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Physical review. B, Condensed matter

Four-wave mixing of Nd3+ -doped crystals and glasses

Richard C. Powell, Stephen A. Payne, Lloyd L. Chase, Gary D. Wilke

Published May 1, 1990• 55 citations
Publisher

Abstract

Degenerate four-wave-mixing measurements have been performed on a wide variety of ${\mathrm{Nd}}^{3+}$-doped oxide and fluoride glasses and crystals. Crossed beams from a cw argon-ion laser were used to excite the ${\mathrm{Nd}}^{3+}$ 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 ${\mathrm{Nd}}^{3+}$ 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.

DOI
10.1103/physrevb.41.8593

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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.

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Journal of the Optical Society of America B•Jul 1, 1999•19 citations
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​.
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 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.
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.
The mechanism for refractive-index changes that accompany changes in population during pumping and amplification of an optical beam is studied in a Nd:YAG laser crystal by both resonant four-wave mixing and interferometric techniques. It is found that these refractive-index changes (connected with the difference in polarizability of excited and unexcited Nd3+ ions) have two components: a small noninertial component that accompanies an amplified optical pulse and the major changes that are intensified with a delay time of ∼3 µs. The latter effect is explained by population (or depopulation) of a higher-lying energy level 2(F2)5/2 of the 4f electron shell of Nd3+ ions, which has large polarizability in near-IR and visible light. The real part of the nonlinear optical resonant susceptibility of the inverted Nd:YAG caused by the refractive-index changes is also discussed.