Theory of Optical Parametric Noise

Optical parametric noise (OPN) is treated as a quantum-mechanical decay process in which a photon ω₃ decays in an optically nonlinear medium into two photons ω₁, ω₂. The correct form of the interaction Hamiltonian is derived in terms of the usual second-order susceptibility, the field is quantized in a simple way, and the transition rate is obtained for an arbitrary field distribution at ω₃. It is shown that focusing does not enhance OPN. The properties of OPN are then described in considerable detail for a plane wave at ω₃ using a rigorous treatment of the crystal optics. OPN will usually be dominated by processes which very nearly conserve momentum and which produce a narrow-band emission whose frequency is determined by the direction of emission. Also considered is the background due to momentum-nonconserving processes, which produce broad-band emission up to a sharp cutoff frequency which depends on the emission direction. Appendices are provided on the group velocity in crystals, the "noise-wave" theory of OPN, second-harmonic generation, and OPN with beams of finite cross section.