Photonic crystals, periodic dielectric structures that control photons in a similar way that atomic crystals control electrons, present opportunities for the unprecedented control of light. Photonic crystals display a wide gamut of properties, such as the photonic band gap, negative index of refraction, slow or stationary modes, and anomalous refraction and propagation effects. This thesis investigates the modeling, simulation, fabrication, and measurement of two-dimensional square lattice photonic crystals. An effective index model was developed to describe the propagation of electromagnetic waves in the media and applied to characterize the behavior of self-collimated beams to discern the effect of the photonic crystal on the evolution of the amplitude and phase of the propagating beam. Potential applications include optical interconnects and stand alone devices such as filters and lasers. Based on design parameters from the simulations, two dimensional photonic crystals were fabricated on amorphous and single crystal silicon-on-insulator substrates utilizing electron beam lithography and inductively coupled plasma etching. A unique etching process utilizing a combination of Cl2 and C4F6 gases was developed and characterized which displayed a vertical profile with a sidewall angle of under 1 degree from vertical and very smooth sidewalls for features as small as 150 nm. The high quality of the etching was the key to obtaining extremely low loss, low noise structures, making feasible the fabrication of large area photonic crystal devices that are necessary to measure propagation phenomena. Reflectivity measurements were used to directly observe the photonic band structure with excellent correlation with theory. A device was designed and fabricated which successfully verified the prediction of the simulations through measurements of the self-collimation effect across a broad range of infrared wavelengths. A solid foundation for the necessary components (simulation, modeling, design, fabrication, and measurement) of two-dimensional photonic crystal has been demonstrated. Elements from solid state physics, materials science, optics, and electromagnetics were incorporated to further the understanding of the mechanism of beam propagation in photonic crystals and illuminating the vast potential of research in periodic media.