# Realization of complex conjugate media using non-PT-symmetric photonic crystals

## TL;DR

This paper demonstrates that non-PT-symmetric photonic crystals with Dirac-like dispersions can have real spectra and behave as complex conjugate media, expanding the understanding of non-Hermitian photonic systems beyond PT-symmetry.

## Contribution

It introduces a class of non-PT-symmetric photonic crystals with real spectra and effective complex conjugate media behavior, supported by a non-Hermitian Hamiltonian and effective medium theories.

## Key findings

- Non-PT-symmetric photonic crystals can exhibit real spectra with zero average non-Hermiticity.
- Such crystals behave like complex conjugate media with real refractive index.
- Lasing phenomena are observed in the effective medium regime.

## Abstract

While parity-time (PT)-symmetric systems can exhibit real spectra in the exact PT-symmetry regime, the PT-symmetry is actually not a necessary condition for the real spectra. Here we show that non-PT-symmetric photonic crystals carrying Dirac-like cone dispersions can always exhibit real spectra as long as the average non-Hermiticity strength within the unit cell for the eigenstates is zero. By building a non-Hermitian Hamiltonian model, we find that the real spectra of the non-PT-symmetric system can be explained using the concept of pseudo-Hermiticity. We demonstrate using effective medium theories that in the long-wavelength limit, such non-PT-symmetric photonic crystals behave like the so-called complex conjugate medium (CCM) whose refractive index is real but whose permittivity and permeability are complex numbers. The real refractive index for this effective CCM is guaranteed by the real spectrum of the photonic crystals and the complex permittivity and permeability comes from the non-PT-symmetric loss-gain distributions. We show some interesting phenomena associated with the CCM, such as the lasing effect.

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Source: https://tomesphere.com/paper/1908.04492