A Quantum Multi-Mode Approach to Diffraction and Nonlinear Interaction

Within the second-quantization framework, we develop a formalism for describing a spatially multimode optical field diffracted through a spatial mask or interacting with an optically nonlinear material and show that this process can be described as an effective interaction between various spatial modes. We first demonstrate a method to calculate the quantum state in the diffracted optical field for any given quantum state in the incident field and compare the result to experiment and suggest several new experiments using Laguerre-Gauss modes. We will also present a second-quantized multimode beam propagation formalism describing the spatial mode structure of the beam generated during a nonlinear interaction and describe several possible experiments to test the ideas using OAM modes.