In this paper, we present an anisotropic metamaterial (AMM) composed of a sub-wavelength metal grating sandwiched with bi-layered double-arrow-shaped (DAS) structure array, which can achieve high-efficiency circular polarization (CP) conversion via giant asymmetric transmission (AT) in terahertz (THz) region. Numerical simulation results indicate that near complete CP conversion with cross-polarization transmission coefficients can reach 0.91 and 0.93, which can be observed at 0.31 and 0.55 THz, respectively. Based on the combination of polarization conversion effects and Fabry-Perot-like cavity-enhanced effect of AMMs, the AT parameter for CP wave can reach a maximum of 0.83 at 0.30 THz, and 0.87 at 0.56 THz, respectively. With appropriate geometric parameters design of each unit-cell, embedded in the proposed AMM, the cross-polarization transmission coefficient and AT parameter for CP waves can be increased to the maximal values of 0.98 and 0.9, respectively. The proposed AMM shows great potential applications in high performance dual-band CP convertor and isolator in THz region.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Metamaterials (MMs) as the artificial composite structure/material with sub-wavelength periodic unit-cells have attracted a great attention for their many exotic phenomena and novel physical properties unavailable in natural materials [1,2]. Polarization manipulation in MMs termed as polarization rotator or convertor has attracted much interest due to its wide applications in astronavigation and communication [3–5]. Compared with conventional birefringent materials or dichroic crystals, polarization controlling devices based on MMs have attracted much attention since they offered high efficiency, lower profile, and lower cost [6–10]. Meanwhile, a Lorentz reciprocal phenomenon termed asymmetric transmission (AT) in MMs was firstly observed by Fedotov et al. . The AT as a novel phenomenon is originated from the interaction of electromagnetic (EM) radiation with the MMs. The AT in MMs is mainly attributed to the different conversion between two orthogonal polarization waves’ propagation backward and forward directions [11–13], which is different from the Faraday Effect in magneto-optical media. Hence, the AT effect via polarization conversion has become a topic of research interest since it is quite useful in realizing nonreciprocal light devices such as isolators, circulators and frequency selector or filter [14–18].
AT effects in many MMs structures for both linear and circular polarization (CP) have been proposed and investigated intensively in microwave [17–27], terahertz [13,28,29], and even optical frequency ranges [15,30–35]. These designs can be used as polarization-controlled devices for many promising applications in imaging, sensing, and communications. In particular, MMs for AT effect of CP waves has attracted great attention in terahertz (THz) region since devices for manipulating wave were considerably limited in this region [36,37]. Consequently, the development of MMs with AT effect via high efficiency CP conversion in THz region is extremely important. Singh et al. achieved giant AT of CP waves for THz radiation with a planar split-ring structure MMs, nevertheless, the AT parameters are less than 0.1 . Then, Li et al. proposed a graphene chiral metasurface, which could achieve tunable AT effect of CP waves in THz region, however, the AT parameters are less than 0.08 . Many efforts have been devoted to increase the magnitude of AT parameter [25–34]. Recently, two-/three-layered chiral and anisotropic MMs were proposed, which could achieve larger AT parameter of CP wave with single bandwidth in microwave [25,26] and infrared region [20–34]. To our best knowledge, there are few reports about the realization of high efficiency CP conversion via giant AT effect in THz region until now. Thus, the effective design of the MMs with giant AT effect of CP waves would be highly desirable in THz frequency range.
In this work, the high efficiency CP conversion via giant AT effect for THz waves in a tri-layered anisotropic metamaterial (AMM) structure has been proposed. The AMM is consisted of sub-wavelength metal grating sandwiched with bi-layered double-arrow-shaped (DAS) structure array. It can convert incident left-circular polarization (LCP) and right-circular polarization (RCP) waves to its orthogonal polarization waves in around two adjacent frequency ranges. The giant AT effect is mainly originated from the combination of polarization conversion effects and Fabry-Perot-like cavity-enhanced effect of AMM. The proposed AMM could be found in many potential applications, such as isolators, wave splitters, CP convertor and circulators.
