Extremize Optical Chiralities through Polarization Singularities

TL;DR

This paper introduces a systematic approach to extremize optical chiralities in photonic structures by analyzing polarization singularities and mode topologies, revealing conditions for maximal or minimal chiral responses.

Contribution

It develops a novel framework linking polarization singularities and quasi-normal modes to control and extremize optical chirality in photonic structures.

Findings

Singularity directions enable ideal chirality maximization or minimization.

Intrinsic structures can exhibit no chirality or opposite chirality depending on incident direction.

The framework applies to both finite and infinite photonic structures.

Abstract

Chiral optical effects are generally quantified along some specific incident directions of exciting waves (especially for extrinsic chiralities of achiral structures) or defined as direction-independent properties by averaging the responses among all structure orientations. Though of great significance for various applications, chirality extremization (maximized or minimized) with respect to incident directions or structure orientations have not been explored, especially in a systematic manner. In this study we examine the chiral responses of open photonic structures from perspectives of quasi-normal modes and polarization singularities of their far-field radiations. The nontrivial topology of the momentum sphere secures the existence of singularity directions along which mode radiations are either circularly or linearly polarized. When plane waves are incident along those directions, the reciprocity ensures ideal maximization and minimization of optical chiralities, for corresponding mode radiations of circular and linear polarizations respectively. For directions of general elliptical polarizations, we have unveiled the subtle equality of a Stokes parameter and the circular dichroism, showing that an intrinsically chiral structure can unexpectedly exhibit no chirality at all or even chiralities of opposite handedness for different incident directions. The framework we establish can be applied to not only finite scattering bodies but also infinite periodic structures, encompassing both intrinsic and extrinsic optical chiralities. We have effectively merged two vibrant disciplines of chiral and singular optics, which can potentially trigger more optical chirality-singularity related interdisciplinary studies.