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Abstract
Asymmetric transmission (AT) is useful for polarization manipulation. We report narrowband AT that utilizes a triple-layered symmetric trimeric metasurface with near-field coupling of the dark mode of the Fano resonance. The coupling strength of the dark mode was tuned by using a mid-layer to break the dim AT between two slit layers. The peak transmission of linearly polarized waves and percentage bandwidth reached 0.7719 and 1.26% (numerical simulations) and 0.49 and 1.9% (experiments), respectively. Coupled-mode theory and field patterns are utilized to explain the underlying physical mechanisms of the mid-layer assisted field coupling. These results are useful for Fano-resonance-based devices.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials with various meta-atoms [1–4] can be designed to exhibit unprecedented electromagnetic properties in many applications [5–9]. In particular, tailoring the polarization state of light for directionally asymmetric transmission (AT) can be useful for polarization rotators [10,11], circular polarizers [12,13], and polarization state filters [14–16]. Many structures have been proposed by breaking the spatial inversion symmetry using artificial structures on the opposite sides of a metasurface [3] and an inserted Fabry–Perot cavity in order to achieve high-performance AT [17,18] in a relatively broad band. The narrow band devices have a significant advantage on selecting the signal and rejecting the noise and interference which may enter the receiver outside its bandwidth. Consequently, transmitter power levels can be low and the effective range of transmissions may be greater than that would typically be the case for technologies which do not provide such selectivity. For narrowband applications, it is difficult to realize AT devices requiring a narrow-band and high-quality factor for intrinsic loss of metallic materials and radiative damping [19,20], even AT devices based on the micro-ring nonlinear effect [21] and plasmonic grating have been proposed recently [22]. The Fano resonance, corresponding to the interference of a broad continuum resonance with a discrete state, has been of significant interest for plasmonic nanostructures [23,24], controllable and tunable materials and devices [25–30], and metamaterials [26] operating over optical to microwave frequencies with asymmetric structures and even symmetric structures [31,32]. The high-Q Fano resonance enables the detection of small spectral shifts from minute quantities of analytes interacting with highly concentrated electric fields [33]. In general, the broad band mode in high-Q Fano resonance is sensitive to particularly polarized waves and the narrow band dark mode is non-radiative mode in common. Blocking the broad band mode and reserving the narrow band mode can naturally realize a narrow band AT. Thus, narrowband AT devices with the dark mode of the high-Q Fano resonance are of practical importance. Moreover, despite of numerous theoretical achievements by transmission matrix method have progressed [34,35], the underlying physics of AT is still far from satisfactory. Recently, L. Zhou proposed the coupling mode theory (CMT) for stacking metasurfaces and a complete phase diagram for dark-bright coupled plasmonic systems which provides a unified picture to understand AT based on metasurfaces [36–38].
Here, we propose a tri-layered symmetric metasurface supporting narrowband AT based on Fano resonance. Polarization conversion in the transmission map was realized by employing the dark mode interaction between the tri-layered structure. The dark mode coupling was enhanced by inserting a mid-layer to break the nonexistent AT between two crossing slit layers. The AT parameters exhibited narrow bandwidth, both in numerical simulations and experimental measurements, in the microwave region. The underlying physical mechanisms based on the CMT theory reveal that the AT is realized by using the mid-layer to tune the coupling strength of the dark mode between two coupling modes. The realization of such narrowband AT offers opportunities for investigation of Fano-resonance-based devices over a sharp range of frequencies.
