Abstract
The field of application of the differential theory of gratings is increased via the use of the recently published multiple reflection series algorithm. The method is developed for both TE and TM polarizations, dielectric and conducting materials. For TE polarization, it strongly increases the range of groove depths which can be computed for both dielectric and metallic gratings. For TM polarization, the improvement is limited to lossless or lossy materials but good reflectors cannot be dealt with. The method is very suitable for studying new diffractive optical elements found in integrated optics, whose basic components are deep dielectric gratings.
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