We discuss two types of optical processing using vortex-producing angular phase plates. In the most common spatial-filtering operation, an input object is Fourier transformed (either by Fraunhofer diffraction or with a lens system). The Fourier transform is then multiplied by an angular phase pattern, and the product is again Fourier transformed. The output is a space-invariant, edge-enhanced version of the input object. Alternatively we can directly image the object using a lens multiplied by the angular phase. The space-variant image is severely distorted along the optical axis of the system. We encode the phase plates onto a liquid-crystal display and present experimental results on both systems.

A three-by-three polarization ray-tracing matrix method for polarization ray tracing in optical systems is presented for calculating the polarization transformations associated with ray paths through optical systems. The method is a three-dimensional generalization of the Jones calculus. Reflection and refraction algorithms are provided. Diattenuation of the optical system is calculated via singular value decomposition. Two numerical examples, a three fold-mirror system and a hollow corner cube, demonstrate the method.

A formulation of rigorous coupled-wave theory for diffraction gratings in bianisotropic media that exhibit linear birefringence and/or optical activity is presented. The symmetric constitutive relations for bianisotropic materials are adopted. All of the incident, exiting, and grating materials can be isotropic, uniaxial, or biaxial, with or without optical activity. The principal values of the electric permittivity tensor, the magnetic permeability tensor, and the gyrotropic tensor of the media can take arbitrary values, and the principal axes may be arbitrarily and independently oriented. Procedures for Fourier expansion of Maxwell's equations are described. Distinctive polarization coupling effects due to optical activity are observed in sample calculations.

We present experimental results for a fractional Fourier transform (FRFT) system implemented with programmable lenses written onto a liquid-crystal spatial light modulator (LCSLM). Because the focal length can be changed, different orders of the FRFT can be obtained without changing the optical setup. The LCSLM can very easily implement more complicated operations, including the realization of simultaneous orders of the FRFT and anamorphic transforms.