2. Theoretical analysis
We assumed that an incident plane wave propagates along the + z direction, and its electric field is defined as ${E_i}({r,t} )= {({{I_{x,}}{I_{y,}}} )^T}{e^{i({kz - \omega t} )}}$, with the annular frequency $\mathrm{\omega }$, wave vector k, and complex amplitudes Ix and Iy in the x and y directions, respectively. The transmitted electric field through the tri-layered structure can be described as ${E_t}({r,t} )= {({{T_{x,}}{T_{y,}}} )^T}{e^{i({kz - \omega t} )}}$. The complex amplitudes of the incident waves and transmitted waves can be linked by the T matrix [34]
3. Physical model and AT characteristics
Figure 1 schematically shows the fabricated sample of the metasurface and the experimental setup. In the cell, three copper layers (period, p = 15 mm) are bonded with a dielectric substrate in vacuum. The top (bottom) layer in Fig. 1(a) (Fig. 1(c)) emerges as trimmers along the y(x)-direction, and the mid-layer in Fig. 1(c) exhibits double-L-shaped slits. The dielectric layer is made up of F4B with the optimal thickness t = 2 mm and permittivity $\varepsilon $ = 2.6, and the tangential loss is tan $\mathrm{\delta }$ = 0.002. The three rectangular slits in the top and bottom layers have the same dimensions (w = 1.8 mm, h = 9 mm, d = 3 mm). The double-L-shaped slits in the mid-layer have the dimensions w = 1.8 mm, length l, and the gaps between the slits and borders are given by g = (p-2d-w)/2. Here, we define m = $l/h$ = 0.44 as a proportionality factor. The dashed ‘L’ shapes denote the shadows of the mid-layer on the top and bottom layers. Figure 1(d) shows the combined view of the cell with three copper layers. The magnetic field H, the wave vector k, and the electric field E of the incident plane wave are oriented in the y, z and x directions, respectively. The positive z direction is considered as the forward direction. Commercial simulation software (CST MICROWAVE STUDIO, Germany) was used for numerical simulations in the 8–12 GHz range of frequencies, by using periodic boundary conditions along the x and y directions and an open boundary condition for the z direction, and the minimum grid interval of the mesh is w/10. Figure 1(e) shows the metasurface array sample fabricated using the standard printed circuit board technique. The sample consists of 12 × 12 unit cells with 180 × 180 mm2 stacked three-layer copper metasurfaces. The 3-D device are assembled by combining the two layers together with several bolts. As is schematically shown in Fig. 1(f), the measurements were made in an anechoic chamber, where the sample was settled between two horn antennas linked to the ports of a vector network analyzer (Agilent N5230C) by 50 Ω coaxial cables. To ensure the illumination of a linear plane wave in Fig. 1(d), the distance between the two antennas was maintained at ∼1300 mm, and the slits of the top layer metasurface were settled as shown in Fig. 1(e).
Fig. 1. Schematic of (a) the top layer, (b) the double-L-shaped mid-layer, (c) the bottom layer, and (d) the combination unit cell with (a) to (c). (e) Profile of the fabricated sample and (f) the experimental setup.
After the optimization of geometric parameters, transmission matrix elements ($T_{yx}^f$, $T_{xy}^f$) were obtained and are shown in Fig. 2(a). There exists one significant peak for $T_{yx}^f$ that reaches 0.7719 at the frequency of 10.252 GHz for proportionality factor m = 0.44. While $T_{xy}^f\; $ is suppressed nearly to zero throughout the entire range, it remains weak and exhibits a slight trend, compared with $T_{yx}^f$. The obviously different cross-polarization across the entire frequency range may contribute to the strong AT effect and polarization conversion. From Fig. 2(a), when the x-polarized wave is normally incident on the structure along the positive z direction, the wave is well-coupled to the structure and is converted mostly into a y-polarized wave. However, a y-polarized wave traveling through the structure in the forward direction can hardly couple with the structure. Furthermore, to verify the results of numerical simulations, the corresponding experimental results are shown in Fig. 2(b), revealing that the experimental data exhibit a roughly consistent frequency response. The transmission of a linearly polarized wave and the percentage bandwidth reached 0.7719 and 1.26% in numerical simulations and 0.49 and 1.9% in experiments, respectively.
Fig. 2. AT coefficients $T_{yx}^f$, $T_{xy}^f$ for different linearly polarized waves, for (a) simulations and (b) experimental tests in the forward direction. (c) Simulated AT spectra and (d) experimental AT spectra.
