Dyadic Green Functions and their applications in Classical and Quantum Nanophotonics

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Van Vlack, Cole Percy
Quantum Optics , Nanophotonics
Research in solid-state nanophotonics and quantum optics has been recently pushing the limits in semiconductor microcavity design. High quality microcavities that confine light into small volumes are now able to drastically alter the local density of states (LDOS). Plasmonic systems can provide smaller effective confinements, however it is unclear if the benefits of confinement are good enough to balance material losses due to non-radiative processes. This thesis presents a compendium of techniques for calculating photonic Green functions in various lossy, inhomogeneous magneto-dielectric systems. Subsequently we derive a rigorous theory of quantum light-matter interactions, valid in both weak and strong coupling limits, and show how the classical photonic Green function is developed to calculate Purcell factors, Lamb shifts, and the near and far field spectra from a single photon emitter. Using these techniques, this work investigates the classical and quantum optical properties of a variety of inhomogeneous structures, including their coupling to single photon emitters. This includes examining Purcell factors above negative index slabs and showing the convergence of many slow-light modes leads to a drastic increase in the LDOS along with large Lamb shifts. The optical trapping of metallic nanoparticles is examined above a negative index slab and a silver half-space, showing the importance of interparticle coupling on the optical forces. Then the interaction between a quantum dot and a metallic nanoparticle is studied where far-field strong coupling effects are observed only when the metallic nanoparticle is considered beyond the dipole approximation. Finally, this work addresses the issue of the LDOS diverging in lossy materials, which necessitates a description of spontaneous emission beyond the dipole approximation; the ``local field problem'' in quantum optics is revisited and generalized to include local field corrections for use in any photonic medium. The strength of finite-difference time-domain techniques is demonstrated in a number of cases for the calculation of regularized Green functions in lossy inhomogeneous media. This thesis presents a comprehensive study of Green function approaches to model classical and quantum light-matter interactions in arbitrary nanophotonic structures, including quantum dots, semiconductor microcavities, negative index waveguides, metallic half-spaces and metallic nanoparticles.
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