Simultaneous Generation of Arbitrary Assembly of Polarization States with Geometrical-Scaling-Induced Phase Modulation

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Simultaneous Generation of Arbitrary Assembly of Polarization States with Geometrical-Scaling-Induced Phase Modulation

Ya-Jun Gao, Xiang Xiong, Zhenghan Wang, Fei Chen, Ru-Wen Peng, and Mu Wang

Phys. Rev. X 10, 031035 – Published 13 August 2020

Abstract

Manipulating the polarization of light on the microscale or nanoscale is essential for integrated photonics and quantum optical devices. Nowadays, the metasurface allows one to build on-chip devices that efficiently manipulate the polarization states. However, it remains challenging to generate different types of polarization states simultaneously, which is required to encode information for quantum computing and quantum cryptography applications. By introducing geometrical-scaling-induced (GSI) phase modulations, we demonstrate that an assembly of circularly polarized ( $C P$ ) and linearly polarized (LP) states can be simultaneously generated by a single metasurface made of $L$ -shaped resonators with different geometrical features. Upon illumination, each resonator diffracts the $C P$ state with a certain GSI phase. The interaction of these diffractions leads to the desired output beams, where the polarization state and the propagation direction can be accurately tuned by selecting the geometrical shape, size, and spatial sequence of each resonator in the unit cell. As an example of potential applications, we show that an image can be encoded with different polarization profiles at different diffraction orders and decoded with a polarization analyzer. This approach resolves a challenging problem in integrated optics and is inspiring for on-chip quantum information processing.

Received 25 June 2019
Revised 18 May 2020
Accepted 18 June 2020

DOI:https://doi.org/10.1103/PhysRevX.10.031035

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Metamaterials Photonics Plasmonics

Atomic, Molecular & Optical

Authors & Affiliations

Ya-Jun Gao ^1,‡, Xiang Xiong^1,‡, Zhenghan Wang¹, Fei Chen ¹, Ru-Wen Peng ^1,*, and Mu Wang ^1,2,†

¹National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
²American Physical Society, Ridge, New York 11961, USA

^*Corresponding author. rwpeng@nju.edu.cn
^†Corresponding author. muwang@nju.edu.cn
^‡Y.-J. G. and X. X. contributed equally to this work.

Popular Summary

Simultaneously generating combinations of circularly and linearly polarized states of light is crucial to encode information for some well-known protocols used in quantum cryptography and quantum communication. The current solution for generating these states involves bulky optical components that are unusable for on-chip applications. While metasurfaces may be an effective way to manipulate light-polarization states, none of the metasurfaces engineered so far have been able to generate different types of polarization states simultaneously. To solve this problem, we have developed a new metasurface design strategy, i.e., geometrical-scaling-induced phase modulation, which can generate a combination of any type of polarization states on the fly.

The unit cell in our metasurface design consists of $L$ -shaped resonators with different geometries combined with their mirror-image counterparts. Depending on the category and spatial arrangement of the resonators in the unit cell, the metasurface can generate any desired combination of left- and right-handed circularly polarized states as well as linearly polarized states with different orientations.

We experimentally demonstrate that an image can be encoded with different polarization profiles at different diffraction orders and be decoded with a polarization analyzer. The encoding and decoding process resembles the secret key distribution in quantum cryptography via the polarization of photons. This study provides a new perspective in generating an assembly of nonorthogonal polarization states. Hence, it can be directly applied for a nanophotonics device light in weight and high in integration degree and is inspiring for portable quantum cryptography and on-chip quantum information processing.

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Vol. 10, Iss. 3 — July - September 2020

