| The design of complex diffractive optical elements requires both a mathematical formulation of the problem and the appropriate optimization method. The mathematical formulations are very complex, since in some circumstances scalar based strategies are acceptable, whereas, in other cases exact solutions to Maxwell's equations are required. Once the mathematical formulations are coupled with the appropriate optimization algorithms, then the design of single and cascaded diffractive optical elements can be exploited. This Dissertation develops the mathematical framework for diffractive optics utilizing scalar based design and exact solutions to complex periodic dielectric structures. Additionally, a new method of optimization is introduced which is based on the foundations of genetics. This methodology is used to design unique elements for wavefront splitting, polarization filtering, and wavelength filtering. An additional algorithm is developed for scalar based solutions using variants of existing methods, resulting in some interesting designs concerning data encryption and beam shaping. |
