$\mathcal{P}\mathcal{T}$ symmetry and anti-symmetry by anti-Hermitian wave coupling and nonlinear optical interactions

Abstract

Light propagation in systems with anti-Hermitian coupling, described by a spinor-like wave equation, provides a general route for the observation of anti parity-time ($\mathcal{P}\mathcal{T}$ ) symmetry in optics. Remarkably, under a different definition of parity operator, a $\mathcal{P}\mathcal{T}$ symmetry can be found as well in such systems. Such symmetries are ubiquitous in nonlinear optical interactions and are exemplified by considering modulation instability in optical fibers and optical parametric amplification.

arXiv comment5 pages, 2 figures, to appear in Optics Letters

References in corpus (17)

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• Parametric instability of non-Hermitian systems near the exceptional point
• Dissipatively Coupled Waveguide Networks for Coherent Diffusive Photonics
• Exceptional points and photonic catastrophe
• Dispersive properties of quasi-phase-matched optical parametric amplifiers
• $CPT$-symmetric coupler with intermodal dispersion

Cited by in corpus (7)

• Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits
• Anti-Parity-Time Symmetric Optical Four-Wave Mixing in Cold Atoms
• Anti-$\mathcal{P}\mathcal{T}$-symmetric Kerr gyroscope
• Non-Hermitian dynamics and $\mathcal{P}\mathcal{T}$-symmetry breaking in interacting mesoscopic Rydberg platforms
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Non-Hermiticity in quantum nonlinear optics through symplectic transformations
• Anyonic $\mathcal{P}\mathcal{T}$ symmetry, drifting potentials and non-Hermitian delocalization