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

Spectral singularities of an infinite planar slab containing homogeneous optically active material at the focal plane a thin lens are investigated. The field distribution beam behind is Gaussian that we approximate by wave concentrated near optical axis lens, such its phase and amplitude distance-dependent. consequences this configuration explored determining threshold gain medium tuning resonance frequencies related to spectral singularities. We find gain, besides that, vary with distance from center beam; also they change relative aperture focusing lens. Numerical studies show for central rays compared side rays, resonances occur lower wavelengths (higher frequencies) highest gain. Also, ray fixed beam, increasing illuminating system leads same results. results confirm theoretical findings.