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Abstract
The abrupt phase changes at the interface can modulate the polarization and wavefront of electromagnetic waves, which is the physical mechanism of the plasmonic metasurfaces. Conventional polarization converters are difficult to obtain pure polarized light, and most of the anomalously reflecting metasurfaces are limited by the specific angle of incident polarization. Here, we present a high-efficient polarization-independent metasurface for broadband polarization conversion and anomalous reflection when a plane wave with an arbitrary polarization angle is incident vertically. We vary the dimensions of the polarization conversion unit cells and arrange them periodically to cover the full 2π phase range of cross-polarized light in two orthogonal directions. The simulation results show that the pure anomalous cross-polarization efficiency is over 80% over a wavelength range from 1400nm to 1800nm. In particular, the metasurface can realize the complementary conversion of polarization angle for incident light at any polarization angle, and deflect it to a specific angle. Our design provides strategies for miniaturization and integration of polarization conversion devices and systems.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Polarization state and propagation direction are important fundamental properties of electromagnetic waves. Precisely controlling and manipulating the polarization state of light can be applied in optical communications [1,2], nonlinear optics [3,4], remote sensing [5,6], and biosensing [7,8]. The conventional method of polarization modulation is to control the intensity of cross-polarized light by generating a phase delay between two orthogonally polarized waves through dichroic materials and birefringent crystals [9,10]. The polarization variation gradually accumulates during the propagation of light, causing the thickness of the waveplate is much larger than the incident light wavelength. And the processing of arbitrarily polarized light generally requires a cascade of multiple polarizing elements, including various polarizers and waveplates. Therefore, traditional optical devices are large and complex, which is not conducive to the miniaturization and integration of optical systems. And spatial modulation of the phase of light to control the wavefront of pure polarized light is also an attractive function of optically integrated systems.
Recently, metasurfaces are receiving increasing attention as artificial structures with subwavelength dimensions due to ultrathin structure, easy integration, and flexible manipulation of the optical field. Metasurfaces have important applications in energy harvesting [11] and optical detection [12]. Through fine subwavelength cell size design and macroscopic layout, a metasurface can precisely modulate the polarization and change the direction of electromagnetic waves. Previous works have found that tightly stacked tilted metal nanostructures, such as V-shaped antenna [13,14], elliptical cylinders [15,16], and split ring resonator structures [17–19], can effectively modulate the polarization state of light. Phase gradient metasurfaces can induce a space variant phase profile and are applied in meta holograms [20,21], optical vortex generation [22–24], metasurface lenses [25,26], waveplates [27,28], anomalous light bending [29,30] or polarization splitting [31,32]. The conventional polarization conversion metasurfaces cannot separate the cross-polarized beam. And anomalous reflection metasurfaces are usually applicable to unidirectional linearly polarized light. When the incident polarization angle changes, only part of the beam can be deflected, resulting in a waste of energy. The polarization modulation and wavefront modulation of incident light at arbitrary polarization angles need to overcome these two limitations. An effective way to obtain pure polarization conversion light is by combining polarization converters and phase gradient metasurfaces. The polarization characteristics of the anomalous beam are determined by the structure of the individual unit cells, while the discontinuous phase gradient depends on the shape, size, and orientation of each building block. Although many metasurfaces integrated with polarization conversion and anomalous diffraction already exist, the question remains open as to how to achieve these two functions for incident light of arbitrary polarization angle. It definitely limits the application of polarization converter in integrated optical systems. This research aims to provide a metasurface design method applicable to multiple incident polarization angles.
