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Nonlinear Spectral Singularities and Lasing Threshold Condition

A spectral singularity is a mathematical notion with an intriguing physical realization in terms of certain zero-width resonances. In optics it manifests as lasing at the threshold gain. We explore the application of their recently-developed nonlinear generalization in the study of the effect of a nonlinearity on the lasing threshold condition for an infinite planar slab of gain medium. In particular, for a Kerr nonlinearity, we derive an explicit expression for the intensity of the emitted waves from the slab and discuss the implications of our results for the time-reversed system that acts as a coherent perfect absorber.