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Cooperative optical nonlinearities in thulium:lithium yttrium tetrafluoride.

Qi-Ze Shu

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

In this work nonlinear refractive index changes associated with avalanche absorption of Tm:LiYF$\sb4$ are reported and compared with a microscopic theory of atomic dynamics. Critical slowing down of the nonlinear response near the avalanche threshold is described and analyzed, and the predominantly dispersive character of the susceptibility at the avalanche resonance is explained for the first time. Curiously, properties of the cooperative nonlinearity are mainly determined by ground state polarization properties, even though the excitation is resonant with an excited state transition and very much off resonance with ground state transitions. Nearly-degenerate two-beam coupling techniques were employed for the bulk of the experimental measurements reported here. Real and imaginary parts of the nonlinear refractive index, as well as response times of the nonlinearities, were determined versus light intensity and wavelength. High resolution spectroscopic studies provided a modified picture of the basic mechanism of avalanche upconversion dynamics. Enhancement of the avalanche nonlinearity in a resonant cavity resulted in self-pulsing of the upconversion emission and cavity transmission. Self-locking of a cavity to the laser frequency without external electronics was also observed, due to avalanche-mediated thermal nonlinearities in the system.

Related papers

Critical slowing down and off-resonant enhancement of avalanche nonlinearities

Q. Z. Shu, Stephen Colby Rand

We report two-beam coupling measurements of temporal response and intensity-dependent index changes in the avalanche crystal LiYF/sub 4/:Tm(3+). Surprisingly, the induced nonlinear response on the excited state resonance is dominated by a real portion arising from a non-resonant ground state transition. Critical slowing down of excited state dynamics is also predicted and observed.

Quantum Electronics and Laser Science Conference•Jun 7, 1996•0 citations

Avalanche upconversion in thulium:lithium yttrium fluoride, thulium:yttrium aluminum oxide and thulium:YAG.

Hui Ni

This thesis reports original observations and theory of strong, induced excited state absorption and emission, known as avalanche upconversion, in thulium doped crystals. The nonlinear dynamics responsible for this phenomenon and its characteristic threshold are studied in great detail, and shown to consist of two distinct cooperative processes, namely near-neighbor cross relaxation(s) and excitation migration among more distant ion pairs. The temperature dependence of avalanche upconversion and cross relaxation in these materials is explained for the first time. Also, phase conjugation with threshold behavior and potential motion sensitivity for novelty filtering is demonstrated utilizing an avalanche nonlinearity. Complex, transverse ring structures observed in Gaussian beam propagation through avalanche media are explained on the basis of numerical simulations of avalanche-induced absorption and dispersion. Evidence is presented of coherent delocalization in Tm-doped solids, in the form of unexpected oscillations in the transient response to incident light pulses. Two theoretical approaches for describing avalanche behavior were compared. A rate equation analysis suitable for weak-coupled impurity ions was used to predict basic avalanche features, including increasing absorption and upconversion emission above a threshold, temporal delay of absorption, and temperature dependence of avalanche threshold. A density matrix approach suitable for arbitrary coupling reproduced these features but also predicted oscillations in excited state populations in the presence of significant interion coherence. This theory incorporated both near-neighbor cross relaxation which gives rise to induced absorption, and excitation migration among distant pair ions necessary for immensely magnifying the effect, in a single formalism. Studies of the concentration and temperature dependence of fluorescence decays of Tm ions from $\sp1$G$\sb4$ and $\sp3$H$\sb4$ states provided firm evidence of pair-wise cross relaxations of ions in both these states. Transient four-wave mixing experiments directly revealed energy migration among $\sp3$F$\sb4$ state Tm ions at a rate rapid enough to support the content ion that migration plays an important role in avalanche dynamics. Additional experiments yielded a temperature dependence of avalanche threshold in good agreement with theory, as well as avalanche phase conjugation and transverse propagation effects due to avalanche dynamics in accord with predictions.

•Jan 1, 1994•0 citations

Critical slowing down and dispersion of avalanche upconversion dynamics

Q. Z. Shu, Stephen Colby Rand

The temporal response time on an avalanche upconversion transition is shown to undergo critical slowing down near the avalanche threshold. Also, the nonlinear refractive index is predominantly real, despite the resonant nature of the avalanche phenomenon. These findings are in excellent agreement with density-matrix analyses showing that cross relaxation dramatically alters the effective excited-state lifetime and that off-resonance absorption curiously dominates the wavelength dependence of the nonlinear refractive index.

