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AIAA Plasmadynamics and Lasers Conference

Influence of Broadband Excitation on the Performance of Diode Pumped Alkali Lasers

Paul Nathaniel Jones, Gordon D. Hager, Glen P. Perram

Published Jun 1, 2011• 3 citations
Publisher

Abstract

A three level model for optically pumped alkali metal vapor lasers is developed by considering the steady state rate equations for the longitudinally averaged number densities of the ground 2 S1/2 and first excited 2 P3/2, and 2 P1/2 states. For efficient operation, the collisional relaxation between the two upper levels should be fast relative to stimulated emission. By assuming a statistical distribution between the upper two levels, the limiting analytic solution for the quasi-two level system is achieved. A second limiting solution is identified for strongly bleached conditions where the atom recycle rate, limited by spin-orbit relaxation, fully specifies the output power. Performance in the intermediate regime depends significantly on pump laser bandwidth and requires numerical simulation. The ratio of populations for the two excited, 2 P3/2,1/2 states completes an analytic solution and depends primarily on pump laser bandwidth, threshold and alkali concentration.

DOI
10.2514/6.2011-4002

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A three level model for optically pumped alkali metal vapor lasers is developed by considering the steady state rate equations for the longitudinally averaged number densities of the ground 2 S1/2 and first excited 2 P3/2, and 2 P1/2 states. For efficient operation, the collisional relaxation between the two upper levels should be fast relative to stimulated emission. By assuming a statistical distribution between the upper two levels, the limiting analytic solution for the quasi-two level system is achieved. A second limiting solution is identified for strongly bleached conditions where the atom recycle rate, limited by spin-orbit relaxation, fully specifies the output power. Performance in the intermediate regime depends significantly on pump laser bandwidth and requires numerical simulation. The ratio of populations for the two excited, 2 P3/2,1/2 states completes an analytic solution and depends primarily on pump laser bandwidth, threshold and alkali concentration.
An analytic model for the cw diode pumped alkali laser is developed by considering the longitudinally averaged number densities of the ground 2S1/2 and first excited 2P3/2, and 2P1/2 states. The pump intensity to reach threshold requires fully bleaching the pump transition and exceeding optical losses, typically about 200 Watts/cm2. Slope efficiency depends critically on the fraction of incident photons absorbed and the overlap of pump and resonator modes, approaching the quantum efficiency of 0.95 - 0.98. For marginal cavity transmission losses, peak performance is achieved for low output coupling. For efficient operation, the collisional relaxation between the two upper levels should be fast to prevent bottlenecking. By assuming a statistical distribution between the upper two levels, the limiting analytic solution for the quasitwo level system is achieved. For properly designed gain conditions, the quasi two level solution is usually achievable and represents ideal performance.
A model for an end-pumped double-pass alkali vapour laser is set up which has considered all the main physical features, including the fine-structure mixing rate that represents the three-level nature of this kind of laser, the spectral dependence of pump light absorption for broadband pumping, the longitudinal population variation and the distributed intra-cavity losses. To solve this model, we have proposed a searching algorithm for a single-pass configuration and developed a novel iterative algorithm for a double-pass case which has taken the single-pass solution as an initial value. The calculation process demonstrates a fast rate of convergence and high degree of accuracy. By this algorithm, some special cases, for example, the non-uniform longitudinal distribution of alkali atom concentration, can also be solved well. The model and the numerical approach described in this paper demonstrate a new method to simulate the CW end-pumped quasi-three- or three-level lasers. In this way, no significant assumptions or simplifications are needed in the model, and both the detailed intra-cavity information and pump power distribution can be obtained. To ensure the correctness of our model, a comparison between our model and Beach et al 's model is made. The result shows that when the non-uniformity of the longitudinal population distribution is less than 20% or the pump intensity is far beyond the threshold, the assumption of longitudinal population average is valid and the two models are equivalent. When the pump intensity is near the threshold, this assumption may be invalid due to the large longitudinal population variation. If this case happens or more detailed laser information is required, we could use this model to obtain a more accurate solution.
