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# Loss calculations in weakly-guiding optical dielectric waveguides

**M.J.Adams**

## Abstract

The application of perturbation theory to a three-layer weakly-guiding slab waveguide composed of lossy dielectric media yields a simple formula for the attenuation coefficient α of a guided mode:

α = (Σ^{3}_{i=1} α_{i}P_{i})/(Σ^{3}_{i=1} P_{i}), where α_{i}, P_{i} are respectively the loss coefficient and model power in region i (i = 1,2,3). It is shown that this result can also be obtained from arguments based purely on geometric optics. The result is easily extended to apply to circularly-symmetric optical fibres where it yields confirmation of an earlier approximation for the power ratios P_{i}/Σ^{2}_{i=1}P_{i}

**Optics Communications** (1977) Vol.23(1) pp.105-108

**doi:** 10.1016/0030-4018(77)90136-5

**Southampton ePrint id:** 78725

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Copyright University of Southampton 2006