In this paper, we demonstrate a high-efficient phase gradient metasurface capable of broadband anomalous reflection and complementary conversion to polarization angles when plane waves with arbitrary polarization angles are incident. The cross-polarized reflection efficiency of a unit cell is over 90% with over 95% polarization conversion ratio (PCR) in the wavelength region from 1200nm to 2000nm. We use the double-phase modulation method [33] to create linear phase shifts and cover full 2π range in two orthogonal directions. The simulation results show that the metasurface is polarization-independent and suitable for incident linearly polarized light at any polarization angle. The anomalous reflectance is over 80% and PCR keeps 1 at +1st diffraction order across a 400nm bandwidth. Further analysis shows the metasurface can perform complementary conversion of polarization angle of the incident light, extending the use scenario of the polarization converter.
2. Geometry and methods
The schematic diagram of the designed polarization converter is shown in Fig. 1(a). A metal-insulator-metal (MIM) structure is used with obliquely arranged dual-nanobricks on the top layer, a dielectric layer in the middle, and a metallic substrate on the bottom. The dielectric material employed is silica whose material parameters are obtained from Palik [34]. The material of metallic nanobricks and substrate layer is silver. The complex dielectric permittivity of silver is described by Drude model [35].
Fig. 1. (a) Schematic of an anisotropic structure that acts as a polarization converter. (b) The top view of unit cell.
3. Results
3.1 Polarization converter performance
The x-polarized light or y-polarized plane wave is illuminated on the anisotropic metasurface. The ratio of the intensity of the cross-polarized light to the intensity of the incident light is defined as the polarization conversion ratio. This ratio plays an important role in enhancing anomalous beams in linear polarization. The numerical solution of the polarization conversion ratio is PCR = Rcross/(Rcross+Rco). The co-polarized reflectance Rco, cross-polarized reflectance Rcross and PCR in the wavelength range from 1000nm to 2000nm are shown in Fig. 2(a). It can be seen that the intensity of cross-polarized beam is much larger than the intensity of the co-polarized beam, and the PCR is kept above 0.95 in the range from 1200nm to 2000nm band. The mechanism of polarization conversion is given in Supplement 1. Under the radiation of incident light, the free electrons on the surface of the metallic structure are excited, forming an oscillating surface current. The surface oscillating current can modulate the electromagnetic field near the metal structure, thus effectively regulating the polarization state of light. The surface currents of nanobricks and metallic substrate at the wavelength of 1550nm are given in Supplement 1. The dielectric interlayer helps to eliminate the amplitude and phase difference dispersion of the reflected co-polarized beam, making the operating bandwidth wider. This is because the introduction of dielectric materials can accumulate light paths in space and multiple reflections occur inside the dielectric layer, making the resonant frequency points increase. By adding a metallic reflection layer below the dielectric layer, the intrinsic dispersion [36] of metallic structure can be canceled out through the optimization of reasonable structural parameters. To understand the response of the polarization transition, the phase of the co-polarized light and the cross-polarized light were calculated respectively. The phase difference Δφ is shown in Fig. 2(b). we can conclude that Δφ is kept at π/2, which means the metasurface is able to excited surface plasmonic resonance and induce a phase delay between the two orthogonal components, enabling efficient polarization conversion.
Fig. 2. (a) The co-polarized reflectance Rco, cross-polarized reflectance Rcross and PCR of polarization converter. (b) The phase difference Δφ of co-polarized reflectance and cross-polarized reflectance.
