Date of Award


Degree Name

Doctor of Philosophy


Electrical Engineering


Raymond C. Rumpf


Photonic crystals are engineered periodic structures that provide great control over electromagnetic waves. One of these mechanisms is self-collimation, in which the electromagnetic wave travels through the photonic crystal along an axis of the lattice without diffracting or spreading. This mechanism of self-collimation is a dispersion phenomenon, which is dependent on the unit cell's physical and geometrical characteristics. An algorithm for generating spatially variant lattices (SVL) was developed that can change geometrical properties in photonic crystals as a function of position, like unit cell orientation, fill fraction, symmetry, and others in a manner that is smooth, continuous, and virtually free of unintentional defects, allowing unprecedented control over electromagnetic waves in self-collimating photonic crystals.

Through the development of analysis tools to analyze photonic crystals in frequency, time and Fourier domains, optimization of lattices and their unit cells, generation of graphics, scientific discoveries through simulations, and the implementation of a novel SVL iterative algorithm, this work provides a way to simultaneously control multiple aspects of an electromagnetic wave by spatially varying different geometrical properties throughout a photonic crystal. Specifically, two significant contributions are shown. First, the phase and power of a wave were controlled independently by changing the unit cell orientation and its fill fraction through the same space, in two- and three-dimensional crystals. Second, the power flow of a wave was arbitrarily controlled in a three-dimensional photonic crystal by spatially varying the unit cell orientation throughout the device.




Received from ProQuest

File Size

111 pages

File Format


Rights Holder

Jesus Javier Gutierrez