Abstract
Spectral singularities and 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 the perfect absorption of nonlinear waves by an idealized infinitely narrow dissipative potential modeled by a Dirac δ-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.
Highlights
The concept of spectral singularities (SSs) has already been known in mathematics for a long time [1,2]
coherent perfect absorption (CPA) was reported for a variety of photonic systems, including plasmonic metasurfaces, graphene-based systems electromagnetic waves interacting with graphene and plasmonic metasurfaces, microcavities, etc.—see a recent review [12] on physical applications of photonic coherent perfect absorbers
The paradigm of CPA was enriched by addressing the absorption of waves of various nature, such as acoustic waves interacting with a fluid absorber [13] and quantum superfluids depleted by a focused electron beam applied to an atomic
Summary
The concept of spectral singularities (SSs) has already been known in mathematics for a long time [1,2]. The related physical phenomenon, known today as coherent perfect absorption (CPA) [3], was discovered independently [4,5,6] (see [7] for a chronological review on the topic) and is characterized by the asymptotic behavior of the field corresponding to only an incoming wave. The interest in physical effects related to the SSs has been revitalized due do to a series of works [3,9,10] establishing direct links between mathematical properties of SSs and their relevance for physical applications, as well as due to the first experimental implementation of a CPA [11]. CPA was reported for a variety of photonic systems, including plasmonic metasurfaces, graphene-based systems electromagnetic waves interacting with graphene and plasmonic metasurfaces, microcavities, etc.—see a recent review [12] on physical applications of photonic coherent perfect absorbers. The paradigm of CPA was enriched by addressing the absorption of waves of various nature, such as acoustic waves interacting with a fluid absorber [13] and quantum superfluids depleted by a focused electron beam applied to an atomic
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