The above polarization converter can realize highly efficient polarization conversion in the broadband wavelength range, but the cross-polarized light and co-polarized light remain in the same direction, which is not conducive to obtaining pure cross-polarized light. To separate out the polarization anomalous beam, we use double-phase modulation for the reflected cross-polarized light. The variation of cross-polarized reflectance Rcross and modulating phase φcross are explored when the width l1 and l2 were changed. The thicknesses of the nanobricks and dielectric layer are kept constant. The incident light is x-polarized or y-polarized light at a fixed wavelength of 1550nm. As shown in Fig. 3(a), the reflection efficiency of cross-polarization stays above 0.8 when l1 and l2 are increased from 100nm to 180nm, ensuring a high conversion efficiency for polarization anomalous beam steering. It is clear that the modulating phase of the reflected light could almost cover the entire 2π completely as the width of the nanobricks changes. Similarly, Figs. 3(c) and 3(d) represent the cross-polarized reflectance and modulating phase of y-polarized light incidence. The results show that for any desired modulating phases of the reflected x-polarized and y-polarized light, there always existed one nanobrick that could satisfy the needs of two orthogonally polarized modulating phases and keep the reflectance of the cross-polarized light high. Therefore, the different phase responses for orthogonal polarization states can be obtained simultaneously by changing the width of the nanobricks, and the local modulating phases for a couple of incident orthogonal polarization states can be manipulated independently. The double-phase modulation adds a modulation dimension and makes polarization-independent metasurface possible. The numerical simulation shows that the polarization converter can also achieve efficient polarization conversion and complete phase change in the same wavelength bandwidth when the upper dual nanobricks are rotated by 90°. Thus, the adding of a rotating structure can provide additional phase variation and avoid the utilization of inefficient structures.
Fig. 3. Simulated cross-polarized reflection (a) and phase (b) as a function of l1 and l2 for normal incidence of the x-polarized light. Simulated cross-polarized reflection (c) and phase (d) as a function of l1 and l2 for normal incidence of the y-polarized light.
3.2 Polarization anomalous beam steering
To achieve anomalous deflection of cross-polarized light, we combine eight individual unit cell resonators into a supercell. Each of the resonators can achieve high cross-polarized reflection and PCR. Cross-polarized light splitting is guided by two structures covering phase change from 0 to 2π in the broadband wavelength range. Figure 4 shows the three-dimensional structure of the phase-gradient GSP metasurface and top view of a long period. The width l1 and l2 of nanobricks in the first four resonators are 100nm, 120nm, 140nm, and 180nm, respectively. The dimensions of the last four resonators are exactly the same as the first four, except that they are rotating by 90° in the z-direction. The use of the rotated structure can bring an additional phase change of π while ensuring an efficient polarization conversion efficiency. According to the generalized Snell’s law, the reflected light after passing through the polarization converter is separated into multiple directions with different polarization, so that the purely polarized beam can be split out. In this design, we regard the +1st diffraction order as the target diffraction order, expecting to modulate the cross-polarized light to the desired direction.
Fig. 4. The top is a long period top view of the anomalous reflective metasurface, and the bottom is a three-dimensional structure with an 8×8 array of unit cell periods.
To demonstrate the reflection efficiency and PCR of the anomalous reflective metasurface, the reflectance on each diffraction order and phase changes are calculated separately. Figure 5(a) shows the reflectance on each diffraction order of the metasurface in the range from 1400nm to 1800nm when x-polarized light is incident, where m is the number of diffraction orders. The reflectance at m = +1 remains above 0.8 and is much higher than other diffraction orders. It is proved that the reflected light is mainly concentrated in the target diffraction order. The embedded figure in Fig. 5(a) shows the cross-polarized and co-polarized reflectance at m=+1. We can see that the co-polarized reflectance Rco,m=+1 is 0, which means only cross-polarized beam exists in the target diffraction order. As shown in Fig. 5(c), the total efficiency of metasurface is over 0.8 and the total PCR is about 0.9. The cross-polarized reflectivity at wavelength 1550nm is 0.9 and the anomalous reflectance angle is 29°. Therefore, the metasurface can reflect light in the expected direction and ensure the polarization purity of reflected light. Figure 5(e) shows the three-dimensional diagram of the phase change in the x-axis of the metasurface in the wavelength range from 1400nm to 1800nm. We observe that the phase of the cross-polarized light undergoes an approximately linear 0-2π variation range. The phase gradient is independent with respect to wavelength in 400nm range, which guarantees broadband anomalous reflection. Figures 5(b), 5(d), and 5(f) demonstrate the reflectance, efficiency, and phase change of the metasurface when illuminated by y-polarized light. The simulation results indicate that the metasurface can achieve broadband and efficient polarization conversion and anomalous reflection in both the x-axis and y-axis polarization directions. The linearity of the phase gradient performs better at y-polarization, and the cross-polarized reflectivity is high at +1st diffraction order.
