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Optics Letters

Dispersion effects in four-wave mixing measurements of ions in solids

Richard C. Powell, Stephen A. Payne

Published Nov 1, 1990• 25 citations
Publisher

Abstract

We have performed nondegenerate four-wave mixing measurements on Cr(3+) ions in three crystals: BeAl(2)O(4), Gd(3)Sc(2)Ga(3)O(12), and LaMgAl(11)O(19). Two laser beams of the same frequency were used to resonantly pump one of the absorption bands of Cr(3+), and probe beams with three different wavelengths ranging from 442 to 1064 nm were used to generate a signal from the laser-induced population grating. The observed four-wave mixing signal strength was found to increase as the wavelength of the probe beam was decreased. A model was utilized to explain these results based on the change in polarizability of the Cr(3+) ions when they are in the metastable state versus the ground state, and it was found that the dispersion effects can be described by a single-oscillator model with the lowest-energy charge-transfer transition of Cr(3+) making the dominant contribution to the signal.

DOI
10.1364/ol.15.001233

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Stephen A. Payne, Lloyd L. Chase, Richard C. Powell

Degenerate four-wave mixing measurements have been performed on a wide variety of Nd3+ doped oxide and fluoride glasses and crystals. Crossed beams from a cw argon-ion laser were used to excite directly the Nd3+ ions and establish population gratings. We have found that an absorptive type grating cannot account for the magnitude of our four-wave mixing signals, but instead, that the nonresonant contribution from a phase grating predominates.

•May 21, 1990•0 citations
We have performed nondegenerate four-wave mixing measurements on Cr(3+) ions in three crystals: BeAl(2)O(4), Gd(3)Sc(2)Ga(3)O(12), and LaMgAl(11)O(19). Two laser beams of the same frequency were used to resonantly pump one of the absorption bands of Cr(3+), and probe beams with three different wavelengths ranging from 442 to 1064 nm were used to generate a signal from the laser-induced population grating. The observed four-wave mixing signal strength was found to increase as the wavelength of the probe beam was decreased. A model was utilized to explain these results based on the change in polarizability of the Cr(3+) ions when they are in the metastable state versus the ground state, and it was found that the dispersion effects can be described by a single-oscillator model with the lowest-energy charge-transfer transition of Cr(3+) making the dominant contribution to the signal.
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.
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.
We have measured the degenerate four-wave-mixing signals from several Cr3+{\mathrm{Cr}}^{3+}Cr3+-doped oxide and fluoride laser crystals. The signals are predominantly generated by scattering of the input beams from a refractive index grating that is due to a spatially modulated excited-state population. From the measured reflectivity, the change in polarizability between the ground and excited states of Cr3+{\mathrm{Cr}}^{3+}Cr3+ is calculated. The polarizability change in the oxide hosts is accounted for by large-oscillator-strength charge-transfer transitions in the energy region of 50 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The fluoride hosts, however, did not give measurable signal levels, and this is attributed to the lack of high-oscillator-strength transitions in this energy range. The polarizability changes in the oxide hosts are observed to depend on the relative thermal population of the 4T2^{4}\mathrm{T}_{2}4T2​ and the 2E^{2}\mathrm{E}2E excited states. The polarizability change between the 4T2^{4}\mathrm{T}_{2}4T2​ excited state and the 4A2^{4}\mathrm{A}_{2}4A2​ ground state is found to be greater than that between the 2E^{2}\mathrm{E}2E and the 4A2^{4}\mathrm{A}_{2}4A2​.
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 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.