Entropic measure of directional emissions in microcavity lasers

We propose a noble notion of the directional emission in microcavity lasers. First, Shannon entropy of the far-field profiles in the polar coordinate can quantify the degree of unidirectionality of the emission, while previous notions about the unidirectionality can not efficiently measure in the robust range against a variation of the deformation parameter. Second, a divergence angle of the directional emission is defined phenomenologically in terms of full width at half maximum, and it is barely applicable to a complicated peak structure. However, Shannon entropy of semi-marginal probability of the far-field profiles in the cartesian coordinate can present equivalent results, and moreover it is applicable to even the cases with a complicated peak structure of the emission.