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Nonlinear modes in finite-dimensional PT-symmetric systems
1Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal.
Physical Review Letters
|September 26, 2012
Summary
Parity-time (PT) symmetry transformations preserve linear spectra but alter nonlinear properties in waveguide arrays. Linear equivalence does not guarantee similar nonlinear mode structures or stability, even with PT symmetry.
Area of Science:
- Nonlinear optics
- Quantum mechanics
- Photonics
Background:
- Parity-time (PT) symmetry in physical systems
- Waveguide arrays and discrete nonlinear Schrödinger equation
- Gain and loss mechanisms in optical systems
Purpose of the Study:
- Investigate the impact of PT symmetry transformations on nonlinear properties of waveguide arrays.
- Determine if linear spectral equivalence implies similarity in nonlinear mode structure and stability.
- Explore the relationship between PT symmetry and the existence and stability of nonlinear modes.
Main Methods:
- Simulating transformations among PT-symmetric waveguide arrays.
- Analyzing systems described by the discrete nonlinear Schrödinger equation with gain and dissipation.
- Utilizing a graph representation for PT-symmetric networks.
Main Results:
- Transformations preserving linear spectra significantly change nonlinear properties.
- Linear spectral equivalence does not ensure similar nonlinear mode structure or stability.
- PT symmetry does not guarantee the existence of nonlinear mode families or directly relate to stability; stable modes can exist outside pure real spectra.
Conclusions:
- Nonlinear behaviors in PT-symmetric systems are not solely dictated by their linear spectral properties.
- Experimental designs for PT-symmetric networks can be simplified using graph representations.
- Further research is needed to fully understand the interplay between PT symmetry and nonlinear dynamics.
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