In this book the author shows you the derivation of three beam propagation modeling and simulation techniques for optical waveguides starting from Maxwell's equation. These techniques include: split-step fast Fourier transform, finite difference, and harmonic expansion. The harmonic expansion technique is new and is the World's fastest electromagnetic beam propagation technique. You’ll learn about both scalar and full-vectoral beam propagation. This book contains links in the text for accessing additional information and the author’s source code in Mathcad™.