Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2011. Cataloged from PDF version of thesis. Includes bibliographical references (p. 99-105). We first demonstrate theoretically and experimentally that electromagnetic resonators with high quality factors (Q) can be used to transfer power efficiently over distances substantially larger than the characteristic dimensions of the resonators by operating in a so-called "strongly coupled" regime. We next generalize the notion of strongly coupled resonances to a system comprising one power source and multiple receivers in a regime of broad practical applicability and show that, by appropriately tuning the parameters of the system, it is possible to significantly improve the overall efficiency of the wireless power transfer relative to the single-source and single-receiver configuration. We experimentally verify the predicted improvement in efficiency for a system consisting of one large source (area ~ 1 m2 ) coupling to two much smaller receivers of dimensions comparable to those of many portable electronic devices (area ~ 0.07 m2 ). Next, we present a novel design for an electrical conductor whose structure is optimized to have the lowest achievable resistance in the 2-20 MHz frequency range, where it can offer performance an order of magnitude better than the best currently available conductors. The two following chapters deal with energy transport in photonic crystals. We first investigate numerically how a square lattice of dielectric rods may be used to collimate a laser beam and the feasibility of using this system as a chemical sensor. Finally, we present and demonstrate through specific examples a systematic and general procedure, which is both computationally inexpensive and straightforward to implement, for coupling strongly dissimilar waveguides with 100% transmission. by André B. Kurs. Ph.D.