Meta-$\mathcal{PT}$ Symmetry in Asymmetric Directional Couplers

TL;DR

This paper explores asymmetric directional couplers that, despite lacking strict parity-time symmetry, can exhibit PT-like behavior through specific gain-loss conditions and mode matching, broadening design possibilities in integrated optics.

Contribution

It introduces an analytical condition for gain and loss in asymmetric couplers to mimic PT-symmetric behavior, expanding the design space beyond symmetric structures.

Findings

Asymmetric couplers can exhibit PT-like behavior with proper parameter tuning.

An analytical condition relates gain and loss for PT-like behavior.

Matching propagation constants of waveguides enhances PT-like mode behavior.

Abstract

Despite the benefits that directional coupler based parity-time symmetric systems may offer to the field of integrated optics, the realization of such couplers relies on rather strict design constraints on the waveguide parameters. Here, we investigate directional couplers built of asymmetric waveguides that do not fulfill parity-time symmetry. Nevertheless, we demonstrate that for properly designed parameters, at least one mode of such couplers shows a behavior similar to the one observed in parity-symmetric systems. We find an analytical condition relating gain and loss that enables such a behavior. Moreover, if the individual waveguides composing the asymmetric coupler are designed such that the propagation constants of their modes are identical, the behavior of both super-modes supported by the coupler resembles that of the parity-time symmetric systems.