# Optical fluxes in coupled $\cal PT$-symmetric photonic structures

## TL;DR

This paper investigates flux behaviors in $ ext{PT}$-symmetric photonic structures, revealing classical aspects of $ ext{PT}$ transitions, limitations of power amplification, and unidirectional power transfer, with extensions beyond coupled-mode theory.

## Contribution

It provides new insights into flux dynamics in $ ext{PT}$-symmetric photonic systems, including classical interpretation of $ ext{PT}$ transitions and flux behaviors in complex structures.

## Key findings

- Longitudinal flux shows $ ext{PT}$ transition as a classical effect.
- Giant amplification in $ ext{PT}$ phase is sub-exponential and not superior to single gain waveguide.
- Power transfer can be unidirectional and cannot be arbitrarily fast near exceptional points.

## Abstract

In this work we first examine transverse and longitudinal fluxes in a $\cal PT$-symmetric photonic dimer using a coupled-mode theory. Several surprising understandings are obtained from this perspective: The longitudinal flux shows that the $\cal PT$ transition in a dimer can be regarded as a classical effect, despite its analogy to $\cal PT$-symmetric quantum mechanics. The longitudinal flux also indicates that the so-called giant amplification in the $\cal PT$-symmetric phase is a sub-exponential behavior and does not outperform a single gain waveguide. The transverse flux, on the other hand, reveals that the apparent power oscillations between the gain and loss waveguides in the $\cal PT$-symmetric phase can be deceiving in certain cases, where the transverse power transfer is in fact unidirectional. We also show that this power transfer cannot be arbitrarily fast even when the exceptional point is approached. Finally, we go beyond the coupled-mode theory by using the paraxial wave equation and also extend our discussions to a $\cal PT$ diamond and a one-dimensional periodic lattice.