Talbot self-imaging in $\mathcal{P}\mathcal{T}$-symmetric complex crystals

Abstract

The Talbot effect, i.e. the self-imaging property of a periodic wave in near-field diffraction, is a remarkable interference phenomenon in paraxial systems with continuous translational invariance. In crystals, i.e. systems with discrete translational invariance, self-imaging has been regarded so far as a seldom effect, restricted to special sets of initial field distributions. Here it is shown that in a class of gapless $\mathcal{P}\mathcal{T}$-symmetric complex crystals at the symmetry breaking threshold Talbot revivals can arise for almost any initial periodic wave distribution which is commensurate with the lattice period. A possible experimental realization of commensurate Talbot self-imaging for light pulses in complex 'temporal' crystals, realized in an optical dispersive fiber loop with amplitude and phase modulators, is briefly discussed.

11 pages, 5 figure

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• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Quantum wave packet revivals
• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• Invisibility in PT-symmetric complex crystals
• Spectral singularities and Bragg scattering in complex crystals
• Complex periodic potentials with real band spectra
• PT-Symmetric Talbot Effects
• PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
• The plasmon Talbot effect
• Spectral Singularities, Biorthonormal Systems, and a Two-Parameter Family of Complex Point Interactions
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• Spectral singularities in PT-symmetric periodic finite-gap systems
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• The energy spectrum of complex periodic potentials of the Kronig-Penney type
• Supersymmetry generated one-way invisible PT-symmetric optical crystals
• SUSY transformations between digonalizable and non-diagonalizable Hamiltonians
• Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
• Scattering cross section resonance originating from a spectral singularity
• Complex Periodic Potentials with a Finite Number of Band Gaps
• SUSY transformations with complex factorization constants. Application to spectral singularities
• Subwavelength fractional Talbot effect in layered heterostructures of composite metamaterials

Cited by in corpus (9)

• Bloch-like waves in random-walk potentials based on supersymmetry
• Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric quantum rotator
• $\mathcal{P}\mathcal{T}$-symmetric mode-locking
• Bloch oscillations in non-Hermitian lattices with trajectories in complex plane
• Quantum decay and amplification in a non-Hermitian unstable continuum
• Anyonic $\mathcal{P}\mathcal{T}$ symmetry, drifting potentials and non-Hermitian delocalization
• Target decoupling in a coupled optical system resistant to random perturbation
• Non-Hermitian Multimode Interference
• Localization of states, Bloch wave and quantum phase transitions in SUSY deformed potentials in non-Hermitian optical systems