Method for propagation of total fields or beams through optical waveguides

A new method for solving the scalar Helmholtz equation to obtain the propagation of total fields or beams through general optical waveguiding structures is presented. The method is based on converting the partial differential equation into a matrix total differential equation using a collocation method and then solving the resulting equation through standard numerical methods. A comparison with the propagating-beam method shows that the present method has better accuracy and is more efficient numerically.