The value of the AT parameter ${\Delta ^y} = {|{T_{xy}^f} |^2} - {|{T_{yx}^f} |^2}$ for the forward-propagating wave is equivalent to ${|{T_{xy}^b} |^2} - {|{T_{yx}^b} |^2}$ for the backward-propagating wave. Therefore, only the AT parameters for the forward wave are illustrated in Figs. 2(c) and 2(d). Obviously, the peaks reach 0.5958 and 0.237 for the frequencies of 10.252 GHz and 10.46 GHz, in simulations (Fig. 2(c)) and experiments (Fig. 2(d)). These results indicate that for the forward propagation direction, an x-polarized wave can transform into a y-polarized wave in a sharp range of frequencies.
Compared with the simulated transmission matrix elements and AT parameters with only one peak in Fig. 2(a) and 2(c), the spectral lines of the experimental results split into two peaks in Figs. 2(b) and 2(d). The 3-D metamaterials are fabricated by combining two F4B board together with bolts. The unavoidable offsets between two layers brings about the bias of m which generates the peak splitting. The underlying physical mechanisms of the tunability of m will be discussed in the following section. Moreover, the tangential loss of the F4B materials may have higher values than that of in simulation tanδ = 0.002. Therefore, the inevitable errors lead to the total deviation between simulation and experimental results.
To validate the critical role of the double-L-shaped layer in forming narrowband AT, the corresponding transmission matrix elements for a structure without the mid-layer are illustrated in Figs. 3(a) and 3(b), respectively. Obviously, in Fig. 3(a),$\textrm{\; }$ all of the transmission coefficients exhibit no sharp peaks in the entire range, except a tiny bump for $T_{yx}^f$. In Fig. 3(b), the trend lines reveal that a linearly polarized wave does not change direction passing through the structure. This confirms the indispensable role of the double-L-shaped layer in narrowband AT, notwithstanding the presence of interference, noise, and fabrication/measurement errors in the experimental results.
Fig. 3. (a) Simulated and (b) experimental transmission maps, for a structure without the double-L-shaped layer.
4. Analysis of the underlying mechanism
Before explaining the mechanism of the sharp AT effect, the Fano resonance in the trimeric system was generated owing to the interference between the antiphase dark and the in-phase bright modes of the stripes in our previous work [39]. In Fig. 4, according to Babinet’s principle, an x-polarized plane wave incident onto the metasurface can also stimulate the Fano resonance by two modes with different phases. The frequencies of Fano resonance are very sensitive to the geometric parameters and the permittivity of the medium. The schematic of Fig. 4 is totally different with the combination unit cell in Fig. 1(d). It is not rigorous to focus the Fano frequency as evidence of AT instead of the field distribution. Hence, the in-phase bright mode (+ + +) with a broad band and the antiphase dark mode (+ $- $ +) with a narrow band are indicated in the inset field maps in Fig. 4. The broad band bright mode has same phases at the ends of the three strips or slits, which is like a dipole mode induced by linear polarized wave. The bright mode is only sensitive to the corresponding linear polarized wave. A typically asymmetric line of Fano resonance is clearly shown that the broad band bright mode interferes with the antiphase dark mode, the phase spectra with red color represents a π-phase difference in the Fano resonance frequency. A linearly polarized wave is hardly transmitted through the crossing trimeric metasurface without a middle layer, as shown in Fig. 3, even for the dark-mode point; this is because the broad-band bright mode of the polarized wave can hardly be rotated without coupling units.
