Photonic crystals are periodically arranged dielectric materials. If the periodicity is broken along a line, i.e. a line defect is formed, then the line defect can behave like a waveguide. In this thesis, a frequency splitting device for electromagnetic waves is designed and tested theoretically using line defect waveguides. The theoretical design of the waveguides is accomplished using the plane wave expansion and the supercell method. The testing is done by the finite difference time domain method. Frequency mixing and splitting, or multiplexers and demultiplexers as they are known in industry, for electromagnetic waves are important since they lead to a multiplication in capacity for optical communications. Multiplexers and demultiplexers have been in use for a long time. However, designing photonic crystal multiplexers has a history of about ten years. In this thesis, a new photonic crystal demultiplexer design is suggested using photonic crystal line defect waveguides.