Optical finite representation of the Lorentz group

Abstract

We present a class of photonic lattices with an underlying symmetry given by a finite-dimensional representation of the 2+1D Lorentz group. In order to construct such a finite-dimensional representation of a non-compact group, we have to design a $\mathcal{P}\mathcal{T}$-symmetric optical structure. Thus, the array of coupled waveguides may keep or break $\mathcal{P}\mathcal{T}$-symmetry, leading to a device that behaves like an oscillator or directional amplifier, respectively. We show that the so-called linear $\mathcal{P}\mathcal{T}$-symmetric dimer belongs to this class of photonic lattices.

11 pages, 4 figures

References in corpus (5)

• Bound states in the continuum in PT-symmetric optical lattices
• Ermakov-Lewis symmetry in photonic lattices
• Gilmore-Perelomov symmetry based approach to photonic lattices
• An introduction to arrays of coupled waveguides
• Propagation and perfect transmission in three-waveguide axially varying couplers

Cited by in corpus (14)

• $\mathcal{P}\mathcal{T}$-symmetry from Lindblad dynamics in an optomechanical system
• Symmetry in optics and photonics: a group theory approach
• Revisiting the optical $PT$-symmetric dimer
• Symmetric supermodes in cyclic multicore fibers
• Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays
• Polarization dynamics in twisted fiber amplifiers: a non-Hermitian nonlinear dimer model
• Necklaces of $\mathcal{P}\mathcal{T}$-symmetric dimers
• All-optical $\mathcal{P}\mathcal{T}$-symmetric amplitude to phase modulator
• Photon propagation through linearly active dimers
• Optical non-Hermitian para-Fermi oscillators
• Phase transitions as a manifestation of spontaneous unitarity violation
• Non-Hermitian coherent states for finite-dimensional systems
• Lasing in para-Fermi class-B microring resonator arrays
• Reconfigurable multiport switch in coupled mode devices