Parity-protected anomalous diffraction in optical phase gradient metasurfaces

Yanyan Cao, Yangyang Fu, Lei Gao, Huanyang Chen, and Yadong Xu

Phys. Rev. A 107, 013509 – Published 13 January 2023

Abstract

Optical phase gradient metasurfaces (PGMs) have provided unprecedented opportunities for arbitrarily controlling wave propagation via the generalized Snell's law (GSL). However, the whole picture of wave diffraction therein has not been clearly presented, particularly for the incident angles beyond the critical angle. Although a parity-dependent diffraction effect was found in acoustic metagratings, little is known about whether this effect holds true in typical optical PGMs. Here we demonstrate the universality of the parity-dependent diffraction effect by employing some optical PGMs with popular designs, such as all-dielectric and plasmonic meta-atoms. It is first shown that the parity in optical PGMs plays a significant role in determining the diffraction physics, producing a robust reversal effect of outgoing waves from the reflection to the transmission side. As an alternative degree of freedom in PGMs, the parity-dependent diffraction effect, together with the GSL, provides a complete theory to manipulate wave fields, further advancing various explorations in unique wave phenomena and promising applications.

Received 18 April 2022
Revised 18 December 2022
Accepted 4 January 2023

DOI:https://doi.org/10.1103/PhysRevA.107.013509

Physics Subject Headings (PhySH)

Metamaterials Optical & microwave phenomena Photonics

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Yanyan Cao¹, Yangyang Fu^3,*, Lei Gao⁴, Huanyang Chen⁵, and Yadong Xu ^1,2,†

¹Institute of Theoretical and Applied Physics, School of Physical Science and Technology, Soochow University, Suzhou 215006, China
²Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China
³College of Physics, Nanjing University of Aeronautics and Astronautics, and Key Laboratory of Aerospace Information Materials and Physics (NUAA), MIIT, Nanjing 211106, China
⁴Department of Photoelectric Science and Energy Engineering, Suzhou City University, Suzhou 215104, China
⁵School of Physics, Xiamen University, Xiamen 361005, China

^*yyfu@nuaa.edu.cn
^†ydxu@suda.edu.cn

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Vol. 107, Iss. 1 — January 2023

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Images

Figure 1
[(a),(b)] Sketch of the phase-gradient metasurfaces (PGMs) with $m$ unit cells which are positioned at the interface between two ordinary media; the phase gradient is $ξ = d Φ / d x$ . For the incident angle below the critical angle (blue incident regions), the incident wave will couple to the transmitted wave (black arrows) of the lowest order [ $n = 1$ in Eq. (1)], corresponding to GSL. For the incident angle beyond the critical angle (gray incident regions), the outgoing wave takes the higher-order diffraction [ $n \leq 0$ in Eq. (1)], with the transmission or reflection (red arrows) depending on the number of unit cells $m$ . (c) Schematic of the types of meta-atoms used to design optical PGMs: propagation phase and resonant phase.
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Figure 2
The parity-dependent phenomena in all-dielectric PGMs. (a) Transmittance variation for the meta-atom and (b) the transmitted phase as a function of nanoblock size $d_{x}$ and $d_{y}$ . Inset is schematic of a high refractive index dielectric nanoblock meta-atom on top of a bulk-fused silica substrate. The height of the nanoblock is $h = 500 nm$ and the lattice constant is $a_{1} = 420 nm$ . In the plots, $A_{1}$ and $A_{2}$ represent the corresponding sizes of two unit cells in the PGM with $m = 2$ ; $B_{1}$ , $B_{2}$ , and $B_{3}$ represent the corresponding sizes of three unit cells in the PGM with $m = 3$ . [(c),(d)] are the simulated total electric field patterns of two PGMs with $m = 2$ ( $ξ_{1} = 1.85 k_{0}$ ) and $m = 3$ ( $ξ_{2} = 1.23 k_{0}$ ) at the normal incidence. [(e),(f)] are the relationships between the transmission and reflection efficiency of the higher diffraction order ( $n = 0$ ) and the incident angle in the two designed PGMs.
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Figure 3
The parity-dependent phenomena in the plasmonic PGMs. [(a),(d)] Numerically calculated transmission amplitude and phase of the unit cells for the plasmonic PGMs with $m = 2$ and $m = 3$ . In both cases, the phase change between every two adjacent unit cells satisfies $2 π / m$ . Insets are 3D illustrations of the designed unit cells for the plasmonic PGMs; the yellow parts are metallic patterns and the blue regions are dielectric spacers. The geometric parameters are obtained from Ref. [31]. [(b),(e)] are simulated total electric field patterns of the two designed PGMs with $m = 2$ ( $ξ_{3} = 2.07 k_{0}$ ) and $m = 3$ ( $ξ_{4} = 1.38 k_{0}$ ) at the normal incidence. [(c),(f)] are the relationships between transmission and reflection efficiency of the higher diffraction order ( $n = 0$ ) and the incident angle in the two designed PGMs.
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Figure 4
[(a),(c)] are the relationships between transmission and reflection of all diffraction orders and the incident angle in the plasmonic PGMs with $m = 2$ and $m = 3$ . (b,d) are simulated total electric field patterns of the plasmonic PGMs with $m = 2$ and $m = 3$ , respectively, at $θ_{in} = - 45^{\circ}$ and $θ_{in} = 45^{\circ}$ . The arrows in the plots represent the propagation directions of incident and reflected or transmitted waves.
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Figure 5
Transient simulations for the plasmonic PGMs with $m = 3$ and the subwavelength uniform plasmonic metasurface with $m = 1$ . The black arrows represent the propagation directions of the incident and transmitted waves, and the working frequency is considered at 10.2 GHz. The time when a snapshot of the fields is taken is marked on the left side of the field patterns. It indicates that the multiple resonance process occurs within the plasmonic PGMs.
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