Using method of Cole Hopf transformation,Helmholtz equation was transformed to Riccati equation,and propagation characteristics of guided modes in planar optical waveguides was analyzed in a simple and direct way.Exact analytic solutions for guided modes in multilayer step index guides and graded index guides were given and illustrated by examples.Numerical melhod for analyzing propagation characteristics of nonlinear planar waveguides was also given and illustrated by example.