2. Structure design, simulation, and fundamental theory
Figures 1(a,b) show schematics of two-dimensional array and unit-cell structure of the proposed AMM, which consists of a sub-wavelength metal grating sandwiched with bi-layered DAS structure array. The anisotropy of the MM structure is vital for generating CP conversion and AT effect of the CP waves. It can be expected that the MMs with both anisotropic and cascading Fabry-Perot-like resonance cavity with tri-layer structures are performed well in CP conversion via AT applications.
As shown in Fig. 1(b), two DAS structure (denoted as A) are introduced in front and back layers, and the sub-wavelength metal grating structure (denoted as B) is used as middle layer of the AMM. In each unit-cell in the AMM, the front DAS structure is identical with the back one, and the arrow direction is tilted 45 degrees relative to the x(y) axis. Thus, an anisotropic is introduced in the unit-cell structure so that it enables the CP conversion and AT effect for normal incident CP wave. In addition, the tri-layered structure can form a cascading Fabry-Perot-like resonance cavity, which could enhance multiple CP reflection and transmission and improve the polarization conversion efficiency and extend the operation bandwidth [28,32]. The optimized geometry parameters are as follow: px = py = 120 μm, d = 20 μm, g = 12 μm, l0 = 100 μm, l = 75 μm, w = 8μm, ts = 70 μm, tm = 0.2 μm.
For our proposed AMM, the numerical simulations were carried out by using the standard ﬁnite-difference-time-domain (FDTD). The periodic boundary conditions along the x- and y-axis directions of the unit-cell structure, and the perfect match layers along z-axis directions were applied. In simulation, the copper films with conductivity of σ = 5.8 × 107 S/m was selected as the metallic structure layers, and the loss-free dielectric substrate benzocyclobutene (BCB) with permittivity of 2.67 was selected as the isotropic dielectric spacer [28,32]. In simulation, the unit-cell structure is illuminated by two orthogonal linear polarization waves, and the corresponding reflection and transmission coefficients can be obtained. Under the Cartesian coordinates of x-y-z, considering an incident EM wave with electric field Ei propagating along the + z axis direction, the expressions of electric field vector of incident and transmitted wave with x-polarization and y-polarization are given as flowing:14]:
The transmission coefficient is defined in terms of the complex amplitude of the electric field of the transmitted and incident waves. The subscripts i and j ( = x, y for linear polarization, = + ,- for circular polarization) represent the polarization states of the transmitted and incident wave, and the superscripts f and b denote forward ( + z) and backward (-z) propagation of the EM wave, respectively. The transmission coefficients of CP waves can be obtained by transforming linear polarization (LP) waves which are propagating along forward ( + z) and backward (-z) directions through using Jones matrix :28]:14]:Eq. (5.1) indicates that the AT for LP wave in a reciprocal system simultaneously requires and . And the Eq. (5.2) indicates that the AT for CP wave in a reciprocal system simultaneously requires and .
3. Results and discussions
Firstly, the responses of single layer structure A bi-layer structure AB for forward ( + z) propagation with LCP and RCP waves are discussed, respectively. As shown in Fig. 2(a), it can be observed that two cross-polarization and co-polarization transmission curves are completely the same, i.e. and . The amplitude of cross-polarization transmission () is up to the maximal value of 0.47 at 0.43 THz and 0.96 THz simultaneously, respectively, meanwhile the co-polarization transmission coefficient () achieves minimal values of 0.36 and 0.47 at 0.41 THz and 0.96 THz, respectively. It indicates that the single DAS structure can convert incident CP waves partially to its transmitted orthogonal polarization waves. Essentially, incident CP waves are converted to transmitted elliptical polarization (EP) waves by a single layer DAS structure. Actually, the DAS structure can excite dipolar oscillation along the arrow direction with two orthogonal components under normal incident LCP and RCP waves, finally resulting in a partial CP conversion.
