Abstract
Microdisk cavities with a smoothly deformed boundary allow for highly directional light emission. The conventional direct problem is to determine the far-field emission pattern of an optical mode for a given cavity shape by solving Maxwell's equations. We introduce the inverse problem of finding the cavity shape for which the far-field intensity pattern of the optical mode best fits a desired profile. We find an optimal solution within a second-order perturbation theory for weakly deformed cavities with a mirror reflection symmetry. Surprisingly, in this case the optimal solution is unique for specified mode numbers and refractive index. The perturbative results are confirmed by full numerical simulations.
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