A comparison of the optical path and differential equation methods for optically thin phase gratings

摘要

It is shown that the optical path method may lead to an approximate solution of the wave equation valid under a wide range of conditions for slanted phase gratings of arbitrary profile. Analytic solutions are given for sinusoidal and sawtooth gratings, and the accuracy of the approximations is checked by comparison with numerical solutions. The conditions under which sawtooth gratings may yield 100 efficiency are clarified.