Dispersion relations of TE-mode in a 3-layer slab waveguide with imaginary-part of refractive index

摘要

We report the theoretical analysis and the numerical calculation of the dispersion relations of TE-mode in a 3-layer slab waveguide whose guide layer is constructed with an absorbing material. From the analysis, we lead to the same equation for such an absorbing waveguide as that from Yeh's formalism. It is shown that the effective extinction coefficient depends not on its sign but on both a mode number and an effective refractive index (n_(eff)) and the n_(eff) has a maximum and a minimum value depend on the bulk extinction coefficient (k). From the calculation of the symmetric absorbing waveguide whose parameters are n_1 = n_3 = 1.51 and n_2 = 1.52, there is no propagation mode in the waveguide for k>0.155. Moreover, it is shown that the minimum guide layer thickness becomes non-zero value for k does not equal 0 even for the first mode of the symmetric waveguide.