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We study spectral singularities and their application in determining thethreshold gain coefficient $g^{(E/M)}$ for oblique transverse electric/magnetic(TE/TM) modes of an infinite planar slab of homogenous optically activematerial. We show that $g^{(E)}$ is a monotonically decreasing function of theincidence angle $\theta$ (measured with respect to the normal direction to theslab), while $g^{(M)}$ has a single maximum, $\theta_c$, where it takes anextremely large value. We identify $\theta_c$ with the Brewster's angle andshow that $g^{(E)}$ and $g^{(M)}$ coincide for $\theta=0$ (normal incidence),tend to zero as $\theta\to 90^\circ$, and satisfy $g^{(E)}<g^{(M)}$ for$0<\theta<90^\circ$. We therefore conclude that lasing and coherent perfectabsorption are always more difficult to achieve for the oblique TM waves andthat they are virtually impossible for the TM waves with$\theta\approx\theta_c$. We also give a detailed description of the behavior ofthe energy density and the Poynting vector for spectrally singular oblique TEand TM waves. This provides an explicit demonstration of the parity-invarianceof these waves and shows that the energy density of a spectrally singular TMwave with $\theta>\theta_c$ is smaller inside the gain region than outside it.The converse is true for the TM waves with $\theta<\theta_c$ and all TE waves.

Lasing Threshold Condition for Oblique TE and TM Modes, Spectral Singularities, and Coherent Perfect Absorption