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Physical review. B, Condensed matter

Four-wave mixing in alexandrite crystals

Ali M. Ghazzawi, Jacek K. Tyminski, Richard C. Powell, John C. Walling

Published Dec 15, 1984• 31 citations
Publisher

Abstract

Degenerate four-wave mixing was observed in alexandrite crystals (Be${\mathrm{Al}}_{2}$${\mathrm{O}}_{4}$: ${\mathrm{Cr}}^{3+}$), 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 ${\mathrm{Cr}}^{3+}$ ions in the ground and metastable states. These gratings can be selectively established with ${\mathrm{Cr}}^{3+}$ ions in the inversion or mirror sites depending on the excitation wavelength. Strong scattering occurs only for pump beams polarized parallel to the $b$ direction of the crystal.

DOI
10.1103/physrevb.30.7182

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 20, 1996•0 citations
Degenerate four-wave mixing was observed in alexandrite crystals (Be{\mathrm{Al}}_{2}$${\mathrm{O}}_{4}: 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.
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.
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.
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​.