Abstract:We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval. Using the uncertainty principle we prove various rigorous lower bounds on the functional; these lower bounds estimate the L 2 error for the beam shaping problem in terms of the design parameters. We also use the method of stationary phase … Show more
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