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arXiv:1006.4887 · Optics Express

Emission of photon echoes in a strongly scattering medium

Florian Beaudoux, Alban Ferrier, O. Guillot-Noël, T. Chanelière, J.-L. Le Gouët, Philippe Goldner

Published Jul 25, 2011• 14 citations
arXivHTMLPDF

Abstract

We observe the two- and three-pulse photon echo emission from a scattering powder, obtained by grinding a Pr3+:Y2SiO5 rare earth doped single crystal. We show that the collective emission is coherently constructed over several grains. A well defined atomic coherence can therefore be created between randomly placed particles. Observation of photon echo on powders as opposed to bulk materials opens the way to faster material development. More generally, time-domain resonant four-wave mixing offers an attractive approach to investigate coherent propagation in scattering media.

DOI
10.1364/oe.19.015236

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Physical Review Letters•Aug 14, 1989•9 citations
We observe the two- and three-pulse photon echo emission from a scattering powder, obtained by grinding a Pr3+:Y2SiO5 rare earth doped single crystal. We show that the collective emission is coherently constructed over several grains. A well defined atomic coherence can therefore be created between randomly placed particles. Observation of photon echo on powders as opposed to bulk materials opens the way to faster material development. More generally, time-domain resonant four-wave mixing offers an attractive approach to investigate coherent propagation in scattering media.
We study photon echo generation in disordered media with the help of multiple scattering theory based on diagrammatic approach and numerical simulations. We show that a strong correlation exists between the driving fields at the origin of the echo and the echo beam. Opening the way to a better understanding of nonlinear wave propagation in complex materials, this work supports recent experimental results with applications to the measurement of the optical dipole lifetime T2{T}_{2}T2​ in powders.
We have observed various types of photon echoes in a rare-earth doped crystal using a broad-band c.w. dye laser. Even at the very low spectral power density of the laser, the quantum efficiency of photon echo generation is as large as those using high-power or narrow-band lasers. We have observed Carr-Purcell type photon echo series for the first time in a rare-earth doped crystal. We have measured relaxation of two-pulse photon echo, three-pulse stimulated photon echo, and many-pulse Carr-Purcell photon echo, and found some new features.
Phase relaxation of optical excitations in condensed matter can be studied by coherent four—wave—mixing experiments in the time domain without requiring assumptions on the spectral properties of the material. For inhomogeneously broadened transitions, three laser pulses at times t = 0, t = t21 and t = T with wave vectors k1, k2 and k3, respectively, generate a stimulated photon echo pulse, emitted time—delayed at t = T+t21 in the momentum—matching direction according to k3+k2−k1. As a function of t21 the echo amplitude decays due to scattering events, described by the dephasing time constant T2 [1].
In a solid-state ensemble of rare-earth ions, we have experimentally generated a photon-echo of a spontaneous emission event, a process referred to as rephased amplified spontaneous emission (RASE). An enabling step for this demonstration was to use a double-Λ energy level structure for the photon-echo, rather than a standard two-pulse/two-level photon echo sequence, such that the single-photon echo is spectrally and spatially distinguishable from the coherent emission that follows imperfect π-pulses.
We apply for the first time a novel coherent transient, the cw photon echo. The propagation direction of the optical coherence prepared in a medium by a broadband cw laser beam is reversed by a pair of counterpropagating laser pulses, resulting in a continuous emission of the signal. The signal decays with a phase relaxation time T2{\mathrm{T}}_{2}T2​ and can have a quantum-beat-type modulation, giving the same wave form in one single shot as the plot of echo intensity versus pulse separation in a standard two-pulse echo experiment. Experimental demonstration is given in a Eu3+{\mathrm{Eu}}^{3+}Eu3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​ crystal.