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Novel Lasers and Devices - Basic Aspects

Spectral correlations of ultrashort pulses in optical fibers

Friedrich König, Gerd Leuchs, M. W. Hamilton

Published Jan 1, 1999• 0 citations
Publisher

Abstract

Sources of quantum correlated light beams will find important applications in quantum communication. Such beams might be generated by Kerr effect induced four wave mixing in fibers where the nonlinear optical pulse evolution is an important issue. The resulting effect of self-phase modulation is used to broaden the spectra of ultrashort pulses in many laser applications.

DOI
10.1364/nlda.1999.ltua5

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Sources of quantum correlated light beams will find important applications in quantum communication. Such beams might be generated by Kerr effect induced four wave mixing in fibers where the nonlinear optical pulse evolution is an important issue. The resulting effect of self-phase modulation is used to broaden the spectra of ultrashort pulses in many laser applications.
Intense light beams propagating in a lossless, dispersionless, single-mode optical fiber are subject to the Kerr effect, i.e., to the intensity-dependent refractive index of the fiber’s fused-silica core. Classically, Kerr-effect-induced self-phase modulation (SPM) can be used for spectral broadening of a picosecond pulse for grating-pair pulse compression down to femtosecond duration. Quantum mechanically, Kerr-effect-induced four-wave mixing (FWM) has been used to produce squeezed-state light. We present a quantum propagation theory for a lossless, dispersionless fiber with the Kerr nonlinearity. The theory includes classical SPM and quantum FWM within their regions of validity. It introduces a material time constant for the Kerr interaction, limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any input field, to develop a coarse-grained time multitemporal mode field analysis. Explicit expressions are obtained for the first and the second output-field moments when the fiber’s input field is in an arbitrary Gaussian state. These results are used to obtain homodyne-detection noise spectra, which are employed, in turn, to seek experimentally accessible manifestations of the Kerr time constant.
Ultrashort light pulses play an important role in the generation, manipulation and characterization of nonclassical light. Nonclassical light is often generated from a classical pump beam using a nonlinear optical process. One might expect that the high peak intensity of ultrashort pulses would provide the necessary driver for such processes, and this is indeed the case. Ultrashort pulses have been used to generate squeezed states, and quadrature entangled states via three and four wave mixing, photon number states, polarization and frequency or directional entangled photon pairs states via three wave mixing.
Concepts and experimental works of ultrashort optical pulse squeezing in nonlinear fibers are reviewed. In a nonlinear fiber, optical fields are squeezed or quantum mechanically correlated by optical Kerr effect. These are, however, unobservable by direct photo-detection. Three kinds of strategies to extract the detectable squeezing have been proposed and implemented experimentally. Recent studies on applications of these squeezed pulses or the intrapulse quantum correlations to the generation of entangled states are also reviewed.
The propagation of a quasimonochromatic beam in an optical fiber may be unstable owing to phase-matched four-wave mixing. The phase matching may arise in a variety of ways, and the resulting instabilities are commonly referred to as modulational instabilities. Here I consider the cross-phase-modulational (XPM) instability arising in a high birefringence optical fiber in the normal dispersion (visible) regime when the pump is polarized at 45° to the principal axes of birefringence.1,2 Orthogonally polarized sidebands are generated along these axes. Phase matching arises from a balance between dispersion and the group velocity mismatch of the sidebands and dictates that the up-shifted sideband travels on the fast axis. The sidebands result in terahertz modulation of the pump and are interesting from the point of view of optical communications. From a quantum-statistical perspective, the quantum correlations, which develop as the sidebands are generated from quantum noise, are the focus of attention here.
Squeezing is a fundamental quantum optical phenomenon - induced by various nonlinear optical processes - in which a special state of the electromagnetic field is generated, for which quantum noise fluctuations are reduced below the shot noise level for certain frequency ranges. Two qualitatively different kinds of squeezing are currently known to take place in optical fibers. The first is the four-wave mixing (FWM) induced quadrature squeezing, in which an intense continuous wave (CW) pump initiates a spontaneous emission of signal and idler waves from vacuum fluctuations at symmetric detunings from the pump. The noise components at the signal and idler frequencies become correlated via the fiber nonlinearity, leading to a reduction of the noise power spectrum below the shot noise level. All the waves participating to the FWM-induced squeezing are monochromatic waves. The second kind of squeezing is the so called self-phase modulation (SPM) induced squeezing, in which the spectral components of an intense short pulse in a coherent state become correlated via the SPM during propagation. We demonstrate theoretically that a third kind of squeezing is possible in optical fibers, in which the noise spectrum of the quasi-monochromatic resonant radiation (RR) emitted by optical solitons when subject to perturbations shows evidence of photon correlation and a reduction of noise below the shot-noise level.