Supersymmetry-generated complex optical potentials with real spectra

Abstract

We show that the formalism of supersymmetry (SUSY), when applied to parity-time (PT) symmetric optical potentials, can give rise to novel refractive index landscapes with altogether non-trivial properties. In particular, we find that the presence of gain and loss allows for arbitrarily removing bound states from the spectrum of a structure. This is in stark contrast to the Hermitian case, where the SUSY formalism can only address the fundamental mode of a potential. Subsequently we investigate isospectral families of complex potentials that exhibit entirely real spectra, despite the fact that their shapes violate PT-symmetry. Finally, the role of SUSY transformations in the regime of spontaneously broken PT symmetry is investigated.

6 pages, 4 figures

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Cited by in corpus (57)

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• Supersymmetric Optical Structures
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• Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities
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• SUSY-inspired one-dimensional transformation optics
• Wave propagation through disordered media without backscattering and intensity variations
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• All-real spectra in optical systems with arbitrary gain and loss distributions
• Bloch-like waves in random-walk potentials based on supersymmetry
• Stable localized modes in asymmetric waveguides with gain and loss
• Symmetry breaking of solitons in two-dimensional complex potentials
• $PT$-symmetric invisible defects and confluent Darboux-Crum transformations
• Observation of supersymmetric scattering in photonic lattices
• Supersymmetry generated one-way invisible PT-symmetric optical crystals
• Necessity of PT symmetry for soliton families in one-dimensional complex potentials
• Low-dimensional optical chirality in complex potentials
• Peregrine Rogue Wave dynamics in the continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity
• Trends in supersymmetric quantum mechanics
• Stability of soliton families in nonlinear Schroedinger equations with non-parity-time-symmetric complex potentials
• An intensity-dependent quantum Rabi model: Spectrum, SUSY partner and optical simulation
• Symmetry in optics and photonics: a group theory approach
• Revisiting the optical $PT$-symmetric dimer
• New classes of non-parity-time-symmetric optical potentials with all-real spectra and exceptional-point-free phase transition
• PT Meets Supersymmetry and Nonlinearity: An Analytically Tractable Case Example
• Metadisorder for designer light in random-walk systems
• Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry
• Supersymmetry-guided method for mode selection and optimization in coupled systems
• An analysis of the zero energy states in graphene
• Supersymmetric Bragg gratings
• Quantum mechanical analogy and supersymmetry of electromagnetic wave modes in planar waveguides
• Designing lasing and perfectly absorbing potentials
• Mode-division (de)multiplexing using adiabatic passage and supersymmetric waveguides
• Digital building blocks for controlling random waves based on supersymmetry
• Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
• Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential
• Acceleration toward polarization singularity inspired by relativistic ExB drift
• Light propagation in periodically modulated complex waveguides
• On the construction of non-Hermitian Hamiltonians with all-real spectra through supersymmetric algorithms
• Continuous supersymmetric transformations in optical waveguides
• Supersymmetric model of a Bose-Einstein condensate in a $\mathcal{P}\mathcal{T}$-symmetric double-delta trap
• Complex oscillator and Painlevé IV equation
• One-Way Optical Transition based on Causality in Momentum Space
• Complex Supersymmetry in Graphene
• Supersymmetric correspondence in spectra on a graph and its line graph: From circuit theory to spoof plasmons on metallic lattices
• Supersymmetry-enhanced Stark-Chirped Rapid-Adiabatic-Passage in multimode optical waveguides
• High Efficiency Topological Pumping with Discrete Supersymmetry Transformations
• Effects of non-uniform distributions of gain and loss in photonic crystals
• New families of non-parity-time-symmetric complex potentials with all-real spectra
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• Supersymmetric reshaping and higher-dimensional rearrangement of photonic lattices
• Double-sided unidirectional reflectivity
• PT-symmetric transport in non-PT-symmetric bi-layer optical arrays
• A Supersymmetric Approach to the Problem of Micro-bending Attenuation in Optical Waveguides
• Analytical construction of soliton families in one- and two-dimensional nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials
• Localization of states, Bloch wave and quantum phase transitions in SUSY deformed potentials in non-Hermitian optical systems
• Construction of non-PT-symmetric complex potentials with all-real spectra