Spectral singularity in composite systems and simulation of laser resonant chamber

A non-Hermitian system with spectral singularity (SS) exhibits fascinating phenomena which never appear in a Hermitian system. We investigate the existence of SS for a composite system which is consisted of two separated scattering centers A and B embedded in a one-dimensional free space, one of which is non-Hermitian at last. We show that the composite system has a SS at $k_{c} $ if the reflection amplitudes $r^{A}\left( {k_{c} } \right)$ and $r^{B}\left( {k_{c} } \right)$ of two scattering centers satisfy the condition $r_{\mbox{R}}^{A} \left( {k_{c} } \right)r_{\mbox{L}}^{B} \left( {k_{c} } \right)e^{i2k_{c} \left( {x_{B} -x_{A} } \right)}=1$, based on the theorem proposed by Ali (PRL 102, 220402 (2009)). Multi-scattering-centers generalization of the theorem is also obtained. As an application, we construct a simple system to simulate the resonant chamber for generating laser light.