Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Four-wave mixing of Nd 3+ impurities in glasses and crystals

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

Published May 21, 1990• 0 citations
OpenAlex

Abstract

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.

Related papers

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

Richard C. Powell, Stephen A. Payne, Lloyd L. Chase +1 more

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.

Physical review. B, Condensed matter•May 1, 1990•55 citations

Four-wave mixing in alexandrite crystals

Ali M. Ghazzawi, Jacek K. Tyminski, Richard C. Powell +1 more

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.

Physical review. B, Condensed matter•Dec 15, 1984•31 citations

Determination of excited-state polarizabilities of Cr3+ -doped materials by degenerate four-wave mixing

S. Catherine Weaver, Stephen A. Payne

We have measured the degenerate four-wave-mixing signals from several ${\mathrm{Cr}}^{3+}$-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 ${\mathrm{Cr}}^{3+}$ 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 $^{4}\mathrm{T}_{2}$ and the $^{2}\mathrm{E}$ excited states. The polarizability change between the $^{4}\mathrm{T}_{2}$ excited state and the $^{4}\mathrm{A}_{2}$ ground state is found to be greater than that between the $^{2}\mathrm{E}$ and the $^{4}\mathrm{A}_{2}$.

Physical review. B, Condensed matter•Dec 1, 1989•29 citations

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

Richard C. Powell, Stephen A. Payne

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.

Optics Letters•Nov 1, 1990•25 citations

Saturated absorption and degenerate four-wave mixing in Nd^3+ beta″ alumina

Robert W. Boyd, Bruce Dunn, Dongliang Yang +3 more

Nd3+ beta″ alumina is one of a family of potentially useful nonlinear-optical materials based on rare-earth ions substituted into a beta″ alumina host. The saturation intensity of Nd3+ beta″ alumina has been measured to be in the range 16 to 35 kW cm−2. Phase conjugation by degenerate four-wave mixing has been demonstrated, and the phase-conjugate reflectivity has been measured as a function of both laser wavelength and intensity.

Optics Letters•Mar 1, 1986•25 citations

Non-degenerate near-resonant two-wave mixing in diode pumped Nd^3+ and Yb^3+ doped crystals in the presence of athermal refractive index grating

R. Soulard, A. Brignon, Jean‐Pierre Huignard +1 more

Non-degenerate two-wave mixing in inverted laser materials is investigated both theoretically and experimentally. A complete model of two-wave mixing in gain media in the presence of an athermal refractive index grating is presented and application to beam-combining is investigated in pumped Nd3+ and Yb3+ laser materials. Experimental results are presented for a Nd:yttrium aluminum garnet crystal fiber.

Journal of the Optical Society of America B•Oct 6, 2010•14 citations
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.
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​.
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.