Spectral singularities and threshold gain of a slab laser under illumination of a focused Gaussian beam

We study spectral singularities of an infinite planar slab of homogeneous optically active material in focus of a thin lens under illumination of a Gaussian beam. We describe the field distribution of the Gaussian beam under this configuration as a plane wave propagated near the optical axis which its phase and amplitude vary with distance from center of the beam. Based on this approximation, we carry out the transfer matrix for the slab. We explore the consequences of this configuration on determining the threshold gain of the active medium and tuning the resonance frequencies related to spectral singularities. We show that the spectral singularities and the threshold gain besides that vary with distance from center of the Gaussian beam, also they change with relative aperture of the focusing lens. As a result, using a thin lens with higher relative aperture, the spectral singularities corresponding resonances shift to the higher frequencies (lower wavelengths). Numerical results confirm the theoretical findings