Quantum Theory Analysis of Counterpropagating Twin Photon Generation by Parametric Downconversion

Integrated nonlinear optical devices for the generation of twin photon beams are expected to be a key element for the development of quantum information techniques. This paper presents a quantum theory analysis of counterpropagating twin photon generation (CPTPG) by spontaneous parametric downconversion. Full descriptions of the quantum states of the twin photon beams having unique features are obtained in the Heisenberg and Schrödinger pictures. Mathematical expressions useful for device design and quantitative prediction of the performances, such as efficiency, wavelength spectrum and bandwidth, and photon correlation time, are deduced. Numerical data are given for specific quasi-phase-matched
${\rm LiNbO}_{\bf 3}$
waveguide CPTPG devices.