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