Abstract
Two first-order analytic solutions and a second-order analytic solution for the case of lossless-dielectric unslanted volume transmission gratings are compared for the case of weak grating index modulation and significantly off-Bragg replay. It is shown that the analytic solution predicted using the Beta-value method, which has previously been found to agree more closely with experimental results for the unslanted case than the first-order K -vector closure method (of Kogelnik), also agrees more closely with the analytic expression produced by the second-order coupled-mode equations of Kong for this case. A numerical comparison of the first order theories and the rigorous coupled wave theory gives a similar result. Thus the Beta-value method offers definite advantages over the Kogelnik K -vector closure method for the unslanted transmission geometry.
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