Lg. Joneckis et Jh. Shapiro, QUANTUM PROPAGATION IN A KERR MEDIUM - LOSSLESS, DISPERSIONLESS FIBER, Journal of the Optical Society of America. B, Optical physics, 10(6), 1993, pp. 1102-1120
Intense light beams propagating in a lossless, dispersionless, single-
mode optical fiber are subject to the Kerr effect, i.e., to the intens
ity-dependent refractive index of the fiber's fused-silica core. Class
ically, Kerr-effect-induced self-phase modulation (SPM) can be used fo
r spectral broadening of a picosecond pulse for grating-pair pulse com
pression down to femtosecond duration. Quantum mechanically, Kerr-effe
ct-induced four-wave mixing (FWM) has been used to produce squeezed-st
ate light. We present a quantum propagation theory for a lossless, dis
persionless fiber with the Kerr nonlinearity. The theory includes clas
sical SPM and quantum FWM within their regions of validity. It introdu
ces a material time constant for the Kerr interaction, limiting the qu
antum phase shifts caused by the broadband zero-point fluctuations tha
t accompany any input field, to develop a coarse-grained time multitem
poral mode field analysis. Explicit expressions are obtained for the f
irst and the second output-field moments when the fiber's input field
is in an arbitrary Gaussian state. These results are used to obtain ho
modyne-detection noise spectra, which are employed, in turn, to seek e
xperimentally accessible manifestations of the Kerr time constant.