Revisiting the optical $PT$-symmetric dimer

Abstract

Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\mathcal{P}\mathcal{T}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar $N$-waveguide couplers that are the optical realization of Lorentz group in 2+1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of Ehrenfest theorem.

25 pages, 12 figures

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• Nonlinear PT-symmetric plaquettes
• Discrete solitons and scattering of lattice waves in guiding arrays with a nonlinear $\mathcal{P}\mathcal{T}$-symmetric defect
• Nonlinear multi-core waveguiding structures with balanced gain and loss
• Tunable waveguide lattices with non-uniform parity-symmetric tunneling

Cited by in corpus (13)

• $\mathcal{P}\mathcal{T}$-symmetry from Lindblad dynamics in an optomechanical system
• Symmetry in optics and photonics: a group theory approach
• Symmetric supermodes in cyclic multicore fibers
• Polarization dynamics in twisted fiber amplifiers: a non-Hermitian nonlinear dimer model
• Photon propagation through linearly active dimers
• Generating high-order exceptional points in coupled electronic oscillators using complex synthetic gauge fields
• Optical non-Hermitian para-Fermi oscillators
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• An attractor dynamics in a non-Hermitian two-level system
• Lasing in para-Fermi class-B microring resonator arrays
• Non-Hermitian coherent states for finite-dimensional systems
• Classical Hamiltonian Systems with Balanced loss and gain
• Reconfigurable multiport switch in coupled mode devices