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Images

Figure 1
Schematics showing the generation of multiple coherent beams with a different type of polarization state from a metasurface made of $L$ -shaped resonators with different geometrical features. The LP incident beam is represented by the purple arrow. Each resonator diffracts a $C P$ state with a certain GSI phase $ϕ$ . By controlling the category and the spatial sequence of the $L$ -shaped resonators in the unit cell, the desired $C P$ (the red clockwise arrow represents RCP, and the blue counterclockwise one represents LCP) and/or LP (illustrated by the large straight arrows) beams can be simultaneously generated. The resonators $P_{j}$ $(j = 1, 2, \dots, 8)$ form the unit cell of the metasurface. The resonators are selected from the pool ${S_{i}}$ and ${S_{i}^{'}}$ $(i = 1, 2, \dots, 8)$ . The resonators in ${S_{i}}$ generate RCP, and those from ${S_{i}^{'}}$ generate LCP, as illustrated in the lower panel.
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Figure 2
Simulation results of 16 $L$ -shaped resonators ( $S_{1}, S_{2}, \dots, S_{8}$ and $S_{1}^{'}, S_{2}^{'}, \dots, S_{8}^{'}$ ), where the $x$ -polarized incident light propagates in the $- z$ direction, and the wavelength is 1300 nm. (a) The simulated reflectance ratio of the $y$ component and the $x$ component of eight resonators in ${S_{i}}$ $(i = 1, 2, \dots, 8)$ . (b) The simulated reflectance ratio of the $y$ component to the $x$ component of eight resonators in ${S_{i}^{'}}$ $(i = 1, 2, \dots, 8)$ . (c) The simulated reflected phase difference between the $y$ and $x$ components of eight resonators in ${S_{i}}$ $(i = 1, 2, \dots, 8)$ . (d) The simulated reflected phase difference between the $y$ and $x$ components of eight resonators in ${S_{i}^{'}}$ $(i = 1, 2, \dots, 8)$ . (e) The simulated GSI phase $ϕ$ added to the diffracted state from the elements in ${S_{i}}$ $(i = 1, 2, \dots, 8)$ . (f) The simulated GSI phase $ϕ$ added to the diffracted state from the elements in ${S_{i}^{'}}$ $(i = 1, 2, \dots, 8)$ .
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Figure 3
GSI phase $ϕ$ and the handedness (represented by the red or blue dots) of each resonator in the unit cell. The metasurface and the unit cell are illustrated on the right. In the unit cell, the geometrical features of each resonator vary. (a) $ϕ$ of eight resonators all selected from ${S_{i}}$ with a linear phase gradient. The output is an RCP state. (b) $ϕ$ of eight resonators, four from ${S_{i}}$ and four from ${S_{i}^{'}}$ . The metasurface generates four LP states. (c) $ϕ$ of another set of eight resonators selected from ${S_{i}}$ and ${S_{i}^{'}}$ , respectively. The output is two $C P$ and two LP states.
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Figure 4
(a) SEM micrograph of the fabricated metasurface as designed in Fig. 3. The unit cell is marked by the dashed-line box. The bar represents $1 μ m$ . (b) Measured angle-resolved diffraction spectra. The four bright lines represent the diffracted beams measured at a different wavelength at different diffraction angles. The color bar stands for the intensity. (c) Normalized beam intensity of four diffracted beams. Note that $I_{pol, num}$ represents the intensity of “num-th” order, with “pol” polarization. In the wavelength range of 1200–1350 nm, the normalized intensity of each diffraction beam is higher than 10%. At 1300 nm, the intensity of each diffraction order is higher than 12%, and the total normalized diffraction intensity reaches 65%. (d) Measured light intensity ratio of each beam, which is defined as the intensity of the measured LP (CP) beam divided by the intensity of its orthogonal (conjugated) beam. The intensity ratio of each beam is larger than 10 for the wavelength between 1200 nm and 1275 nm, and the maximum reaches 168 at 1260 nm.
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Figure 5
(a) SEM micrograph of the fabricated metasurface as designed in Fig. 3. The unit cell is marked by the dashed-line box. The bar stands for $1 μ m$ . (b) Measured angle-resolved diffraction spectra. Four bright lines represent the diffracted beams measured at a different wavelength at different diffraction angles. The color bar stands for the intensity. (c) Normalized beam intensity of four diffracted beams. Here, $I_{pol, num}$ represents the intensity of “num-th” order with “pol” polarization. Within the wavelength range of 1200–1325 nm, the normalized intensity of each diffracted beam is higher than 8%. At 1275 nm, the intensity of each diffraction beam is higher than 16%, and the total normalized intensity reaches 68%. (d) Measured light intensity ratio of each diffracted beam, which is defined as the intensity of the measured LP (CP) beam divided by the intensity of its orthogonal (conjugated) beam. The intensity ratio of each beam is larger than 10 for the wavelength between 1210 nm and 1300 nm, and the maximum reaches 76 at 1225 nm.
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Figure 6
(a) Schematic of the overlapped circle and square, where three regions (1, 2, and 3) can be identified. These regions are selected for polarization encoding. (b) Morphology of three types of unit cells ${S 1}$ , ${S 2}$ , and ${S 3}$ and the corresponding polarization states appearing at diffraction orders $- 3$ , $- 1$ , $+ 1$ , and $+ 3$ , respectively. Three different sequences are designated to regions 1, 2, and 3, respectively. The incident beam is $x$ polarized. The green and yellow straight arrows represent the $- 45 °$ -LP and $+ 45 °$ -LP states. The blue counterclockwise (red clockwise) arrow represents the LCP (RCP) state. (c) Micrograph of the fabricated pattern. The bar represents $100 μ m$ . (d) SEM micrograph of the unit cell designated to regions 1, 2, and 3, respectively. The bar represents $1 μ m$ . (e) Diffraction images at orders $- 3$ , $- 1$ , $+ 1$ , and $+ 3$ visualized by the CCD camera. Four types of analyzers are put in front of the CCD, respectively, which is represented by the colored symbols on the left side. Two linear polarized analyzers are oriented at the $- 45 °$ (green arrow) and 45° (yellow arrow) directions, and two circular polarized analyzers are for RCP (red circle) and LCP (blue circle), respectively. Three different shades—bright, dark, and grey—appear at different regions depending on the selection of the analyzer.
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