When the 2.8 µm erbium laser is pumped well above threshold an instability is observed at a unique pumping wavelength which causes the laser inversion to be produced by interactions among neighboring impurity ions. We show experimentally that this instability does not occur at equivalent levels over threshold when excitation is provided at wavelengths other than 1.5 µm. This behavior is compared with the results of two theoretical approaches to a description of the nonlinear dynamics, namely a rate equation and a density matrix solution. It is shown theoretically that instabilities may originate from two different physical mechanisms in pair-pumped laser systems, both of which are related to the nonlinear upconversion terms. Oscillatory solutions for the laser output may arise either from interplay of the nonlinear upconversion response with cavity photon density or from delocalization of the pair interaction. Details of these predictions are compared with time series of the laser output to shed light on the true origin of the observed instabilities. A possible explanation of excess amplitude noise in conventional infrared Erbium lasers is offered.
When the 2.8 µm erbium laser is pumped well above threshold an instability is observed at a unique pumping wavelength which causes the laser inversion to be produced by interactions among neighboring impurity ions. We show experimentally that this instability does not occur at equivalent levels over threshold when excitation is provided at wavelengths other than 1.5 µm. This behavior is compared with the results of two theoretical approaches to a description of the nonlinear dynamics, namely a rate equation and a density matrix solution. It is shown theoretically that instabilities may originate from two different physical mechanisms in pair-pumped laser systems, both of which are related to the nonlinear upconversion terms. Oscillatory solutions for the laser output may arise either from interplay of the nonlinear upconversion response with cavity photon density or from delocalization of the pair interaction. Details of these predictions are compared with time series of the laser output to shed light on the true origin of the observed instabilities. A possible explanation of excess amplitude noise in conventional infrared Erbium lasers is offered.
Here we describe a class of cw upconversion lasers in which inversion is due exclusively to cooperative interactions of rare earth ions in highly doped solids, resulting in unique opportunities for output wavelength agility, large upconversion factors, and high quantum efficiencies through nonlinear dynamics. We have isolated capabilities of the cooperative mechanism by performing experiments in Er:CaF2 and Er:LiYF4 with infrared pumping of the first Er3+ resonance at 1.53 μm. At liquid helium temperatures, laser action at 544 nm was achieved in an astigmatically compensated, three-mirror cavity with 5% efficiency in LiYF4. The upconversion factor (ratio of pump to laser wavelength) was 2.81, to our knowledge the highest ever reported for cw upconversion lasers. At 77 K, laser action at 551 nm was observed. Surprisingly, output at both 544 and 551 nm was truly cw with cooperative pumping, unlike earlier green erbium lasers, which exhibited self-pulsing. Also at 77 K, near infrared laser action was obtained at 0.855 pm with exceptionally high efficiency in CaF2(28%) and LiYF4 (20%) on self-quenching transitions. Successful demonstration of cw laser action on such transitions also suggests a means whereby quantum efficiencies may exceed unity. The lower laser level in such cases is the origin of cooperative pumping to the upper laser level, but also receives population as the result of stimulated emission. Hence population can be recycled for enhanced quantum efficiency. Additionally, population pulsations can occur and sustained oscillations in laser output have been observed in a cooperative erbium upconversion laser at 2.8 μm.
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.
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 0.55μm, 0.70μm, 0.85μm and 2.8μm using infrared excitation in the range λ = 1.48-1.70μm 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.
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.
Here we report and discuss the avalanche-like up-conversion behavior in absence of the avalanche. We experimentally observed significant changes in the slope of the curve for the intensity dependence of up-conversion luminescence of erbium ions in the green band (520-560 nm) on the pump intensity of the diode laser. Such changes are typical for the photon avalanche. However, the concentration of erbium ions is insufficient for an efficient exchange of energy between them, and the excitation of a photon avalanche is not possible. Using a simple three-level approximation of the up-conversion process model, we have shown that the observed avalanche-like luminescence process can also occur in the absence of a photon avalanche due to the nonlinear relation between the efficiency of two pumping channels of erbium ions caused by the intensity dependence of the pump spectrum.
The possibilities to obtain efficient 3-?m lasing in erbium systems on the self-saturated transition 4/ 11/2?4/13/2 are analyzed. In the frame of the mathematical model based on analytical expressions for population inversion, photon flux density, and quantum efficiency, obtained in the stationary regime, and which explains the main characteristics of 3-?m generation, the influence of various interaction mechanisms such as cross-relaxations, transfer to impurities, excited-state absorption (ESA) and so on is analyzed. It is shown that, although ESA from the terminal laser level could improve the generation characteristics, the driving mechanism for 3-?m erbium lasers is the cooperative upconversion from the terminal laser level.