Phase transition through the splitting of self-dual spectral singularity in optical potentials

Abstract

We consider optical media which feature antilinear symmetries. We show that: (i) spectral singularities of such media (if any) are always self-dual, i.e., correspond to CPA-lasers; (ii) under the change of a system's parameter the self-dual spectral singularity may split into a pair of isolated complex conjugate eigenvalues, which corresponds to an unconventional and overlooked in the most of previous studies scenario of the phase transition (known as $PT$-symmetry breaking in systems obeying parity-time symmetry); (iii) if the antilinear symmetry is local, i.e., does not involve any spatial reflection, then no spectral singularity is possible. Our findings are illustrated with several examples including a $PT$-symmetric bilayer and other complex potentials discussed in recent literature.

5 pages, 2 figures; submitted

References in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• Coherent Perfect Absorbers: Time-reversed Lasers
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• New classes of non-parity-time-symmetric optical potentials with all-real spectra and exceptional-point-free phase transition

Cited by in corpus (9)

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• A universal form of complex potentials with spectral singularities
• Metastable two-component solitons near an exceptional point
• Spectral singularities of a potential created by two coupled microring resonators
• Construction of potentials with multiple spectral singularities
• Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields
• Construction of non-PT-symmetric complex potentials with all-real spectra