Arbitrary Polarization-Independent Backscattering or Reflection by Rotationally-Symmetric Reciprocal Structures

TL;DR

This paper demonstrates that rotational symmetry in reciprocal structures guarantees polarization-independent backscattering and reflection invariance, with potential applications in stable photonic devices.

Contribution

It reveals that n-fold rotational symmetry ensures invariant backscattering and reflection for polarized waves, independent of structure parameters, and extends to transmission and absorption with added symmetries.

Findings

n-fold rotational symmetry guarantees backscattering invariance

Reflection invariance applies to periodic structures without losses

Additional symmetries ensure transmission and absorption invariance with losses

Abstract

We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further demonstrated that the same principle is also applicable for infinite periodic structures in terms of reflection, which simultaneously guarantees the transmission invariance if there are neither Ohmic losses nor extra diffraction channels. At the presence of losses, extra reflection symmetries (with reflection planes either parallel or perpendicular to the incident direction) can be incorporated to ensure simultaneously the invariance of transmission and absorption. The principles we have revealed are protected by fundamental laws of reciprocity and parity conservation, which are fully independent of the optical or geometric parameters of the photonic structures. The optical invariance obtained is intrinsically robust against perturbations that preserve reciprocity and the geometric symmetries, which could be widely employed for photonic applications that require stable backscatterings or reflections.