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Physical review. B, Condensed matter

Investigation of four-wave mixing in NdxLa1−xP5O14

Jacek K. Tyminski, Richard C. Powell, Walter K. Zwicker

Published Jun 1, 1984• 44 citations
Publisher

Abstract

Four-wave mixing has been investigated in ${\mathrm{Nd}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{P}}_{5}{\mathrm{O}}_{14}$ crystals as a function of temperature, laser excitation wavelength, and power. The results are interpreted in terms of scattering from a population grating, and the relative intensity of the scattered signal is investigated as well as the grating decay time. The power dependence of the scattered intensity is explained by a model involving interaction with a three-level system, and the properties of the grating decay are associated with the exciton dynamics of the ions in the excited state. Decay patterns characteristic of both incoherent and partially coherent exciton migration can be observed under different experimental conditions. Enhanced migration due to vibronic generation of phonons resonant with the metastable state splitting is also observed. The temperature dependence of the results shows a weak coupling between the excitions and the acoustic phonons of the host. Local heating effects are found to affect the ion-ion and ion-phonon interaction parameters and produce a thermal grating under certain experimental conditions.

DOI
10.1103/physrevb.29.6074

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Physical review. B, Condensed matter•Apr 15, 1987•29 citations
Four-wave mixing has been investigated in NdxLa1\ensuremath−xP5O14{\mathrm{Nd}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{P}}_{5}{\mathrm{O}}_{14}Ndx​La1\ensuremath−x​P5​O14​ crystals as a function of temperature, laser excitation wavelength, and power. The results are interpreted in terms of scattering from a population grating, and the relative intensity of the scattered signal is investigated as well as the grating decay time. The power dependence of the scattered intensity is explained by a model involving interaction with a three-level system, and the properties of the grating decay are associated with the exciton dynamics of the ions in the excited state. Decay patterns characteristic of both incoherent and partially coherent exciton migration can be observed under different experimental conditions. Enhanced migration due to vibronic generation of phonons resonant with the metastable state splitting is also observed. The temperature dependence of the results shows a weak coupling between the excitions and the acoustic phonons of the host. Local heating effects are found to affect the ion-ion and ion-phonon interaction parameters and produce a thermal grating under certain experimental conditions.
Four-wave-mixing techniques were used to establish and probe population gratings of Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions in alexandrite crystals at temperatures between 10 and 300 K. The results were interpreted in terms of the interaction of the laser radiation with a two-level atomic system. They provide information about the characteristics of four-wave-mixing signals for this physical situation as well as being useful in characterizing the properties of energy transfer and dephasing within the ensemble of Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions. The patterns of the transient four-wave-mixing signals are consistent with a model based on the pumping dynamics of ions in the mirror and inversion crystal-field sites. The variation of the signal intensity with laser power is strongly affected by beam depletion. The characteristics of exciton migration among Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions in mirror sites were determined from the results of measuring the variation of the signal decay rate with grating spacing. The temperature dependences of the ion-ion interaction rate, the exciton-phonon scattering rate, and the diffusion coefficient were determined. These are found to be essentially the same for pumping into the 4T2^{4}\mathrm{T}_{2}4T2​ and 2E^{2}\mathrm{E}2E levels, but the effects of scattering from a grating of ions in inversion sites is much stronger for 4T2^{4}\mathrm{T}_{2}4T2​ pumping. The dephasing times for the atomic system were found from analyzing the variation of the signal intensity with grating spacing. For pumping into the 4T2^{4}\mathrm{T}_{2}4T2​ level the dephasing is dominated by radiationless decay processes. A model is presented for the decay channel that provides a theoretical explanation for the decay process which is consistent with the measured temperature and frequency dependences of the results as well as their variation with crystal-field strength. For pumping into the 2E^{2}\mathrm{E}2E level the dephasing is dominated by dephasing processes associated with the inhomogeneous linewidth of the transition.
Four-wave mixing signals from transient population gratings established in NdP5O14crystals were analyzed to obtain information on the pumping dynamics and exciton migration characteristics in this material. As the laser pump wavelength is scanned through an Nd3+absorption band, the exciton diffusion coefficient is found to vary in a manner consistent with site selection within the inhomogeneously broadened profile. Deviations from simple signal decay patterns are observed whenever the laser is tuned to excited state resonances. In addition, recent theoretical developments are applied to the grating decay data to determine the degree of coherence in the exciton motion.
Degenerate four-wave mixing was observed in alexandrite crystals (BeAl2{\mathrm{Al}}_{2}Al2​O4{\mathrm{O}}_{4}O4​: Cr3+{\mathrm{Cr}}^{3+}Cr3+), and the signal beam efficiency and decay rate were measured as functions of pump beam-crossing angle, wavelength, and power. The results are consistent with scattering from excited-state population gratings related to the difference in dispersion of the Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions in the ground and metastable states. These gratings can be selectively established with Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions in the inversion or mirror sites depending on the excitation wavelength. Strong scattering occurs only for pump beams polarized parallel to the bbb direction of the crystal.
Degenerate four-wave-mixing measurements have been performed on a wide variety of Nd3+{\mathrm{Nd}}^{3+}Nd3+-doped oxide and fluoride glasses and crystals. Crossed beams from a cw argon-ion laser were used to excite the Nd3+{\mathrm{Nd}}^{3+}Nd3+ ions directly and establish population gratings. Absolute measurements of the signal strengths were made, and their magnitudes were found to be sensitively influenced by the composition of the host. A theoretical model was developed to interpret the results, and it was found that the dominant contribution to the signal is associated with the difference in polarizability of the Nd3+{\mathrm{Nd}}^{3+}Nd3+ ions in the metastable state versus the ground state. The magnitude of the observed change in the polarizability indicates that the 4f\ensuremath{\rightarrow}5d transitions are responsible for this effect, and as a result, the value of the 〈4f\ensuremath{\Vert}r\ensuremath{\Vert}5d〉 radial integral sensitively affects the calculated polarizability change.
Four-wave-mixing techniques were used to establish and probe population gratings of Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions in both mirror and inversion sites in BeAl2{\mathrm{BeAl}}_{2}BeAl2​O4{\mathrm{O}}_{4}O4​:Cr3+{\mathrm{Cr}}^{3+}Cr3+ crystals as a function of temperature between about 6 and 300 K. The four-wave-mixing signal intensity and decay rate were monitored as a function of the crossing angle of the laser ``write'' beams. The variation of the signal intensity with crossing angle is explained theoretically with use of a model based on the interaction between the laser and a two-level atomic system. Theoretical fits to the results provide information concerning the relative importance of the absorption and dispersion contributions to the signal, and the dephasing time of the atomic system. The latter is found to be 2.2 psec for the mirror site ions and 80 psec for the inversion site ions. The signal decay rate of the inversion site ions was found to be independent of crossing angle at all temperatures, while the signal decay rate for ions in the mirror site increased with increasing crossing angle at temperatures below about 150 K. This indicates the presence of long-range energy migration, and the diffusion coefficient describing this process was found to increase to about 4.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ cm2{\mathrm{cm}}^{2}cm2?${\mathrm{c}}^{\mathrm{\ensuremath{-}}1}$ at 6 K.