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Journal of the Optical Society of America B

Coherence coupling effect in a space- and time-resolved, nonlinear-correlation measurement in a multiple-scattering medium

Makoto Tomita

Published Mar 1, 2005• 2 citations
Publisher

Abstract

The coherence-coupling effect in a space- and time-resolved, nonlinear-correlation measurement in a multiple-scattering medium was investigated. In this measurement, two laser beams are injected into the medium, and the total nonlinear optical signal is measured as a function of the relative time delay, spatial separation, and frequency and wave-vector differences between the two beams. Besides the general importance of the nonlinear-correlation measurement, the coherence-coupling effect is interesting because it could provide a novel method of investigating the fluctuations and the correlation effects inside the multiple-scattering medium. We examined the form factor of the coherence-coupling effect as a function of the frequency and wave-vector differences between the two beams.

DOI
10.1364/josab.22.000537

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The coherence-coupling effect in a space- and time-resolved, nonlinear-correlation measurement in a multiple-scattering medium was investigated. In this measurement, two laser beams are injected into the medium, and the total nonlinear optical signal is measured as a function of the relative time delay, spatial separation, and frequency and wave-vector differences between the two beams. Besides the general importance of the nonlinear-correlation measurement, the coherence-coupling effect is interesting because it could provide a novel method of investigating the fluctuations and the correlation effects inside the multiple-scattering medium. We examined the form factor of the coherence-coupling effect as a function of the frequency and wave-vector differences between the two beams.
In this theoretical paper, we investigate coherence properties of the near-resonant light scattered by two atoms exposed to a strong monochromatic field. To properly incorporate saturation effects, we use a quantum Langevin approach. In contrast to the standard optical Bloch equations, this method naturally provides the inelastic spectrum of the radiated light induced by the quantum electromagnetic vacuum fluctuations. However, to get the right spectral properties of the scattered light, it is essential to correctly describe the statistical properties of these vacuum fluctuations. Because of the presence of the two atoms, these statistical properties are not Gaussian: (i) the spatial two-points correlation function displays a specklelike behavior and (ii) the three-points correlation function does not vanish. We also explain how to incorporate in a simple way propagation with a frequency-dependent scattering mean-free path, meaning that the two atoms are embedded in an average scattering dispersive medium. Finally we show that saturation-induced nonlinearities strongly modify the atomic scattering properties and, as a consequence, provide a source of decoherence in multiple scattering. This is exemplified by considering the coherent backscattering configuration where interference effects are blurred by this decoherence mechanism. This leads to a decrease of the so-called coherent backscattering enhancement factor.
The effect of parametric coupling between pump and probe beams in time-resolved optical Kerr effect is theoretically discussed for various experimental configurations. It is shown that with a cicularly polarized pump beam, the polarization changes induced on a nearly collinear probe beam are due to this coherence effect only. In other configurations, this parametric coupling can appear as an additional contribution to the observed signal, especially when pump and probe are derived from the same laser beam. It is pointed out that this coupling can occur not only when the pump and probe beams are at the same wavelength, but also when the difference or the sum of their frequencies can excite a Raman or a two-photon resonance in the medium.
We present angle-resolved correlation measurements between photons after propagation through a three-dimensional disordered medium. The multiple-scattering process induces photon correlations that are directly measured for light sources with different photon statistics. We find that multiple-scattered photons between different angular directions with angles much larger than the average speckle width are strongly correlated. The time dependence of the angular photon correlation function is investigated, and the coherence time of the light source is determined. Our results are found to be in excellent agreement with the continuous mode quantum theory of multiple scattering of light. The presented experimental technique is essential in order to study quantum phenomena in multiple-scattering random media, such as quantum interference and quantum entanglement of photons.
A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.
We present theoretical and experimental results on spatial quantum correlations induced by multiple scattering of nonclassical light. A continuous-mode quantum theory is derived that enables determining the spatial quantum correlation function from the fluctuations of the total transmittance and reflectance. Utilizing frequency-resolved quantum noise measurements, we observe that the strength of the spatial quantum correlation function can be controlled by changing the quantum state of an incident bright squeezed-light source. Our results are found to be in excellent agreement with the developed theory and form a basis for future research on, e.g., quantum interference of multiple quantum states in a multiple scattering medium.