Analytical beam shaping with application to laser-diode arrays

In contrast to numerical methods for beam shaping, analytical beam shaping consists of two steps: first, finding a purely geometrical distortion between the input plane and the output plane redistributing the intensity of the incoming wave front; and, second, computing a phase-only element realizing this coordinate transform. For the latter the method of stationary phase may be applied. The known classes of possible analytical wave transformation are extended to comprise separable and isotropic super-Gaussian-to-super-Gaussian conversion as well as transformation of Gaussian arrays to super-Gaussian distributions, and vice versa. The resulting optical phase elements contain no spiral phase dislocation and may thus be realized as refractive or diffractive elements. In addition, the outgoing wave front does not contain spiral phase dislocations.