MODELING OF TITANIUM INDIFFUSED LITHIUM-NIOBATE CHANNEL WAVE-GUIDE BENDS - A MATRIX APPROACH

An analytical model for computation of bending loss of Ti:LSTbO3 chann el waveguide bends has been presented. The analytical steps involved a re as follows, The 2D refractive index profile over the cross-section of Ti:LiNbO3 waveguide is first transformed to 1D effective-index prof ile along the lateral direction. A conformal mapping technique is then used to transform the effective-index profile of the waveguide bend t o that of an equivalent straight waveguide. A stair-case type step-ind ex profile is generated from the equivalent effective-index profile in lateral direction by partitioning the latter into a large number of t hin sections of varying refractive indices. The overall transfer matri x of the step-index layered structure so obtained may be computed by t he progressive multiplication of individual 2X2 transfer matrices rela ting the field components in adjacent layers. The excitation efficienc y of the wave in the guiding layer shows a resonance peak around the m ode propagation constant, The full-width-half-maximum (FWHM) of this p eak determines the power attenuation coefficient of the bent waveguide . The losses due to the discontinuity of the curvature are also comput ed. The computed results for different bends including S-bends are in good agreement with the published experimental data. The computation u sing the model is quite fast and versatile to consider arbitrary waveg uide dimensions, Ti-film thickness, diffusion parameters and wavelengt h of light for both TE and TM polarizations. The model, in principle, is not limited to Ti:LiNbO3 channel waveguides only but is valid for a ny arbitrary graded-index channel waveguide bends provided that the re fractive index profile and the wavelength dependence of the refractive index are known. (C) 1998 Elsevier Science B,V. All rights reserved.