Passive $\mathcal{PT}$-symmetric couplers without complex optical potentials

TL;DR

This paper demonstrates that passive $ ext{PT}$-symmetric optical couplers can be realized without complex potentials by using a unitarily equivalent Hamiltonian, enabling simpler implementation with real refractive indices and asymmetric couplings.

Contribution

It introduces a method to implement passive $ ext{PT}$-symmetric systems without complex optical potentials using operator algebra and unitarily equivalent Hamiltonians.

Findings

Passive $ ext{PT}$-symmetric couplers can be realized with real refractive indices.

Implementation does not require active gain and loss control.

Potential for practical realization with existing optical components.

Abstract

In addition to the implementation of parity-time ($\mathcal{PT}$)-symmetric optical systems by carefully and actively controlling the gain and loss, we show that a $2\times 2$ $\mathcal{PT}$-symmetric Hamiltonian has a unitarily equivalent representation without complex optical potentials in the resulting optical coupler. Through the Naimark dilation in operator algebra, passive $\mathcal{PT}$-symmetric couplers can thus be implemented with a refractive index of real values and asymmetric coupling coefficients. This opens up the possibility to implement general $\mathcal{PT}$-symmetric systems with state-of-the-art asymmetric slab waveguides, dissimilar optical fibers, or cavities with chiral mirrors.