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Physical review. B, Condensed matter

Intensity-dependent photon-echo relaxation in rare-earth-doped crystals

Stefan Kröll, E. Y. Xu, M. K. Kim, Masaharu Mitsunaga, Ravinder Kachru

Published Jun 1, 1990• 33 citations
Publisher

Abstract

Photon-echo-relaxation measurements made on the $^{3}\mathrm{H}_{4}$${\mathrm{\ensuremath{-}}}^{3}$${\mathrm{P}}_{0}$ transition of 0.01 at. % ${\mathrm{Pr}}^{3+}$:YAG (where YAG represents yttrium aluminum garnet), $^{3}\mathrm{H}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathrm{D}}_{2}$ transition in 0.1 at. % ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$, and $^{7}\mathrm{F}_{0}$${\mathrm{\ensuremath{-}}}^{5}$${\mathrm{D}}_{0}$ transition in 0.25 at. % ${\mathrm{Eu}}^{3+}$:${\mathrm{YAlO}}_{3}$ show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in ${\mathrm{Pr}}^{3+}$:YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring ${\mathrm{Pr}}^{3+}$ ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.

DOI
10.1103/physrevb.41.11568

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Photon-echo-relaxation measurements made on the ^{3}\mathrm{H}_{4}$${\mathrm{\ensuremath{-}}}^{3}$${\mathrm{P}}_{0} transition of 0.01 at. % Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAG (where YAG represents yttrium aluminum garnet), ^{3}\mathrm{H}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathrm{D}}_{2} transition in 0.1 at. % Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​, and ^{7}\mathrm{F}_{0}$${\mathrm{\ensuremath{-}}}^{5}$${\mathrm{D}}_{0} transition in 0.25 at. % Eu3+{\mathrm{Eu}}^{3+}Eu3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​ show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring Pr3+{\mathrm{Pr}}^{3+}Pr3+ ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.
Systematic measurements of stimulated-photon-echo intensities as a function of the first-to-second (\ensuremath{\tau}) and second-to-third (T) pulse separations allow the investigation of the dynamical properties of the spectral diffusion for the 7^{7}7F0{\mathit{F}}_{0}F0​${\mathrm{\ensuremath{-}}}^{5}$D0{\mathit{D}}_{0}D0​ transition of a cryogenic Eu3+{\mathrm{Eu}}^{3+}Eu3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​ sample. The existence of spectral diffusion was verified by the significant broadening (from 1.2 to 7.2 kHz) of the homogeneous linewidth (\ensuremath{\Gamma}) as T increases from microseconds to milliseconds, the effect being attributed to the flip flop of nearby aluminum nuclear spins surrounding the Eu3+{\mathrm{Eu}}^{3+}Eu3+ ion. A similar broadening effect (from 0.61 kHz, to a few kHz) was also observed in the presence of a static magnetic field H0{\mathit{H}}_{0}H0​=137 G, but with a much slower diffusion rate. To explain these observations, we use three theoretical models: the Bai-Fayer model, the diffusion-equation model, and the Monte Carlo model. Each agrees reasonably well with the experimental data and indicates the flip rates of sub-kHz order at H0{\mathit{H}}_{0}H0​=0 and an order of magnitude lower at 137 G.
Eu-doped yttrium orthosilicate (Eu(3+) : Y2SiO5) had been a subject being investigated for coherent time-domain optical memory and information processing applications since its ultraslow optical dephasing was discovered several years ago. In this crystal the weakly allowed (7)F0 - (5)D0 transition of europium ions exhibits a sufficient long dephasing time and no spectral difli.usion on a time scale of several hours at low temperature, thus an information pattern or data can be stored as a population grating in the ground state hyperfine levels. On the other hand, the study on photon-echo relaxation shows that the dephasing time T2 of Eu (3+) and other rare-earth ions doped YAG, YAlO3 strongly depends on the intensity of the excitation pulses. In Eu (3+) :YAlO3, an exponential decay of photon-echo with T2 = 53 microseconds if the excitation pulses are weak (5 vJ/pulse) was observed. However, when the excitation pulses are strong (80 pJ/pulse) they observed a much shortened T2 with a highly nonexponential decay pattern. The conclusion they derived is that the intensity-dependent dephasing rate effects are quite general, and it depends on how much the excitation intensity varies. In this paper we use transient grating formation technique showing that a temporal lattice distortion may only occur along crystal c axis, caused by EU (3+) excitation. At high excitation level the produced exciton in conduction band may also couple to the dynamical lattice relaxation process, giving rise to an apparently much shortened dephasing time.
