Analysis of the chromaticity of near-field binary beam shapers

The chromatic properties of binary beam shapers inducing a spatially dependent transmission on the near field of an optical source after far-field filtering and imaging are derived. Beam shapers using pixels with two transmission states are highly versatile and have been experimentally realized with distributions of amplitude pixels, phase pixels, or polarization pixels that can be designed using a half-toning algorithm. The amplitude of the shaped beam in an image plane has a precisely controlled continuous profile given by the local density of the two pixel types in the object plane. The wavelength dependence of the field transmission corresponding to the full range of design transmission between 0 and 1 is studied analytically to assess the general performance of the corresponding beam shapers for broadband sources, with an example of a specific 2D transmission profile relevant to laser engineering. Amplitude beam shapers have no significant chromaticity, but have low damage threshold. The high-damage-threshold twisted nematic liquid crystal and phase shapers induce a wavelength-dependent transmission and phase on the shaped beam.