Tilt operator for harmonic fields and its application to propagation through plane interfaces

The propagation of harmonic fields between non-parallel planes is a challenging task in optical modeling. Many well-known methods are restricted to parallel planes. However, in various situations a tilt of the field is demanded, for instance in case of folded setups with mirrors and tolerancing with tilted components. We propose a rigorous method to calculate vectorial harmonic fields on tilted planes. The theory applies a non-equidistant sampling in the k-space of the field before rotation in order to obtain an equidistant sampling of the rotated field. That drastically simplifies the interpolation challenge of the tilt operation. The method also benefits from an analytical processing of linear phase factors in combination with parabasal field decomposition. That allows a numerically efficient rotation of any type of harmonic fields. We apply this technique to the rigorous propagation of general harmonic fields through plane interfaces. If the field is known on the interface a fast algorithm results from a plane wave decomposition of the field. However in general, the field is not known on the interface. Then a rotation operator must be applied first.