Low-symmetry lattices of non-chiral meta-atoms for resonant handedness-preserving reflection

Technical Summary: Low-symmetry lattices of non-chiral meta-atoms for resonant handedness-preserving reflection

Problem Statement
Optical mirrors that preserve the handedness (spin) of circularly polarized radiation upon reflection are critical for designing resonant nanophotonic structures capable of enantiomeric discrimination, such as handedness-preserving (HP) cavities for chiral media. Conventional metallic and Bragg dielectric mirrors are unsuitable for this purpose as they flip the handedness of the electromagnetic field upon reflection at normal incidence. While previous approaches utilizing complex chiral metasurfaces have shown promise, they often require the fabrication of intricate geometries that introduce significant uncertainty. There is a need for simpler design strategies that utilize high-symmetry, non-chiral meta-atoms to achieve HP reflection through lattice symmetry engineering alone.

Methodology
The authors present a detailed numerical and theoretical analysis of low-symmetry periodic lattices composed of high-symmetry, non-chiral meta-atoms (specifically circular dielectric disks and holes). The study focuses on two lattice symmetries:

1. Rhombic lattices ($C_{2v}$ or $D_{2h}$ symmetry): These possess a vertical mirror plane, ensuring equal reflection efficiencies for right-handed-to-right-handed ($r_{RR}$) and left-handed-to-left-handed ($r_{LL}$) conversion.
2. Monoclinic (oblique) lattices ($C_2$ or $C_{2h}$ symmetry): These lack a vertical mirror plane, enabling asymmetric reflection where only one handedness is preserved (e.g., $r_{RR} \approx 1$ and $r_{LL} \approx 0$).

The analysis employs full-wave numerical simulations using the Fourier Modal Method (FMM) with quasi-Newtonian optimization to maximize the HP intensity reflection coefficient ($|r_{RR}|^2$) or a handedness-selective figure of merit (FoM). The study investigates three specific geometries:

• Arrays of circular disks in air.
• Arrays of circular disks on a dielectric substrate.
• Arrays of circular holes within a dielectric membrane.

The robustness of these structures is evaluated against geometric deviations, material losses (complex permittivity), and oblique incidence. Furthermore, the resonant mechanisms are analyzed using the temporal coupled-mode theory (CMT) formalism, specifically modeling the interaction of two quasi-normal modes (QNMs) of opposite parity coupled to scattering channels.

Key Results

• Rhombic Lattices: The study demonstrates that rhombic lattices of circular disks or holes can achieve near-perfect HP reflection ($|r_{RR}|^2 \approx 1$) at normal incidence within the sub-diffraction regime. The response is robust against geometric variations, particularly in the case of circular holes in a dielectric membrane. The resonant behavior is governed by a dense collection of QNMs, which can be effectively described by a two-mode CMT model involving TE- and TM-polarized guided modes that undergo Brillouin zone folding to become nearly degenerate.
• Monoclinic Lattices: By lowering the symmetry to monoclinic (oblique) lattices, the authors achieve asymmetric HP reflection, where one circular polarization is nearly perfectly reflected while the other is transmitted. The optimal monoclinic array of circular holes in a membrane achieves a FoM of approximately 0.93–0.96. Similar to the rhombic case, this response is driven by two nearly-degenerate QNMs of opposite parity, describable by a modified two-mode CMT model.
• Material and Geometric Robustness: Near-unity HP performance is maintained for materials with low absorption (e.g., BN, Si$_3$N$_4$, TiO$_2$ in the near-IR). The hole-in-membrane geometry proves more robust and converges faster in simulations compared to disk arrays.
• Angular Dependence: The study reveals a pronounced dependence of the HP response on the angle of incidence. The monoclinic array of holes exhibits particularly strong angular sensitivity due to high Q-factors (>300) and the dispersion of folded guided modes. In contrast, the monoclinic array of disks shows the least angular dependence among the tested structures.

Significance and Claims
The paper claims to provide a new class of structures and design rules for HP metasurface mirrors based on low-symmetry lattices of simple, non-chiral inclusions. The primary significance lies in demonstrating that optical chirality and handedness-preserving reflection can be engineered solely through lattice symmetry (rhombic or monoclinic) without requiring structurally chiral unit cells. This approach offers a simpler alternative to complex chiral metasurfaces, potentially reducing fabrication uncertainty.

The authors conclude that while these structures offer near-perfect HP reflection at normal incidence, the strong angular dependence remains a challenge for broadband and wide-angle applications. They note that while recent work suggests strategies for broadband symmetric HP response, the design of a broadband and wide-angle asymmetric HP metasurface remains an open question. The work establishes a theoretical and numerical foundation for utilizing simple geometric perturbations in non-chiral meta-atoms to control spin-selective reflection.