The propagation characteristics of a step-index and graded-index optical planar waveguides with arbitrary refractive index profile have been analyzed by using different techniques: Transfer Matrix Method (TMM), Characteristic Matrix Method (CMM), Modified Transfer Matrix Method (MTMM) and the effective index method (EIM). These methods has been suggested and applied to a single mode LiNbO3 surface planar waveguide sample. Modal analysis of multilayer slab waveguides is studied and the applications are made for 2-channel Directional Coupler. We proposed analytical expressions of the dispersion equations for both TE and TM polarization modes. This method is a simplified form of TMM, which is allowed us to distinct modes by its order. Also, the applications are made, for comparison propose, to the multi-channel directional couplers. The results obtained from MTMM are fit with results obtained by TMM and CMM. Finally, the effective index method (EIM) was used together with the three methods TMM, CMM and MTMM to determine the mode propagation constants and the field profiles to a number of more complex structures.