We report a systematic study of the stimulated-photon-echo relaxation on the 3^{3}3P0{\mathit{P}}_{0}P0​${\mathrm{\ensuremath{-}}}^{3}$H4{\mathit{H}}_{4}H4​ transition of Pr3+{\mathrm{Pr}}^{3+}Pr3+:LaF3{\mathrm{LaF}}_{3}LaF3​ and the 3^{3}3P0{\mathit{P}}_{0}P0​${\mathrm{\ensuremath{-}}}^{3}$H4{\mathit{H}}_{4}H4​ and 1^{1}1D2{\mathit{D}}_{2}D2​${\mathrm{\ensuremath{-}}}^{3}$H4{\mathit{H}}_{4}H4​ transitions of Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAG (yttrium aluminum garnet). The stimulated-echo intensity is measured as a function of the delay between the first and the second pulses and the delay between the second and the third pulses. The stimulated-echo relaxation is modulated by the hyperfine interaction in the ground and the excited electronic states. We find that the modulation patterns can be quite distinct from those for two-pulse photon-echo relaxation and give complementary information about the hyperfine structures. We use the density-matrix theory of stimulated-photon-echo modulation, and the resulting simulation shows satisfactory agreement with the experimental data.
Two-pulse photon-echo measurements on the 0.1 at. % Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​ 3^{3}3H4{\mathit{H}}_{4}H4​${\mathrm{\ensuremath{-}}}^{1}$D2{\mathit{D}}_{2}D2​ transition suggest that the relaxation time depends on the density of excited states created by the excitation pulses. The dependence of the relaxation time on the intensity of each excitation pulse shows that our results are inconsistent with instantaneous spectral diffusion, a model often invoked in this type of experiment, where excited states created by the second pulse chiefly influence the relaxation time. A homogeneous linewidth contribution, noted in previous work as being of unknown origin, is eliminated at low excitation fluences.
We study the photon-echo attenuation by various dynamical processes in rare-earth-ion-doped crystals. The experimental investigations concentrate on a Pr3+:Eu3+:Nd3+{\mathrm{Pr}}^{3+}:{\mathrm{Eu}}^{3+}:{\mathrm{Nd}}^{3+}Pr3+:Eu3+:Nd3+ codoped Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ crystal at low temperatures. Two-pulse photon-echo intensities are measured as a function of the pulse intensities when either the Pr3+{\mathrm{Pr}}^{3+}Pr3+ or the Eu3+{\mathrm{Eu}}^{3+}Eu3+ ions are excited. For the quantitative interpretation we consider primarily excitation-induced frequency shifts (EFS) by diagonal and off-diagonal interactions and show that for the systems under consideration EFS are dominated by diagonal interactions. The observed echo attenuation by EFS is compared with the predictions calculated from independent Stark-field measurements and reasonable agreement is obtained. The broadening by spin-ion interactions, by nonequilibrium phonons and the dependence of the echo attenuation on the frequency position in the inhomogeneously broadened band are further investigated.
We study the optical properties of rare-earth-ion-doped inorganic crystals with an emphasis on the dependence of two-pulse photon echoes on the excitation density in the system. The experimental investigations concentrate on Pr3+{\mathrm{Pr}}^{3+}Pr3+:Nd3+{\mathrm{Nd}}^{3+}Nd3+:Eu3+{\mathrm{Eu}}^{3+}Eu3+ codoped Y2{\mathrm{Y}}_{2}Y2​SiO5{\mathrm{O}}_{5}O5​ and YAlO3{\mathrm{O}}_{3}O3​ crystals at low temperatures. With two pulses of one laser the echo is induced in one ion species and with a third, "scrambler" pulse of a second laser another species is excited. These scrambler excitations lead to a dephasing and thus to an echo attenuation which depends on the strength, frequency, and time of the scrambler pulse. The spectral sensitivity of the echo attenuation is used for a spectroscopic technique: "photon-echo attenuation spectroscopy." As a function of the delay time ts{t}_{s}ts​ between the scrambler pulse and the onset of the two-pulse echo sequence the attenuation shows a very specific behavior dictated by the excitation-induced frequency shifts (EFS's). For ts{t}_{s}ts​ between the two echo-inducing pulses the echo intensity is partially regained by the "dephasing-rephasing balancing" of the reversible EFS's. For the theoretical description a stochastic model is introduced and the dephasing by excitation-induced lattice vibrations and by EFS's are analyzed in detail. The present results are discussed in the light of previous experimental and theoretical investigations.