Direct path-integral solution for a reflection grating.


In two previous papers, we considered the path-integral formulation of optical multiple scattering problems.These occur in x-ray diffraction, ultrasonics, holography, microwave directional couplers, and integrated optics. The method was based on that of Feynman in quantum mechan­ ics; Ref. 3 is a convenient collection of many of the key papers on the subject. A similar Feynman diagram representation of acoustooptic scattering has also been presented by Korpel and Poon. Most of the discussion in Refs. 1 and 2 concerned transmis­ sion systems and was therefore written conveniently in terms of matrices. The solution for a contradirectional system—a reflection grating—was also presented, but we consider it far less satisfactory. First, the solution was obtained only at the device outputs (i.e., not for arbitrary position), and second, the diagrams did not emerge from the mathematics in a coherent way. In this Letter, therefore, we present an alter­ native direct procedure for the generation of path-integral solutions, which seems equally valid for codirectional, con­ tradirectional, and mixed systems. The starting point is, as before, approximate first-order coupled wave theory. We consider a lossless 180° reflection grating, replayed at Bragg incidence. The differential equa­ tions for this case may be taken as

DOI: 10.1364/AO.27.000029

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@article{Syms1988DirectPS, title={Direct path-integral solution for a reflection grating.}, author={Richard Syms}, journal={Applied optics}, year={1988}, volume={27 1}, pages={29-31} }