The distribution of population in the ground-state sublevels of an optically pumped alkali-metal vapor has been found to be strongly dependent on the mechanism assumed responsible for relaxation. Two modes of optical pumping zero mixing and complete mixing in the excited state, and three modes of alkali relaxation, uniform, Zeeman, and electron randomization, are considered. Calculations of the sublevel relative populations are made in terms of experimentally measurable parameters for all six combinations of pumping and relaxation modes. Optical-pumping transient signals are then used to demonstrate that alkali relaxation due to wall collisions is of the low-frequency "Zeeman" variety, while relaxation due to alkali-rare-gas collisions takes place through randomization of the spin of the alkali valence electron. Equations for the rate of change of the electronic spin polarization are derived for all cases, and are found to be nonexponential, in contrast with the case of an alkali of zero nuclear spin.
Alternative wavelengths for optically pumped alkali vapor lasers have been developed using single photon excitation of higher lying P-states, stimulated Raman processes, two-photon excitation of S and D states, and electric quadruple excitation on S-D transitions. Two photon excitation of Cs 72D leads to competing and cascade lasing producing red and infrared lasers operating on the D-P transitions, followed by ultraviolet, blue, the standard near infrared DPAL transitions operating on P-S transitions. The S-D pump transitions are fully bleached at pump intensities exceeding 1 MW/cm2, allowing for lasing transitions that terminate on the ground state. The kinetics of these systems are complex due to competition for population inversion among the many optical transitions. An optically pumped mid-infrared rubidium pulsed, mirrorless laser has also been demonstrated in a heat pipe along both the 62P3/2 - 62S1/2 transition at 2.73 μm and the 62P1/2 - 62S1/2 transition at 2.79 μm with a maximum energy of ~100 nJ. Performance improves dramatically as the rubidium vapor density is increased, in direct contradiction with the prior work. No scaling limitations associated with energy pooling or ionization kinetics have been observed. Practical application for infrared counter measures depends on the further development of blue diode pump sources. Finally, stimulated electronic Raman scattering and hyper-Raman processes in potassium vapor near the D1 and D2 lines have been observed using a stable resonator and pulsed laser excitation. First and second order Stokes and anti-Stokes lines were observed simultaneously and independently for a pump laser tuning range exceeding 70 cm-1. When the pump is tuned between the K D1 and D2 lines, an efficient hyper-Raman process dominates with a slope efficiency that exceeds 10%. Raman shifted laser may be useful as a target illuminator or atmospheric compensation beacon for a high power diode pumped alkali laser.
We study the influence of optical pumping on Doppler-broadened alkali-metal-atom DDD line spectra by solving the time-dependent density matrix for an open two-level system. The time-dependent absorption is averaged over the distribution of interaction times obtained from the three-dimensional beam geometry and atomic velocity distribution and over the longitudinal velocity distribution. The optical pumping is significant at much lower intensities than saturation and depends strongly on the intensity, beam radius, vapor cell length, and spontaneous-decay branching ratio. The result is in agreement with our earlier steady-state solution for a wide range of parameters and predicts two interesting line-shape features.
Rate equations for the optical pumping of alkali-metal vapors simultaneously subject to pumping, relaxation in the excited state, and relaxation in the ground state are shown to yield analytic solutions for the alkali-metal electronic and nuclear-spin polarizations in the limit of weak pumping. Nuclear-spin and hyperfine-interaction effects are properly included. Analysis of the double-exponential form of the pumping transient of the ground-state electronic-spin polarization is shown to yield new methods for the measurement of cross sections for collisional relaxation in both the ground and excited states. Formulas are derived that relate relaxation cross sections to experimentally measurable parameters. Formulas describing the influence of nuclear spin on signals obtained from standard depolarization of resonance-radiation experiments also are provided. Ambiguities in earlier optical-pumping experiments and calculations arising from oversimplified descriptions of relaxation processes are discussed.