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

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) $ofthetwoscatteringcenterssatisfythecondition$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.