Spontaneous parametric down-conversion in waveguides: A backward Heisenberg picture approach

We develop a fully quantum-mechanical approach for the description of spontaneous parametric down-conversion in waveguides. Our method allows us to write an expression for the quantum state easily and directly, even when multiple photon pairs are generated in the process. The role of material dispersion in the normalization of the modes of the system, usually neglected, is properly treated here. The example of an Al(y)O(x)/Al(0.5)Ga(0.5)As ridge waveguide is discussed to illustrate the application of the formalism.