Mode pairs in $\mathcal{PT}$-symmetric multimode waveguides

TL;DR

This paper investigates mode pairing and symmetry-breaking phenomena in $ ext{PT}$-symmetric multimode optical waveguides, revealing how modes evolve and pair under varying gain/loss levels, with implications for waveguide design.

Contribution

It introduces the concept of mode pairs in $ ext{PT}$-symmetric waveguides and describes their behavior and symmetry-breaking characteristics as gain/loss parameters change.

Findings

Mode pairs form between modes of successive orders.

Modes experience simultaneous $ ext{PT}$ symmetry breaking.

New modes emerge and pair with existing modes as gain/loss increases.

Abstract

We study mode properties in multimode optical waveguides with parity-time($\mathcal{PT}$) symmetry. We find that two guiding modes with successive orders 2\emph{m}-1 and 2\emph{m} form a mode pair in the sense that the two components of the pair evolve into the same mode when the loss and gain coefficient increases to some critical values, and they experience $\mathcal{PT}$ symmetry breaking simultaneously. For waveguides that in their conservative limit support an odd number of guiding modes, a new mode with a proper order emerges upon the increase of the gain/loss level, so that it pairs with the already existing highest-order mode and then break their $\mathcal{PT}$ symmetry simultaneously. Depending on the specific realizations of $\mathcal{PT}$-symmetric potentials, higher-order mode pair may experience symmetry breaking earlier or later than the lower-order mode pairs do.