Fig. 5. Reflectance on each diffraction order of the polarization converter under the x-polarized (a) and y-polarized (b) light incidences with different wavelength. The embedded figures in Figs 5(a) and 5(c) show the cross-polarized and co-polarized reflectance at m=+1. The total efficiency and PCR of metasurface under the x-polarized (c) and y-polarized (d) light incidences. The cross-polarized reflection phase along the x-axis (e) and y-axis (f) under the x-polarized and y-polarized light incidences.
When a linearly polarized light is normally illustrating on the lattice of the metasurface, surface plasmons are excited on the metal-dielectric interfaces, and strongly coupled to each other due to the subwavelength spacer. The strong magnetic fields occur in the middle dielectric spacer and antiparallel currents oscillate in two metallic layers, forming the so-called GSP resonances. The GSP resonance can be described by a simple Fabry-Perot resonator formula [37,38]:
where λ0 is the free-space wavelength, ngsp is the effective refractive index of the resonance mode, φ is an additional phase induced by the GSP upon its reflection at the resonator terminations and p is an integer defining the order of the GSP mode. In the vicinity of the GSP resonances, the nanobrick dimensions l1 and l2 allow us to independently control the phase of reflected light within the whole coverage of up to 2π for the respective orthogonal linear polarizations. Therefore, the metasurface can work in both x-polarized and y-polarized incident light illustrated. To investigate the polarization-independent properties of the metasurface, we calculate the intensity of each diffraction order at arbitrary polarization angles. Figure 6 represents the normalized intensity of each diffraction order on the metasurface at the incident of polarized light at any polarization angles. In the wavelength band from 1400 nm to 1800nm, almost all the intensities are directed to the target diffraction order. And the anomalous reflection angle can be calculated by Snell’s law: where βi is the incident angle and Λ is the length of one period on the metasurface. The result shows that the same diffraction pattern can be excited when incident light with arbitrary polarization angle is illuminated, and the energy is mainly concentrated in the target diffraction order. The range of the anomalous diffraction angle is from 26° to 34° in the wavelength band of 1400nm to 1800nm.Fig. 6. The relationship between the intensity and reflection angles of each diffraction orders in the range from 1000nm to 2000nm when linearly polarized light of the arbitrary polarization angles is incident. The diffraction patterns were calculated separately for incident polarization angles of 0°-90°, and all the results were the same.
3.3 Polarization anomalous beam mechanism
Although the metasurface has the same diffraction pattern at an arbitrary polarization angle, the percentage of Ex and Ey in the target diffraction order is different due to the polarization conversion function of the individual unit cell. By judging the polarization direction of the reflected beam, we find that the metasurface can perform the complementary conversion of the polarization angle for incident light of arbitrary polarization angles. Figure 7(a) is the schematic diagram of the complementary conversion of the polarization angle, where α is the polarization angle. The polarization angle of the reflected wave changes to 90°-α by the reflections from the metasurface. Figure 7(b) shows a schematic diagram of the principle of the complementary conversion and anomalous reflection. In the 4×8 unit cells array, the metasurface can be seen as an array of two tilted trapezoidal antennas, which are rotated 45° clockwise and counterclockwise, respectively. From the previous works, it is known that both discrete array metasurface and continuous metasurface are capable of linear phase change. As shown in the schematic diagram, arbitrary linear polarization can be decomposed into two linear polarizations of Ex and Ey. Each discrete unit cell generates a phase delay by excitation of the plasmon resonance, causing the electric field components in the two directions to be interchanged. And the tilted approximate trapezoids have geometric structure changes in both x- and y-axis, so that phase gradient can be generated in both directions. A single unit cell can achieve polarization conversion, and the dimensional changes bring about linear phase change in two orthogonal directions to reflect anomalously. Thus, the metasurface combines modulation of the polarization state and propagation direction, while achieving polarization complementary conversion and anomalous reflection.
