Superpositions of bright and dark solitons supporting the creation of balanced gain and loss optical potentials
arXiv:1805.00058 · doi:10.1002/mma.6666
Abstract
Bright and dark solitons of the cubic nonlinear Schrodinger equation are used to construct complex-valued potentials with all-real spectrum. The real part of these potentials is equal to the intensity of a bright soliton while their imaginary part is defined by the product of such soliton with its concomitant, a dark soliton. Considering light propagation in Kerr media, the real part of the potential refers to the self-focusing of the signal and the imaginary one provides the system with balanced gain-and-loss rates.
6 figures, 17 pages, LaTeX file. The manuscript has been re-organized (abstract, introduction and conclusions rewritten), and it now includes an appendix with detailed calculations of some relevant results reported in the paper. New references were added
References in corpus (6)
- Stable localized modes in asymmetric waveguides with gain and loss
- Bi-Orthogonal Approach to Non-Hermitian Hamiltonians with the Oscillator Spectrum: Generalized Coherent States for Nonlinear Algebras
- Soliton dynamics in symmetric and non-symmetric complex potentials
- Interplay between Riccati, Ermakov and Schroedinger equations to produce complex-valued potentials with real energy spectrum
- Interlace properties for the real and imaginary parts of the wave functions of complex-valued potentials with real spectrum
- On the construction of non-Hermitian Hamiltonians with all-real spectra through supersymmetric algorithms