PT-symmetry in optics beyond the paraxial approximation

TL;DR

This paper explores PT-symmetry in optics beyond the paraxial approximation, demonstrating that PT symmetry can remain unbroken or be restored in deeply subwavelength structures with balanced gain and loss, depending on the scale.

Contribution

It extends PT-symmetry analysis beyond the paraxial approximation by solving Maxwell's equations in subwavelength structures, revealing symmetry restoration phenomena.

Findings

PT symmetry can stay unbroken in subwavelength structures.

PT symmetry can be restored after initial breaking.

Critical gain/loss levels depend on the structure's scale.

Abstract

The concept of the PT-symmetry, originating from the quantum field theory, has been intensively investigated in optics, stimulated by the similarity between the Schr\"odinger equation and the paraxial wave equation that governs the propagation of light in a guiding structure. We go beyond the bounds of the paraxial approximation and demonstrate, using the solution of the Maxwell's equations for light beams propagating in deeply subwavelength waveguides and periodic lattices with "balanced" gain and loss, that the PT symmetry may stay unbroken in this setting. Moreover, the PT-symmetry in subwavelength optical structures may be restored after being initially broken upon the increase of gain and loss. Critical gain/loss levels, at which the breakup and subsequent restoration of the PT symmetry occur, strongly depend on the scale of the structure.