| In this thesis I develop a formalism for analyzing quantum optics in photonic crystal slab cavities which may be coupled, lossy, and non-orthogonal. Using a tight-binding approximation I find classical coupled-cavity quasimodes which overlap in space and frequency. These classical modes are used to develop a multiphoton basis for quantum optics with non-orthogonal photon states. I develop creation and annihilation operators with a novel commutation relation as a consequence of the non-orthogonality of the quasimodes. With these operators the effective Hamiltonian, number operator, electric field operator and quadrature operators are obtained.;I use a combination of analytic results and characteristic functions to examine the evolution of coherent and squeezed states in a single lossy quasimode. The analysis is then extended to two non-orthogonal quasimodes. States are investigated using reduced characteristic functions.;The quantum jump technique is applied to handle the effects of loss. This technique is compared with the master equation, and conditions for the quantum jump technique being preferable are described. The quantum jump technique is implemented numerically, allowing for time-dependent linear and chi (2) non-linear pumping. |
