  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.
