold, ε(ω) = 1 − ωp2/[ω(ω + iωc)], where the plasma frequency is ωp = 1.37 × 1016 s−1 and the damping constant is ωc = 4.08 × 1013 s−1 for bulk gold. The simulation results of the optical stereometamaterial are obtained using a damping constant that is three times larger than the bulk value.
Fig. 6 Coherent absorption spectra of an optical stereometamaterial with a twist angle of θ = 0°. (a) The unit cell of the optical ASR dimer. The gold ASRs are patterned on both sides of a SiO2 dielectric layer. The geometry parameters are d́ = 520 nm, ẃ = 40 nm, and ŕ = 185 nm, t́ = 120 nm, ά = 148°, β́ = 180°. (b) Polarization-dependent coherent absorption spectra of the optical stereometamaterial for the phase differences of φ = 0° and 180°. The green dashed and blue solid lines refer to x-polarized coherent absorption spectra at the phase differences φ = 0° and φ = 180°, respectively. The magenta dotted-dashed and red dotted lines refer to y-polarized coherent absorption spectra at the phase differences φ = 0° and φ = 180°, respectively. The labels x1, y1, y2 and y3 refer to coherent absorption peaks. (c) Phase-dependent coherent absorption at mode x1 for x-polarized wave. (d) Phase-dependent coherent absorption at modes y1-y3 for y-polarized wave. Modes x1, y1-y3 are labeled in the panel b.
Based on the simulated results shown in Figs. 6(b)-6(d), the optical stereometamaterial exhibits polarization-dependent multifrequency CPAs. The coherent absorption spectra of the optical stereometamaterial are presented for two limiting cases with the phase differences of φ = 0° and 180° in Fig. 6(b). According to electrical and magnetic characteristics of modes, the coherent absorption can be selectively enhanced or suppressed as well as depending on the phase difference. For the identical phase difference, the alternation from x- to y- polarized wave illumination can modulate the operation frequencies up to 100 THz. Figure 6c-d shows the phase dependences of the coherent absorption peaks labeled by x1, y1, y2 and y3 in Fig. 6(b). The magnetic mode x1 has enhanced coherent absorption at the phase difference of φ = 180° and correspondingly the x-polarized wave allows coherent absorption modulation from 0.2 to 0.85 in Fig. 6(c). From Fig. 6(d), the magnetic mode y1 has enhanced coherent absorption up to 1 and the electric modes y2 and y3 have suppressed coherent absorption nearly down to zero at the phase difference of φ = 180°. The performance of optical CPAs can further be improved by optimizing the structural shape and parameters. The polarization state offers alternative route to control optical CPAs.
5. Conclusions
In summary, we have numerically and experimentally demonstrated polarization-controlled multifrequency CPAs in microwave and optical stereometamaterials with twist ASR dimers. The electromagnetic modes in the stereometamaterials are dominated by the twist angles of the ASR dimers and can be recognized by their coherent absorption spectra. The zero and unitary absorption at each CPA can be coherently modulated by interferometric effect of two counter-propagating coherent beams. The manipulation of the operation frequencies of the CPAs has been accomplished by changing the polarization state of incident waves. The polarization state offers a freedom to design coherent perfect absorbers and the proposed scheme is beneficial to realize tunable polarization-dependent multifrequency absorbers and opens up a new opportunity for coherent spectroscopy.
Funding
National Natural Science Foundation of China (NSFC) (61675054, 91750107); China Postdoctoral Science Foundation (2016M600668); Natural Science Foundation of Heilongjiang Province (A2015014); Postdoctoral Scientific Research Developmental Fund of Heilongjiang Province (LBH-Q15036); 111 Project to the Harbin Engineering University (B13015); Fundamental Research Funds for Harbin Engineering University (HEU) of China.
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