This thesis deals with the implementation of a numerical method to describe how electromagnetic waves propagate through a one-dimensional photonic crystal waveguide. The one-dimensional photonic crystal waveguide is a periodic arrangement of dielectric slabs of alternating dielectric constant with an impurity slab introduced as the guiding layer. This impurity guides, and connes light within a given range of frequencies by producing waveguide modes within the photonic band gap. These modes are different from those of conventional waveguides that use total internal reflection as the basic guiding mechanism. Photonic crystal waveguides are expected to lead to compact photonic integrated circuits.