Spectral singularity in composite systems and simulation of a resonant lasing cavity

Abstract

We investigate herein the existence of spectral singularities (SSs) in composite systems that consist of two separate scattering centers A and B embedded in one-dimensional free space, with at least one scattering center being non-Hermitian. We show that such composite systems have an SS at $k_c$ if the reflection amplitudes $r^A\left(k_c\right)$ and $r^B\left(k_c\right)$ of the two scattering centers satisfy the condition $r_{\mathrm{R}% }^{A}\left( k_{c}\right) r_{\mathrm{L}}^{B}\left( k_{c}\right) e^{i2k_{c}\left( x_{B}-x_{A}\right) }=1$. We also extend the condition to the system with multi-scattering centers. As an application, we construct a simple system to simulate a resonant lasing cavity.

arXiv comment12 pages, 5 figures

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• Spectral singularities and tunable slab lasers with 2D material coating
• Solving scattering problems in the half-line using methods developed for scattering in the full line