Light with finite rotation - an attempt for a theoretical description

The metamaterial filter introduced in the form of the so-called METATOY Johannes Courtial et al., j. opt. 13 (2011))[ 1] has a series of interesting properties, although it can presently only be realized as an array of discrete elements, being it an array of Dove prisms or lens arrays. Nevertheless, a theoretical analysis of field propagation through such a twisting filter is still lacking. Based on the complex-valued ray matrix formalism (ABCD-matrices/canonical transforms), the propagation through such a filter can be mimicked by using the known Green's function (e.g. Aykut et al. Journal of the Optical Society of America a (2010) 27(9) 1896)[ 2]. This matrix for an entire system including a flipping filter is non-symplectic, which in fact indicates that this filter's perturbation is ray-optically forbidden. However, if we proceed and insert the matrix-values into this Green's function, we arrive at results that are in agreement with the previously shown examples with METATOY. It is further shown how e.g. Fourier transformation of this filter will give rise to unexpected ray transformations. Finally, a new ray-optically forbidden element is discussed, as will possible future applications.