Electrooptic modulation in an arbitrary cross section waveguide

The electromagnetic field of an optical wave of frequency omega , traveling through a long, electrooptic waveguide of arbitrary cross section and composition in the presence of an arbitrary external field of strength E/sup ext/ and radio frequency Omega , is derived by a perturbative argument, assuming Omega / omega <<1 and mod r/sub ijk/E/sup ext/ mod <<1, where r/sub ijk/ are the linear electrooptic coefficients. An idealized model is solved exactly in the context of rigorous perturbation theory, and the solution is shown to be valid whenever (r/sub ijk/E/sup ext/)/sup 2/ omega / Omega <<1, without restriction on r/sub ijk/E/sup ext/ omega / Omega . The arbitrary cross section formula, when evaluated in the model case, agrees exactly with the rigorous result, so it is argued that the arbitrary cross section formula should also be valid whenever (r/sub ijk/E/sup ext/)/sup 2/ omega / Omega <<1.<
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