On the another hand, two obvious resonances emerge around 0.32 THz and 0.55 THz in the case of bi-layer structure AB. For the bi-layer structure AB under normal incident LCP and RCP waves (as shown in Fig. 2(b)), cross-polarization and co-polarization transmission curves are near the same, i.e. and. At resonance frequencies of 0.32 THz and 0.55 THz, the cross-polarization and co-polarization transmission simultaneously reach up to 0.58 and 0.68 for normal incident RCP and LCP waves, respectively, i.e. and . At the same time, the cross- and co-polarization transmission coefficients are simultaneous decreased to the minimal values of 0.02 and 0.12, respectively, i.e. at 0.32 THz, and at 0.55 THz. Obviously, the transmitted RCP and converted LCP waves are almost equal for the incident RCP waves at the lower frequency, while transmitted LCP and converted RCP waves are also almost equal for the incident LCP waves, indicating that the transmitted wave is LP essentially. In addition, as shown in Fig. 2(c), the two co-polarization reflection coefficients are equivalent and decreased to the minimal values of about 0.05 and 0.16 at 0.32 THz and 0.55 THz, respectively. Around 0.32 THz, cross-polarization reflection coefficient () is up to the maximal value of 0.99, revealing that the incident RCP wave is near completely converted to the LCP wave by the structure AB after reflection. In contrary, the incident LCP wave is nearly completely converted to the RCP wave by the structure AB after reflection at 0.55 THz.
To illustrate the mechanism of the polarization conversion in the bi-layer structure AB, a schematic of the functionally independent Fabry-Perot-like resonance cavity is carried out (shown in Fig. 2(d)). In this bi-layer structure AB, the front layer A is responsible for CP conversion, including the processes of transmission and reflection . Although the layer B has the excellent ability to select LP wave, i.e. polarization with an electric field perpendicular to the wires is reflected totally while a full transmission can be achieved when the electric field is parallel to the wires. Therefore, the middle layer B and front layer A can act as reflected mirrors and compose a polarization conversion combined Fabry-Perot-like resonance cavity . When the incident RCP and LCP waves are propagating along the + z axis direction onto the structure AB, around 0.32 THz, the LCP wave is completely converted to the RCP after reflection, and the partial RCP wave is converted to LP (x-polarization) through the structure after transmission. Around 0.55 THz, the case is contrary, the incident RCP wave is near completely converted to the LCP after reflection, and the partial LCP wave is converted to LP (y-polarization) after transmission. In the Fabry-Perot-like resonance cavity, multiple transmission and reflection of CP waves finally result in the enhanced transmission of (), which are confirmed by the Figs. 2(b) and 2(c). For the practical application of the CP convertor, both cross-polarization transmission of CP waves and the conversion efficiency should be engineered as high as possible. To improve the CP conversion efficiency, another layer structure A is added to bi-layer structure AB to construct a tri-layer structure ABA, as shown in Fig. 1(b). This composite structure can form a two cascading mirror symmetrical Fabry-Perot-like resonance cavity, which could enhance one of or while weaken another one.
The transmission coefficients of the tri-layer structure ABA for the normal incident CP waves along the + z and –z axis directions are presented in Fig. 3(a) and 3(b). For normal incident CP waves propagation along + z and –z axis direction, as shown in Fig. 3(a) and 3(b), co-polarization transmission coefficients are equivalent () and simultaneous decrease to minimal values of about 0.07 and 0.16 at 0.31 THz and 0.55 THz, respectively. At 0.31 THz, the amplitude of cross-polarization transmission coefficient () is up to maximal value of 0.91, while the one of () is reduced to a minimal value of about 0.036 for normal incident CP waves propagating along + z (-z) axis direction. It means that the incident RCP (LCP) wave propagation along + z (-z) axis direction is near completely converted to the transmitted LCP (RCP) wave around 0.31 THz. In contrary, the amplitude of () is up to the maximal value of 0.93, while the one of () is suppressed to 0.04 around 0.55 THz. It also means that the incident LCP (RCP) wave propagation along + z (-z) direction is near completely converted into its orthogonal polarization component after transmission around 0.55 THz. Thus, for the normal incident CP waves propagation along forward ( + z axis) direction, the proposed AMM structure has two CP conversion frequency bands corresponding to RCP-to-LCP and LCP-to-RCP, which is reversed in the case of backward (-z axis) direction incidence. These results demonstrate that this tri-layer AMM structure can significantly improve the CP conversion efficiency. Thus, the proposed AMM can be functioned as a dual-band transparent CP convertor. In addition, the cross-polarization transmission coefficients and are interchanged with each other when the propagation direction is reversed. Thus, it can be predicted that this AMM structure can realize completely CP conversion with giant AT effect.