Fig. 7. (a) The diagram of the complementary conversion of the polarization angle by the metasurface. (b) The schematic diagram of the principle of complementary conversion and anomalous reflection realized by metasurface.
To verify the polarization conversion performance of the metasurface, we calculated the total reflectance, the reflectance in the x-direction and the reflectance in the y-direction, respectively. From the theoretical analysis, the relation of the electric field components before incidence satisfies |Ey/Ex|=tanα. After complementary conversion, the relation of the electric field components at target diffraction order should satisfy |Ey/Ex|=cotα. As shown in Fig. 8(a), the change in polarization angles has little effect on the total reflectance of the target diffraction order, and the average reflectance remains around 0.87. Figures 8(b) and 8(c) show that Rx= |rx|2 and Ry=|ry|2 maintain opposite trends as the polarization angles change from 0° to 90°. The sum of Rx and Ry is equal to the total reflectance on the +1st diffraction order. In order to observe the proportional relationship between the two orthogonal components after reflection, the values of the electric field components Ex and Ey were calculated separately for different polarization angles. We are mainly interested in the comparison and the ratio relationship between the two electric field component values and therefore visualize them in Fig. 8(d). The values of |Ex| and |Ey| are expressed by the area of the red region and the blue region. As can be seen in Fig. 8(d), the areas of the two colors are interchanged after the reflection from the metasurface, proving that the two electric field components undergo polarization conversion respectively. And the ratios of |Ex| and |Ey| before and after reflection satisfy the proportional relationship of |Ey/Ex|=tanα and |Ey/Ex|=cotα. Therefore, we can conclude that the two components Ex and Ey are transformed orthogonally in proportion to each other, and this result proves that the metasurface can perform complementary conversion of the polarization angle of the incident light.
Fig. 8. (a) Total reflectance |r|2, (b) reflectance in the x-direction |rx|2 and (c) reflectance in the y-direction |ry|2 at the +1st diffraction order. (d) The areas of the red and blue regions indicate the values of the electric field components Ex and Ey. The incident and reflected polarization angles correspond to each other, such as 0° and 90°, 10° and 80°. The incident wavelength ranges from 1400 nm to 1800 nm.
4. Conclusions
In conclusion, we propose a high-efficient polarization-independent metasurface based on GSP resonance in the near-infrared range. Broadband polarization conversion and anomalous reflection are achieved when the linearly polarized light with arbitrary polarization angle is illuminated. The unit cell of the polarization converter has a cross-polarized reflectivity of 90% and PCR of 95% in a wavelength band from 1200nm to 2000nm. Adjusting the size of nanobricks modulating the operating bandwidth while ensuring a high conversion efficiency. We use double-phase modulation method to control the phase of cross-polarized reflected light and separate out the cross-polarized light. The results show that the metasurface reflects the pure cross-polarized light at the +1st diffraction order in the 400nm bandwidth and keeps a reflection efficiency of more than 80%. The dimensional changes of nanobricks l1 and l2 bring degrees of freedom in both orthogonal directions of the phase change, which enables polarization-independent capability of the metasurface. Further analysis reveals that metasurface can achieve efficient anomalous reflection and polarization angle complementary conversion when the incident light of any polarization angle is irradiated. The proposed metasurface can maintain high efficiency over a wide bandwidth and can be easily generalized to other bandwidths. It provides a new idea for miniaturization and integration of polarization conversion systems.
Funding
National Key Research and Development Program of China (2016YFA0301300); National Natural Science Foundation of China (61875021); Beijing Municipal Natural Science Foundation (2192036); Fundamental Research Funds for the Central Universities; Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing, Guilin University of Electronic Technology.
Disclosures
The authors declare no conflicts of interest.
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.
Supplemental document
See Supplement 1 for supporting content.
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