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Photonic innovation is becoming ever more important in the modern world.Optical systems are dominating shorter and shorter communications distances,LED's are rapidly emerging for a variety of applications, and solar cells showpotential to be a mainstream technology in the energy space. The need fornovel, energy-efficient photonic and optoelectronic devices will only increase.This work unites fundamental physics and a novel computational inverse designapproach towards such innovation.  The first half of the dissertation is devoted to the physics ofhigh-efficiency solar cells. As solar cells approach fundamental efficiencylimits, their internal physics transforms. Photonic considerations, instead ofelectronic ones, are the key to reaching the highest voltages and efficiencies.Proper photon management led to Alta Device's recent dramatic increase of thesolar cell efficiency record to 28.3%. Moreover, approaching theShockley-Queisser limit for any solar cell technology will require lightextraction to become a part of all future designs.  The second half of the dissertation introduces inverse design as a newcomputational paradigm in photonics. An assortment of techniques (FDTD, FEM,etc.) have enabled quick and accurate simulation of the "forward problem" offinding fields for a given geometry. However, scientists and engineers aretypically more interested in the inverse problem: for a desired functionality,what geometry is needed? Answering this question breaks from the emphasis onthe forward problem and forges a new path in computational photonics. Theframework of shape calculus enables one to quickly find superior, non-intuitivedesigns. Novel designs for optical cloaking and sub-wavelength solar cellapplications are presented.

Photonic Design: From Fundamental Solar Cell Physics to Computational Inverse Design