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Michigan Univ. Final Report

Coherent Cooperative Radiation in Solids

Stephen Colby Rand

Published Oct 30, 1991• 0 citations
OpenAlex

Abstract

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.

Related papers

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

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

Continuous-wave, cooperative upconversion lasers.

Ping Xie

Continuous-wave lasers in which the emitted photon energy may be up to three times greater than that of the incident pump light by virtue of cooperative (coupled atom) upconversion processes are reported for the first time in this thesis. Cw upconversion laser action was obtained at wavelengths of 0.55$\mu$m, 0.70$\mu$m, 0.85$\mu$m and 2.8$\mu$m using infrared excitation in the range $\lambda$ = 1.48-1.70$\mu$m in concentrated crystals of Er:CaF$\sb2$ and Er:LiYF$\sb4$. Detailed aspects of the behavior and internal dynamics of these systems have been considered both experimentally and theoretically in this work. Two limiting approaches were applied to gain theoretical insight into possible unique features of cooperative upconversion lasers. These corresponded to strong and weak coupling theories. A density matrix approach describing the strong coupling limit predicted several new results of cooperative interactions, including enhanced quantum efficiency, enhanced energy transfer, and cooperative instabilities. A rate equation analysis appropriate to weaker coupling was used to confirm that cooperative upconversion lasers can operate continuously on self-terminating transitions and established threshold conditions for pair- and trio-pumped lasers. Time dependent upconversion fluorescence measurements were performed to investigate the pumping mechanism of the new lasers experimentally. These observations and measurement of the intensity dependence of upconversion emission established that the inversion mechanism was exclusively cooperative in nature. Upconversion laser instabilities were also studied and related to nonlinear, cooperative dynamics. Unique features of cooperative upconversion lasers were identified, compared with other upconversion pumping schemes, and exploited to demonstrate the first cw mode-locked solid state laser operating in the visible spectral range. On the basis of this work, it may be concluded that cooperative upconversion provides a practical means of generating coherent radiation in new spectral regions, even on self-terminating transitions.

•Jan 1, 1992•1 citation

Nonlinear dynamics of cooperative reconversion

P. Xie, S. C. Rand

We describe several new aspects of light–matter interactions for solids in which interatomic coupling of impurity atoms plays a dominant role in population dynamics. We explore the implications of spatial coherence in such multiatom interactions by introducing a density-matrix theory of cooperative upconversion, focusing on pair systems for which analytic results can be obtained. We predict population pulsations in coherent cooperative upconversion, enhanced quantum efficiency, enhanced energy transfer, and pair-mediated instabilities, not only in cooperative upconversion media without external cavities but in upconversion lasers and conventional lasers in highly doped solids as well. These predictions are compared with rate equation solutions and observations in lasers with inversions sustained by cooperative processes, particularly the 2.8-μm Er laser. Rate equations fail to predict the observed steady-state instabilities of this laser, which are well reproduced by density-matrix theory, furnishing evidence of weak coherent delocalizations in a rare-earth system.

Journal of the Optical Society of America B•May 1, 1994•11 citations

Cooperative optical nonlinearities in thulium:lithium yttrium tetrafluoride.

Qi-Ze Shu

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.

