Perfectly absorbed and emitted currents by complex potentials in nonlinear media
arXiv:2111.06864 · doi:10.1103/PhysRevA.104.053527
Abstract
Recently it was demonstrated that the concept of a spectral singularity (SS) can be generalized to waves propagating in nonlinear media, like matter waves or electromagnetic waves in Kerr media. The corresponding solutions represent nonlinear currents sustained by a localized linear complex potential in a nonlinear Schrödinger equation. A key feature allowing the nonlinear generalization of a SS is a possibility to reduce a nonlinear current to the linear limit, where a SS has the unambiguous definition. In the meantime, known examples of nonlinear modes bifurcating from linear spectral singularities are few and belong to the specific class of constant-amplitude waves. Here we propose to extend the class of nonlinear SSs by incorporating solutions whose amplitudes are inhomogeneous. We show that the continuation from the linear limit requires a deformation of the complex potential, and this deformation is not unique. Examples include the deformation preserving the gain-and-loss distribution and the deformation preserving geometry of the potential. For the case example of a rectangular potential, we demonstrate that the nonlinear currents can be divided into two types: solutions of the first type bifurcate from the linear spectral singularities, and solutions of the second type cannot be reduced to the linear limit.
accepted for Phys. Rev. A
References in corpus (6)
- The physics of exceptional points
- Coherent Perfect Absorbers: Time-reversed Lasers
- Quantum Zeno dynamics: mathematical and physical aspects
- Lasing Threshold Condition for Oblique TE and TM Modes, Spectral Singularities, and Coherent Perfect Absorption
- Nonlinear currents in a ring-shaped waveguide with balanced gain and dissipation
- A universal form of complex potentials with spectral singularities