Modelling of titanium indiffused lithium niobate channel waveguide bends: a matrix approach

An analytical model for computation of bending loss of Ti:LSTbO3 channel waveguide bends has been presented. The analytical steps involved are as follows, The 2D refractive index profile over the cross-section of Ti:LiNbO3 waveguide is first transformed to 1D effective-index profile along the lateral direction. A conformal mapping technique is then used to transform the effective-index profile of the waveguide bend to that of an equivalent straight waveguide. A stair-case type step-index profile is generated from the equivalent effective-index profile in lateral direction by partitioning the latter into a large number of thin sections of varying refractive indices. The overall transfer matrix of the step-index layered structure so obtained may be computed by the progressive multiplication of individual 2X2 transfer matrices relating the field components in adjacent layers. The excitation efficiency of the wave in the guiding layer shows a resonance peak around the mode propagation constant, The full-width-half-maximum (FWHM) of this peak determines the power attenuation coefficient of the bent waveguide. The losses due to the discontinuity of the curvature are also computed. The computed results for different bends including S-bends are in good agreement with the published experimental data. The computation using the model is quite fast and versatile to consider arbitrary waveguide dimensions, Ti-film thickness, diffusion parameters and wavelength 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 any arbitrary graded-index channel waveguide bends provided that the refractive index profile and the wavelength dependence of the refractive index are known. (C) 1998 Elsevier Science B,V. All rights reserved.