PT-symmetry in optics beyond the paraxial approximation

Abstract

The concept of the PT-symmetry, originating from the quantum field theory, has been intensively investigated in optics, stimulated by the similarity between the Schrödinger equation and the paraxial wave equation that governs the propagation of light in a guiding structure. We go beyond the bounds of the paraxial approximation and demonstrate, using the solution of the Maxwell's equations for light beams propagating in deeply subwavelength waveguides and periodic lattices with "balanced" gain and loss, that the PT symmetry may stay unbroken in this setting. Moreover, the PT-symmetry in subwavelength optical structures may be restored after being initially broken upon the increase of gain and loss. Critical gain/loss levels, at which the breakup and subsequent restoration of the PT symmetry occur, strongly depend on the scale of the structure.

arXiv comment5 pages, 7 figures, to appear in Optics Letters

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Cited by in corpus (16)

• Non-Hermitian Physics
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
• Parity-time symmetry in optical microcavity systems
• Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential
• PT-symmetric phase in kagome photonic lattices
• Low-power optical bistability in $\mathcal{P}\mathcal{T}$-symmetric chirped Bragg gratings with four-wave mixing
• Analysis of unidirectional non-paraxial invisibility of purely reflective PT-symmetric volume gratings
• Phase transition in PT symmetric active plasmonic systems
• Small-amplitude nonlinear modes under the combined effect of the parabolic potential, nonlocality and $\mathcal{P}\mathcal{T}$ symmetry
• Superoscillatory PT-symmetric potentials
• Making the PT symmetry unbreakable
• Dipole and quadrupole nonparaxial solitary waves
• Nonparaxial electromagnetic Bragg scattering in periodic media with PT symmetry
• On the integrability aspects of nonparaxial nonlinear Schrödinger equation and the dynamics of solitary waves