According to the above simulation results, it can be inferred that the physical mechanism for the high efficiency CP conversion of the proposed AMM rely on the Fabry-Perot-like resonance [39,40]. As shown in Fig. 3(c) and 3(d), we present the Fabry-Perot-like resonance cavity model at the lower and higher frequencies of 0.31 THz and 0.55 THz, respectively. At 0.31 THz, as shown in Fig. 3(a), the incident RCP and LCP waves propagation along + z axis direction are converted to EP waves with the major axis in the x and y direction by front layer A, respectively. Then, the x component of the EP waves will be transmitted by middle layer B, while the y component will be reflected and then convert to x component in reflection. Similarly, middle layer B and back layer A compose a reverse cavity which is responsible for the EP - CP conversion. Finally, the incident RCP wave from the front layer A realizes the selective total transmission and is converted to LCP wave through the back layer A, whereas the incident LCP wave are totally reflected. Though the conversion efficiency of the layer A is relatively low, after multiple reflections and polarization conversions, the x component of the EP waves from the middle layer B finally convert to the transmitted LCP waves, as shown in Fig. 3(a) and 3(c). At 0.55 THz, as shown in Fig. 3(b) and 3(d), the case is contrary, only the LCP wave is selected to pass through the cavity and then converted to the transmitted RCP wave, whereas the incident RCP wave is totally reflected. Therefore, the unselected polarization waves are effectively converted to the selected ones by the combination of polarization conversion and cascading mirror symmetrical Fabry-Perot-like resonance cavity enhanced effects.
To provide a deep insight for the CP conversion mechanism of the proposed AMM, the z-component distributions of electric filed for the normal incident RCP and LCP waves propagating along + z axis direction at resonance frequencies are analyzed, as shown in Fig. 4. At 0.31 THz, as shown in Fig. 4 (a1), 4(a2), 4(b1), and 4(b2), it is clearly that the responses to resonances excited by the incident RCP and LCP waves are essentially magnetic dipole in the back layer (see a2) and electric dipole in the front layer (see b1), respectively. As shown in Figs. 4(a2) and 4(b2), obviously, the incident RCP waves propagating along + z axis direction are transmitted while the LCP ones are reflected, which is in an excellent agreement with the transmission coefficients curves in Fig. 3(a). At 0.55 THz, as shown in Fig. 4 (c1), the front layer A is excited by the incident RCP wave is essentially electric dipole resonance. In a rather complicated case (as shown in Fig. 4(d1) and 4(d2)), the structure is excited by the incident LCP wave is essentially the mixtures of the electric and magnetic dipole resonances. As shown in Figs. 4(c2) and 4(d2), the incident RCP waves are reflected while the LCP ones are transmitted, which achieves good accordance with the transmission as shown in Fig. 3(a). Thus, It can be concluded that the conversion of RCP-to-LCP at 0.31 THz is originated from the magnetic dipole resonance, while the one of the LCP-to-RCP at 0.55 THz is due to the mixtures of the electric and magnetic dipole resonances [41,42].
According to above simulation analysis, it can be expected that the desgined AMM structure can realize the giant AT effect for CP waves. To validate it, as shown in Fig. 5(a) and 5(b), we calculated the total transmittance T+ of the proposed AMM structure for normal incident RCP wave along the forward ( + z) and backward (-z) directions, and AT parameter for LP and CP waves, respectively.
As shown in the Fig. 5(a), the T+ for the RCP wave propagation long –z axis direction is significantly different from the one along the + z axis direction. At 0.31 THz, the magnitude of T+ is up to 0.88 along the backward (-z) direction, while decreases to near zero in the reverse direction. At 0.55 THz, the case is contrary, the magnitude of T+ is decreased to 0.02 along the backward (-z) direction, while increases to 0.92 in the reverse direction. Obviously, this function is similar to near perfect diode-like effect for the CP waves. As shown in Fig. 5(b), the AT parameter () for CP wave is 0.83 and −0.87, while the one () for is −0.83 and 0.87 at 0.30 THz and 0.56 THz, respectively. In addition, the AT parameter for LP waves is zero across the whole frequency range. Thus, the designed AMM structure exhibits a giant AT effect only for CP waves.
