Nonlinear Spectral Singularity and Laser Output Intensity for the TE and TM Modes

The nonlinear spectral singularity arising from a Kerr nonlinearity is explored in [Phys. Rev. A 87, 063838 (2013)]. This reference studies the effect of nonlinearity in Lasing condition and shows that Kerr nonlinearity with spectral singularity for a normally incident wave provides an explanation of lasing at gain coefficient $g$. Lasing occurs when it exceeds threshold gain $g_{0}$. For oblique waves, Ref. [Phys. Rev. A 91, 043804 (2015)] looks at the behavior of threshold gain coefficient $g_{0}$ which is given by the condition that there is a linear spectral singularity. We investigated imposing the condition of the existence of nonlinear spectral singularity in the $TE/TM$ modes of a mirrorless slab of gain materials and studied the $\theta$-dependence of intensity.