The quantum theory of three-wave optical parametric interactions in a crystal such as LiNb ${\mathrm{O}}_{3}$ is formulated in a symmetrical manner with respect to interaction time and distance. The formalism leads to a unique treatment of parametric interactions of both cavity type and propagation type, in that the resemblance between time in the cavity type and distance in the propagation type of interaction in the classical description is preserved. Three-wave effects of harmonic generation, parametric amplification (including spontaneous emission), and frequency conversion are treated in a unique and symmetric manner. Using Feynman's operator techniques, quantum states resulting from parametric interactions, previously unavailable, are derived, from which characteristics of the processes are deduced.The quantum theory of three-wave optical parametric interactions in a crystal such as LiNb${\mathrm{O}}_{3}$ is formulated in a symmetrical manner with respect to interaction time and distance. The formalism leads to a unique treatment of parametric interactions of both cavity type and propagation type, in that the resemblance between time in the cavity type and distance in the propagation type of interaction in the classical description is preserved. Three-wave effects of harmonic generation, parametric amplification (including spontaneous emission), and frequency conversion are treated in a unique and symmetric manner. Using Feynman's operator techniques, quantum states resulting from parametric interactions, previously unavailable, are derived, from which characteristics of the processes are deduced.

Physical ReviewDec 10, 19689 citations

Parametric interaction of oppositely propagating light waves of identical frequency

Nelson V. Tabirian

ZhETF Pisma RedaktsiiuFeb 1, 19830 citations

Quantum properties of optical images in coupled nondegenerate parametric processes

M. Yu. Saygin, A. S. Chirkin

Quantum properties of parametric amplification and frequency conversion of an optical image in coupled parametric interactions are analyzed for the case of a remote object. The coupled-wave interaction consists of a traditional process of parametric amplification in the high-frequency pump field accompanied by the frequency mixing of generated and pump waves. The photon number density and signal-to-noise ratio at the interacting frequencies are studied in the image plane at the output of the nonlinear frequency converter in the fixed pump field approximation. The degree of entanglement of optical images at frequencies above and below the pump frequency is investigated.Quantum properties of parametric amplification and frequency conversion of an optical image in coupled parametric interactions are analyzed for the case of a remote object. The coupled-wave interaction consists of a traditional process of parametric amplification in the high-frequency pump field accompanied by the frequency mixing of generated and pump waves. The photon number density and signal-to-noise ratio at the interacting frequencies are studied in the image plane at the output of the nonlinear frequency converter in the fixed pump field approximation. The degree of entanglement of optical images at frequencies above and below the pump frequency is investigated.

Optics and SpectroscopyJan 1, 20115 citations

Parametric interaction of oppositely propagating light waves of identical frequency

Nelson V. Tabiryan

JETPLFeb 1, 19830 citations

The quantum theory of three-wave optical parametric interactions in a crystal such as LiNb

{\mathrm{O}}_{3}

is formulated in a symmetrical manner with respect to interaction time and distance. The formalism leads to a unique treatment of parametric interactions of both cavity type and propagation type, in that the resemblance between time in the cavity type and distance in the propagation type of interaction in the classical description is preserved. Three-wave effects of harmonic generation, parametric amplification (including spontaneous emission), and frequency conversion are treated in a unique and symmetric manner. Using Feynman's operator techniques, quantum states resulting from parametric interactions, previously unavailable, are derived, from which characteristics of the processes are deduced.