Physical review. B, Condensed matter•Apr 1, 1997•14 citations

Coherent Cooperative Radiation in Solids

Stephen Colby Rand

Avalanche upconversion dynamics and associated nonlinear optical response was also reported for the first time in Tm:YALO crystals at room temperature. The avalanche mechanism involves a cooperative down conversion (cross relaxation) step and is a promising method of pumping rare earth lasers at entirely new (diode compatible) wavelengths, corresponding to excited state absorptions rather than ground state absorptions. Quantum theory describing the threshold for photo-darkening and the role of energy migration in avalanches was developed, and semi quantitative agreement obtained with preliminary measurements of nonlinear susceptibilities. Cooperative dynamics in general, and avalanche dynamics in particular, were shown to furnish a promising new mechanism not only for solid state lasers but for nonlinear optical interactions as well, opening the door to practical signal processing and switching applications exploiting the low intensity thresholds of avalanche processes.

Michigan Univ. Final Report•Oct 30, 1991•0 citations

Negative nonlinear susceptibility of cesium vapor around 1.06 μm

Robert H. Lehmberg, John F. Reintjes, Robert C Eckardt

We outline a complete theory of the nonlinear susceptibility of cesium around 1.06 \ensuremath{\mu}m, and present the first measurements of the negative nonlinear refractive index ${n}_{2}$ primarily responsible for the self-defocusing that is observed. For linearly polarized light, our measured value of ${n}_{2}$ is $\ensuremath{-}(1.4\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}N$ esu, where $N$ is the atomic density. This is in reasonable agreement with our calculated value of $\ensuremath{-}2.62\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}N$. The main portion of ${n}_{2}$ comes from a two-photon resonance between the $6s$ and $7s$ levels, and an additional negative term arises from induced population changes between $6s$ and $6p$. For circular polarization, ${n}_{2}$ arises mainly from the induced population changes, giving the measured and calculated values of $\ensuremath{-}(0.26\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}N$ and $\ensuremath{-}0.525\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}N$, respectively. In our experiments where the 35-psec pulses were shorter than the $6s\ensuremath{-}6p$ inverse linewidth, the nonlinear susceptibility depends mainly on the instantaneous intensity; however, for longer pulses, one would obtain additional contributions proportional to time integrals over the intensity. Since the useful output power from large Nd laser systems is limited by self-focusing due to the laser glass, our results suggest the possibility of increasing this power by using Cs vapor for compensation.

Physical Review A•Mar 1, 1976•25 citations

Avalanche upconversion in Tm:YALO_3

H. Ni, Stephen Colby Rand

We report the sudden appearance of upconversion fluorescence and resonant increasing absorption above a threshold intensity in Tm YALO3 at room temperature. These effects are shown to arise from nonlinear, cooperative, excited-state dynamics. Comparison with quantum theory reveals essential roles both for pairwise cross relaxation and excitation migration among Tm impurity ions.

