Quantum Theory For Optical Parametric Process

Carson L. Tang, L.K. Cheng

This chapter outlines the noise source on the basis of a quantum theory. A quantum theory is, however, needed for a rigorous analysis of the spontaneous parametric scattering process and a clear understanding of the spontaneous parametric process is important for a number of reasons. First, since the frequency and phase-matching conditions for the spontaneous emission are the same as those for the corresponding stimulated parametric process, the tuning characteristics of optical parametric oscillators and amplifiers can be determined from the spontaneous parametric emission prior to the construction of an actual oscillator or amplifier. It is, however, far from clear whether such an amplifier can be made practical, although there are interesting fundamental issues related to squeezing in optical parametric processes that have attracted a great deal of attention. For optical parametric processes, one is usually interested in the transparent region of the optical media.

Jui‐Teng Lin, B. J. Feldman

D. A. Kleinman

Optical parametric noise (OPN) is treated as a quantum-mechanical decay process in which a photon ${\ensuremath{\omega}}_{3}$ decays in an optically nonlinear medium into two photons ${\ensuremath{\omega}}_{1}$, ${\ensuremath{\omega}}_{2}$. 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 ${\ensuremath{\omega}}_{3}$. It is shown that focusing does not enhance OPN. The properties of OPN are then described in considerable detail for a plane wave at ${\ensuremath{\omega}}_{3}$ 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.

N. A. Hussain

Sintayehu Tesfa

E. V. Makeev, A. S. Chirkin

We develop quantum theory of process of the parametric optical image amplification at high-frequency pumping which is accompanied by up - conversion one. Such interactions can be implemented by two coupled three-frequency optical processes. The theory developed takes into account the diffraction effect and the difference of group velocities of interacting waves. The expressions for mean photon numbers and noise figures of the interacting waves are obtained and the dependence of these parameters on the interaction length are examined.