Asymmetric perfect absorption and lasing of nonlinear waves by a complex -potential
arXiv:2009.09681 · doi:10.3390/sym12101675
Abstract
Spectral singularities and the coherent perfect absorption are two interrelated concepts that have originally been introduced and studied for linear waves interacting with complex potentials. In the meantime, the distinctive asymptotic behavior of perfectly absorbed waves suggests considering possible generalizations of these phenomena for nonlinear waves. Here we address perfect absorption of nonlinear waves by an idealized infinitely narrow dissipative potential modeled by a Dirac -function with an imaginary amplitude. Our main result is the existence of perfectly absorbed flows whose spatial amplitude distributions are asymmetric with respect to the position of the absorber. These asymmetric states do not have a linear counterpart. Their linear stability is verified numerically. The nonlinear waveguide also supports symmetric and constant-amplitude perfectly absorbed flows. The stability of solutions of the latter type can be confirmed analytically.
arXiv commentfinal version; several minor corrections made; accepted for Symmetry
References in corpus (17)
- Coherent Perfect Absorbers: Time-reversed Lasers
- PT-symmetric laser-absorber
- Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
- Coherent perfect absorbers: linear control of light with light
- Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials
- Coherent perfect absorption of nonlinear matter waves
- Dissipation-induced coherent structures in Bose-Einstein condensates
- Spontaneous symmetry breaking of solitons trapped in a double-channel potential
- Geometric Analysis of Bifurcation and Symmetry Breaking in a Gross-Pitaevskii equation
- Nonlinear Spectral Singularities for Localized Nonlinearities
- Delta-Function Potential with a Complex Coupling
- Macroscopic Zeno effect and stationary flows in nonlinear waveguides with localized dissipation
- Curvature-induced symmetry breaking in nonlinear Schrodinger models
- Light-controlled perfect absorption of light
- Coherent perfect absorber and laser for nonlinear waves in optical waveguide arrays
- Nonlinear currents in a ring-shaped waveguide with balanced gain and dissipation
- Symmetry breaking in competing single-well linear-nonlinear potentials