Optics Letters•Sep 15, 1991•75 citations
In this work nonlinear refractive index changes associated with avalanche absorption of Tm:LiYF\sb4\sb4\sb4 are reported and compared with a microscopic theory of atomic dynamics. Critical slowing down of the nonlinear response near the avalanche threshold is described and analyzed, and the predominantly dispersive character of the susceptibility at the avalanche resonance is explained for the first time. Curiously, properties of the cooperative nonlinearity are mainly determined by ground state polarization properties, even though the excitation is resonant with an excited state transition and very much off resonance with ground state transitions. Nearly-degenerate two-beam coupling techniques were employed for the bulk of the experimental measurements reported here. Real and imaginary parts of the nonlinear refractive index, as well as response times of the nonlinearities, were determined versus light intensity and wavelength. High resolution spectroscopic studies provided a modified picture of the basic mechanism of avalanche upconversion dynamics. Enhancement of the avalanche nonlinearity in a resonant cavity resulted in self-pulsing of the upconversion emission and cavity transmission. Self-locking of a cavity to the laser frequency without external electronics was also observed, due to avalanche-mediated thermal nonlinearities in the system.
This thesis reports original observations and theory of strong, induced excited state absorption and emission, known as avalanche upconversion, in thulium doped crystals. The nonlinear dynamics responsible for this phenomenon and its characteristic threshold are studied in great detail, and shown to consist of two distinct cooperative processes, namely near-neighbor cross relaxation(s) and excitation migration among more distant ion pairs. The temperature dependence of avalanche upconversion and cross relaxation in these materials is explained for the first time. Also, phase conjugation with threshold behavior and potential motion sensitivity for novelty filtering is demonstrated utilizing an avalanche nonlinearity. Complex, transverse ring structures observed in Gaussian beam propagation through avalanche media are explained on the basis of numerical simulations of avalanche-induced absorption and dispersion. Evidence is presented of coherent delocalization in Tm-doped solids, in the form of unexpected oscillations in the transient response to incident light pulses. Two theoretical approaches for describing avalanche behavior were compared. A rate equation analysis suitable for weak-coupled impurity ions was used to predict basic avalanche features, including increasing absorption and upconversion emission above a threshold, temporal delay of absorption, and temperature dependence of avalanche threshold. A density matrix approach suitable for arbitrary coupling reproduced these features but also predicted oscillations in excited state populations in the presence of significant interion coherence. This theory incorporated both near-neighbor cross relaxation which gives rise to induced absorption, and excitation migration among distant pair ions necessary for immensely magnifying the effect, in a single formalism. Studies of the concentration and temperature dependence of fluorescence decays of Tm ions from $\sp1$G$\sb4$ and $\sp3$H$\sb4$ states provided firm evidence of pair-wise cross relaxations of ions in both these states. Transient four-wave mixing experiments directly revealed energy migration among $\sp3$F$\sb4$ state Tm ions at a rate rapid enough to support the content ion that migration plays an important role in avalanche dynamics. Additional experiments yielded a temperature dependence of avalanche threshold in good agreement with theory, as well as avalanche phase conjugation and transverse propagation effects due to avalanche dynamics in accord with predictions.
The temporal response time on an avalanche upconversion transition is shown to undergo critical slowing down near the avalanche threshold. Also, the nonlinear refractive index is predominantly real, despite the resonant nature of the avalanche phenomenon. These findings are in excellent agreement with density-matrix analyses showing that cross relaxation dramatically alters the effective excited-state lifetime and that off-resonance absorption curiously dominates the wavelength dependence of the nonlinear refractive index.
Avalanche upconversion dynamics and associated nonlinear optical response was also reported for the first time in Tm:YALO crystals at room temperature. The avalanche mechanism involves a cooperative down conversion (cross relaxation) step and is a promising method of pumping rare earth lasers at entirely new (diode compatible) wavelengths, corresponding to excited state absorptions rather than ground state absorptions. Quantum theory describing the threshold for photo-darkening and the role of energy migration in avalanches was developed, and semi quantitative agreement obtained with preliminary measurements of nonlinear susceptibilities. Cooperative dynamics in general, and avalanche dynamics in particular, were shown to furnish a promising new mechanism not only for solid state lasers but for nonlinear optical interactions as well, opening the door to practical signal processing and switching applications exploiting the low intensity thresholds of avalanche processes.
We outline a complete theory of the nonlinear susceptibility of cesium around 1.06 \ensuremath{\mu}m, and present the first measurements of the negative nonlinear refractive index n2{n}_{2}n2​ primarily responsible for the self-defocusing that is observed. For linearly polarized light, our measured value of n2{n}_{2}n2​ is $\ensuremath{-}(1.4\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}N$ esu, where NNN is the atomic density. This is in reasonable agreement with our calculated value of $\ensuremath{-}2.62\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}N$. The main portion of n2{n}_{2}n2​ comes from a two-photon resonance between the 6s6s6s and 7s7s7s levels, and an additional negative term arises from induced population changes between 6s6s6s and 6p6p6p. For circular polarization, n2{n}_{2}n2​ arises mainly from the induced population changes, giving the measured and calculated values of $\ensuremath{-}(0.26\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}N$ and $\ensuremath{-}0.525\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}N$, respectively. In our experiments where the 35-psec pulses were shorter than the $6s\ensuremath{-}6p$ inverse linewidth, the nonlinear susceptibility depends mainly on the instantaneous intensity; however, for longer pulses, one would obtain additional contributions proportional to time integrals over the intensity. Since the useful output power from large Nd laser systems is limited by self-focusing due to the laser glass, our results suggest the possibility of increasing this power by using Cs vapor for compensation.