论文标题
复杂的$δ$ - 优势的非对称完美吸收和非线性波的激光
Asymmetric perfect absorption and lasing of nonlinear waves by a complex $δ$-potential
论文作者
论文摘要
光谱奇异性和连贯的完美吸收是两个相互关联的概念，这些概念最初被引入并研究了与复杂电位相互作用的线性波。同时，完美吸收的波的独特渐近行为表明，考虑到非线性波的这些现象可能概括。在这里，我们通过理想化的无限狭窄的耗散潜力来解决非线性波的完美吸收，该潜在由dirac $δ$ function建模，具有虚构的幅度。我们的主要结果是存在完全吸收的流动，其空间幅度分布相对于吸收剂的位置不对称。这些不对称状态没有线性对应。它们的线性稳定性经过数值验证。非线性波导还支持对称和恒定振幅完美吸收的流。可以通过分析确认后一种溶液的稳定性。
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 $δ$-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.
