Here we present a fully quantum mechanical transfer function model for travelling wave whispering gallery mode
resonators. Micro-resonators, such as ring and disk resonators, have been key to the development of high performance
chip-scale photonic systems due to their compact footprint, sensitivity and low power operation. In this work we present
the first understanding of these resonators to any arbitrary multi-photon state. This was achieved by developing a model
that utilizes an efficient scheme for determining the quantum electrodynamic transfer functions relating the Bosonic
input/output mode operators in the resonator. This approach has been applied to the understanding of both single photon
and two-photon states. In this work we will present a key result on a resonant Hong-Ou-Mandel effect that is inherently
realized for any resonator-waveguide coupling constants and can operate over a wide range of resonance conditions.
Furthermore, the transfer function approach allows for the straightforward understanding of any resonator-waveguide
network with arbitrary modes. This will directly enable the application of quantum resonators to the realization of robust,
scalable and efficient Linear Optical Quantum Computing (LOQC) gates. Consequently, it is expected that resonators
can be used for both Nonlinear Sign Shift and CNOT gates. And these gates can robustly controlled and efficiently tuned
using standard electro-optic effects available in a variety of material systems, such as, Silicon.