Abstract

The question sometimes arises as to whether an interference filter affects the shape or the direction of propagation of a reflected or transmitted beam. The answer can be found by expressing the incident beam (which is assumed to be spatially and temporally coherent) in terms of its spectrum of angular plane wave components. The amplitude reflectance and transmittance of the filter act on each plane wave, and the shape and direction of the reflected and transmitted beams can be determined from the composite of all the waves. A 2-D theory is employed, and several elementary results are obtained. In particular, in regions of slowly varying reflectance amplitude, the derivative of the phase of the reflectance with respect to incident angle in related to a lateral translation of the reflected beam. The second derivative of the phase with respect to angle corresponds to a shift in focus of the reflected beam. The results for reflectors and narrow bandpass filters are presented. The theory is also consistent with the behavior observed in the case of wave guiding structures and surface plasmons.

© 1988 Optical Society of America