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 $r^B\left(k_c\right)$ of the two scattering centers satisfy the condition $r_R^A\left(k_c\right)r_L^B\left(k_c\right)e^{i2k_c(x_B-x_A)}=1$. 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. (paper)