•Jan 1, 1996•0 citations

Pair-pumped upconversion solid-state laser

Stephen Colby Rand, S. A. Pollack

A new class of laser is reported in which inversion is due to pair-mediated upconversion, quite distinct from conventional sequential one-photon or multiphoton excitation mechanisms. Upconversion of radiation is standardly accomplished by multiphoton processes relying on linear or nonlinear susceptibilities of individual atoms. However, more efficient upconversion can occur by cooperative multiatom processes involving simultaneous transitions on two or more atoms. Cooperative pair pumping in 5% Er:LiYF4 produces laser action from upconverted energy states following pumping at 1.54 µm with a flashlamp-pumped Er:glass laser on the ground to the 4/13/2 transition. Two neighboring 4/13/2 ions decay cooperatively to yield one 4/9/2 ion (which relaxes quickly to 4/11/2), competing effectively with spontaneous emission because of strong interatom coupling and long 4/13/2 lifetime. The upconversion pair process is shown for the first time to be so effective in Er:YLF that this mechanism alone can invert the 4/11/2 state with respect to lower states, generating long delays proportional to inverse pump energy in the onset of lasing.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations
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.
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.
Continuous-wave lasers in which the emitted photon energy may be up to three times greater than that of the incident pump light by virtue of cooperative (coupled atom) upconversion processes are reported for the first time in this thesis. Cw upconversion laser action was obtained at wavelengths of 0.55μ\muμm, 0.70μ\muμm, 0.85μ\muμm and 2.8μ\muμm using infrared excitation in the range λ\lambdaλ = 1.48-1.70μ\muμm in concentrated crystals of Er:CaF$\sb2$ and Er:LiYF$\sb4$. Detailed aspects of the behavior and internal dynamics of these systems have been considered both experimentally and theoretically in this work. Two limiting approaches were applied to gain theoretical insight into possible unique features of cooperative upconversion lasers. These corresponded to strong and weak coupling theories. A density matrix approach describing the strong coupling limit predicted several new results of cooperative interactions, including enhanced quantum efficiency, enhanced energy transfer, and cooperative instabilities. A rate equation analysis appropriate to weaker coupling was used to confirm that cooperative upconversion lasers can operate continuously on self-terminating transitions and established threshold conditions for pair- and trio-pumped lasers. Time dependent upconversion fluorescence measurements were performed to investigate the pumping mechanism of the new lasers experimentally. These observations and measurement of the intensity dependence of upconversion emission established that the inversion mechanism was exclusively cooperative in nature. Upconversion laser instabilities were also studied and related to nonlinear, cooperative dynamics. Unique features of cooperative upconversion lasers were identified, compared with other upconversion pumping schemes, and exploited to demonstrate the first cw mode-locked solid state laser operating in the visible spectral range. On the basis of this work, it may be concluded that cooperative upconversion provides a practical means of generating coherent radiation in new spectral regions, even on self-terminating transitions.
We describe several new aspects of light–matter interactions for solids in which interatomic coupling of impurity atoms plays a dominant role in population dynamics. We explore the implications of spatial coherence in such multiatom interactions by introducing a density-matrix theory of cooperative upconversion, focusing on pair systems for which analytic results can be obtained. We predict population pulsations in coherent cooperative upconversion, enhanced quantum efficiency, enhanced energy transfer, and pair-mediated instabilities, not only in cooperative upconversion media without external cavities but in upconversion lasers and conventional lasers in highly doped solids as well. These predictions are compared with rate equation solutions and observations in lasers with inversions sustained by cooperative processes, particularly the 2.8-μm Er laser. Rate equations fail to predict the observed steady-state instabilities of this laser, which are well reproduced by density-matrix theory, furnishing evidence of weak coherent delocalizations in a rare-earth system.
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.
A new class of laser is reported in which inversion is due to pair-mediated upconversion, quite distinct from conventional sequential one-photon or multiphoton excitation mechanisms. Upconversion of radiation is standardly accomplished by multiphoton processes relying on linear or nonlinear susceptibilities of individual atoms. However, more efficient upconversion can occur by cooperative multiatom processes involving simultaneous transitions on two or more atoms. Cooperative pair pumping in 5% Er:LiYF4 produces laser action from upconverted energy states following pumping at 1.54 µm with a flashlamp-pumped Er:glass laser on the ground to the 4/13/2 transition. Two neighboring 4/13/2 ions decay cooperatively to yield one 4/9/2 ion (which relaxes quickly to 4/11/2), competing effectively with spontaneous emission because of strong interatom coupling and long 4/13/2 lifetime. The upconversion pair process is shown for the first time to be so effective in Er:YLF that this mechanism alone can invert the 4/11/2 state with respect to lower states, generating long delays proportional to inverse pump energy in the onset of lasing.