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Fresnel laws, the quantitative information of the amount of light that isreflected from a planar interface in dependence on its angle of incidence, areat the core of ray optics. However, these formulae do not hold at curvedinterfaces and deviations are appreciable when wavelength and radius ofcurvature are comparable. This is of particular interest for opticalmicrocavities that play an important role in many modern research fields andapplications such as microlasers. Their convexly curved interfaces modifyFresnel's law in a characteristic manner: the onset of total internalreflection is shifted to angles larger than the critical angle. Here, we derivethe missing Fresnel laws for concavely curved refractive index boundaries,enabling the analytical description of light in complex mesoscopic opticalstructures that will be important in future nano- and microphotonicapplications.

Analytical Fresnel laws at generic curved interfaces