Herein, the middle layer was confirmed to play an important role in the AT. To examine the physical origin of this narrowband AT effect, the plane wave-induced current density and magnetic field Hy distributions at 10.252 GHz are shown in detail in Fig. 5. Figure 5(a) shows that groups of vectors marked with black arrows distribute along the center line, and a vortex current is observed to generate the magnetic field Hy in the figure below. The antiphase dark mode of the sharp Fano resonance is induced by the plane wave on the top layer. The profiles of the mode are similar with that of shown in Fig. 4. The same vortex current pierces the top layer and couples to the top surface of the middle layer in Fig. 5(b). On the other hand, the distributions of the current vectors and magnetic field on the bottom surface of the middle layer are almost rotated by 90° in the plane in Fig. 5(c). Therefore, a similar coupled vortex current generates the antiphase dark mode in the bottom layer. The polarized wave Hy becomes Hx. This mechanism suggests that sharp-band AT strongly depends on the length of the elaborated ‘L’ shape. In the following, we further pinpoint the AT evolution with respect to the proportionality factor m.
Fig. 5. The current density vector and magnetic field distributions at 10.252 GHz for (a) z = −2.019 mm relative to the bottom layer, (b) z = −0.019 mm relative to the top surface of the middle layer, (c) z = 0.019 mm relative to the bottom surface of the middle layer and (d) z = 2.019 mm relative to the top layer.
In Fig. 6, transmittance is quantified as a function of m. A clear sharp AT transmission band appears in Fig. 6 with an appropriate m. From the schematic in Fig. 1(a) with dashed lines, three regimes can be identified, depending on l (m). In cases where l is smaller than d or close to d (m < 0.33), the coupling between the electric field and the middle slit of the bottom layer is quite weak. Neither the broad-band bright mode nor the dark mode is motivated in the bottom layer. The energy leak owing to the ‘L’ shape yields minor transmission, as shown in Fig. 6(b) for m = 0.36. As l increases to d + w (0.33 < m < 0.43), the ‘L’ shape starts to overlap with the middle slits of both the top and bottom layers. Only the dark mode in the middle slits, which has the antiphase field and vortex current characteristics as shown in Fig. 5, can convert the x-polarized wave from the top layer into the y-polarized wave passing through the bottom layer. Transmission attains a peak value of 0.7719 for m = 0.44, as shown in Fig. 6(b). However, the transmission lines split into two peaks and the band width are enlarged in Figs. 6(a) and 6(b), as l continues to increase (m = 0.48, 0.52).
Fig. 6. Transmittance obtained by varying m (a) simulated transmission as a function of m, (b) transmission plots for different m and (c) comparison of transmission obtained by simulation (black) and CMT method (red).
For further explore the underlying physical mechanisms, we employ the CMT model to exhibit the independently controlled transmission properties due to the parameter m [37–39]. Noting that the metallic mesh can well block electromagnetic waves at frequencies below 20 GHz, thus severing as an optically opaque background for the whole system, and the trimeric slits of the two layers provide Fano resonances. We can describe such a system as a two-port model with two resonators embedded inside the background. According to the CMT method, the time evolution of the amplitudes of the two resonant modes are governed by the following equations [37].
5. Conclusions
A triple-layered Babinet metasurface structure with a double-L-shaped slit was designed. This structure supports narrowband AT and exhibits a high peak value, indicating that it is able to convert a forward-propagating x-polarized waves into a y-polarized waves or convert a backward-propagating y-polarized waves into an x-polarized waves. This proposed structure can be categorized as a reciprocal medium. Based on the Fano resonance phenomenon, a magnetic dark mode was induced in the top trimeric metasurface when forward-propagating x-polarized electromagnetic waves illuminated the structure. This magnetic dipole was rotated by 90° with double-L-shaped slits on the mid-layer surface. Then, coupling with the dark mode in the slits at the bottom metasurface yielded the outward propagation of linearly y-polarized waves from the metasurface structure. Finally, we utilized the CMT to explain the underlying physical mechanisms of AT. The coupling strength between the two modes of two layers plays an important role on AT management. The currently proposed structure supports narrowband AT and can be used in filters, polarization switches, and wavelength division multiplexers.
Funding
National Natural Science Foundation of China (11965009, 61761010, 61764001, 61765004); Natural Science Foundation of Guangxi Province (2018GXNSFAA281193, 2018JJA170010).
Disclosures
The authors declare no conflicts of interest.
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