Furthermore, we also study CP conversion and AT effect of the proposed AMM with different geometric parameters of the unit-cell structure: mainly including thickness of dielectric substrate (ts), wire width (w), lattice length (l0) and wire length (l) of the DAS structure. Figure 6 shows the simulated cross-polarization transmission coefficients ( and ) and AT parameter ( and ) with different geometric parameters (ts, w, l0 and l).
As shown in Fig. 6(a1) and 6(a2), the resonance frequencies decrease slightly when increasing ts, which can be considered as typical Fabry-Perot-like resonance behavior [32,39,40]. Around the lower frequency region, as the increasing of ts, the magnitude of, and are nearly unchanged, whereas the is decreased slightly. Around the higher frequency region, the magnitudes of both and , and are increased gradually when increasing ts. In addition, when ts = 80 μm, the maximal values of cross-polarization transmission coefficient and AT parameter are up to 0.96 and 0.91, respectively. As shown in Fig. 6(b1) and 6(b2), when w changes, both resonance frequency and magnitude of cross-polarization transmission (and ) and AT parameter ( and ) are nearly unchanged. It means that the CP conversion and AT effect are affected slightly by the width (w) of the DAS structure of the proposed AMM. From the Fig. 6(c1), 6(c2), 6(d1), and 6(d2), it can be seen that the resonance frequencies gradually decrease with increase of lattice length (l0) and wire length (l) of the DAS structure, which can be interpreted by the LC resonance circuit theory . The resonance frequencies for CP conversion and AT effect can be expressed as, where equivalent inductance L and capacitance C are mainly determined by l0 and l. When lengthening l0 and l, the L value reveals a gradually increase while the resonance frequencies. The magnitudes of both, , and are nearly unchanged around the lower frequency region, while the ones will decrease gradually around the higher frequency region when the l0 and l increase. When l0 = 95 μm and l = 85 μm, the cross-polarization transmission coefficient and AT parameter are up to the maximal values of 0.98 and 0.97, 0.9 and 0.9, respectively. Obviously, the lattice length (l0) and wire length (l) of the DAS structure show a significantly affect on the CP conversion and AT effect compared with the width (w) and the dielectric substrate thickness (ts).
In conclusion, a tri-layered AMM structure is proposed and investigated numerically, which can realize a high-efficiency dual-band CP conversion and giant AT effect in THz region. The proposed AMM structure consists of a sub-wavelength metal grating sandwiched between two layers of DAS structure array, which can form a CP conversion effect combined with two cascading Fabry-Perot-like cavities. Numerical results show that the complete CP conversion for LCP and RCP waves is realized at 0.31 and 0.55 THz with cross-polarization transmission coefficients of 0.91 and 0.93, respectively. Moreover, two opposite AT effects for CP waves are realized with a giant AT parameter of about 0.83 and 0.87 at 0.30 and 0.56 THz, respectively, which is attributed to the structural anisotropy of the AMM. Finally, by delicately designing of the geometric sizes of the unit-cell structure of the AMM, the cross-polarization transmission coefficient and AT parameter are up to the maximal values of 0.98 and 0.9, respectively. The photolithography, electron-beam metal deposition, and lift-off can be applied fabricate this AMM in THz region . The detail fabrication usually experience following steps : firstly, 10 nm/200 nm thick Ti/Au layers are deposited on a bare GaAs substrate by using electron-beam evaporation; secondly, a 75 µm thick BCB layer is then spin coated, and thermally cured; thirdly, the DAS and grating array are defined by standard photolithographic methods, deposition of 10 nm / 200 nm thick Ti/Au films, and a lift-off process, finally, the GaAs substrate is mechanically removed by peeling off the polyimide encapsulated structure to establish the freestanding samples. The proposed AMM has great potential to be used as a CP convertor, isolator or circulators device in THz systems.
National Natural Science Foundation of China (NSFC) (U1435209, 61605147, 61701185, 61801186); Natural Science Foundation of Hubei Province (2017CFB588); Science and Technology Research Project of Education Department of Hubei China (D20181107).
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