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IEEE Journal of Quantum Electronics

Modeling and Analysis of the Pumping Threshold Characteristics in One-Color Two-Photon Excited Cs Vapor

Hanghang Yu, Fei Chen, Qikun Pan, Yang He, Jijiang Xie

Published Dec 30, 2019• 4 citations
Publisher

Abstract

The pumping threshold is an important parameter for laser sources. Limited by the intricate transition mechanism of the one-color two-photon excitation, there has been a shortage of theoretical studies on the pumping threshold characteristics of alkali vapors. Thus, we propose a physical model of the pumping threshold by innovatively combining the coupled wave equation and the rate equation for one-color two-photon excited Cs vapor. To verify the validity of the model, we compare our simulation results with the available experimental data and show that they agree well with each other. By analyzing the main factors influencing the pumping threshold, we find that the cell temperature and frequency detuning of the pumping laser have a decisive impact on the pumping threshold. These results can provide a valuable reference for the selection of appropriate pumping parameters in further experiments.

DOI
10.1109/jqe.2019.2963074

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The pumping threshold is an important parameter for laser sources. Limited by the intricate transition mechanism of the one-color two-photon excitation, there has been a shortage of theoretical studies on the pumping threshold characteristics of alkali vapors. Thus, we propose a physical model of the pumping threshold by innovatively combining the coupled wave equation and the rate equation for one-color two-photon excited Cs vapor. To verify the validity of the model, we compare our simulation results with the available experimental data and show that they agree well with each other. By analyzing the main factors influencing the pumping threshold, we find that the cell temperature and frequency detuning of the pumping laser have a decisive impact on the pumping threshold. These results can provide a valuable reference for the selection of appropriate pumping parameters in further experiments.
Based on an analysis of kinetic processes in the continuous-wave (CW) single-wavelength two-photon pumped Rb-vapor laser (Rb-TPAL), a three-dimensional computational model is established using the rate equation. Based on the application of the model to cavity-enhanced Rb-TPAL [Yuanet al.,Optics Express29, 4858 (2021)], the calculated and measured dependences of the laser power on the pump power show good agreement. We simulate the Rb-TPAL pumped by a high-power CW laser diode and analyze the effects of temperature, vapor cell length, pump waist, vapor cell transmission, and output mirror reflectance on the characteristics of the blue laser. The results suggest that the output power and efficiency of blue laser can be improved by optimizing the above parameters; however, the particles in the52D5/25^{2}\text{D}_{5/2}52D5/2​level face difficulty to transition to the62P3/26^{2}\text{P}_{3/2}62P3/2​level, and this limits the further improvement of blue laser efficiency; therefore, an approach is proposed to improve the efficiency of Rb-TPAL. This study can be useful for designing a two-photon pumped alkali metal laser with high-power output.
The narrow-band coherent N-type resonance, promising for the development of advanced atomic clocks, can be considered as a type of three-photon resonance, where a two-photon Raman excitation is combined with a resonant optical pumping field. In this communication, we present an experimental study and a theoretical analysis related to three-photon, bi-chromatic excitation of Cs atomic vapor contained in an 8-mm long cell with 20 Torr of neon. If a coupling laser is fixed at a frequency that is lower by several GHz than the position of the absorption profile of the F g = 4 set of transitions, and a probe laser is tuned over the D 2 line (λ = 852 nm), a narrow high-contrast enhanced absorption N-resonance will be observed in the probe light profile, superimposed on the absorption profile of the F g = 4 set of transitions. We present theoretical modeling aimed to clarify the processes behind the efficiency of the N-resonance preparation for different frequency positions of the coupling laser within the D 2 line of Cs.
The optimal detuning of the pump light at the rubidium D2 line is calculated and experimentally validated. A three-level optically end-pumped model in a hot rubidium vapor cell is demonstrated, which takes into account the hyperfine structure of the ground state, various collisional processes, and the nonlinear absorption of the pump light along the cell length. By developing a constrained optimization model, we calculate the optimal detuning of the pump light that maximizes the average excited state atom concentration in the cell. Experimentally, a 1529 nm probe light at higher levels, which is attenuated to the weak-probe limit, is introduced to accurately characterize the excited state atom concentration. Coupling with the experimental results, the variation of the pump light optimal detuning with the temperature and the pump light intensity at the unsaturated pumping is analyzed. At the optimal detuning point, the theoretical decay function of the pump light percentage along the vapor cell length almost coincides regardless of the temperature and the pump light intensity changes. Moreover, the theoretical fitted pump light decay function at optimal detuning is predicted. The fitted pump light percentage exiting the vapor cell is 4.75%. A fast implementation method to achieve the maximal average excited state atom concentration in the experiment is demonstrated.
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 image-converter streak camera with picosecond time resolution was used in a study of the kinetics of formation of pulses in a traveling-wave laser in which molecular dye solutions were subjected to two-photon optical pumping. An analytic expression was obtained for the lasing threshold of a nonresonator traveling-wave laser in the case of pulsed (τp τe) and quasicontinuous (τp > τe) pumping. Satisfactory agreement was obtained between the calculated and experimental lasing threshold. The kinetics of the compression of output pulses, determined as a function of the pump radiation intensity, was described by rate equations. At pumping rates up to 10 times the threshold a qualitative agreement between the experimental and calculated results was obtained employing a two-band energy model of the dye with a short (compared with the duration of the pump pulses τp) vibrational relaxation time τe. At rates of excitation well above the threshold the kinetics of compression and delay changed, and the output pulses were split into two components, which was interpreted (in the specific case of rhodamine 6G) using a four-band energy scheme. A practical conclusion of this investigation was in the form of recommendations on the use of the proposed approach as a simple method for generating high-intensity single picosecond superradiance pulses of duration τsr with frequency up-con version and a compression coefficient τp/τsr ~ 10.