Abstract
A theoretical model is established to describe the kinetic processes and laser mechanism for a nanosecond-pulse exciplex pumped Cs vapor laser (XPCsL). A new simulation method is proposed to solve a set of non-stationary rate equations considering high energy levels and the results of simulation are consistent with the experimental data. The effects of cell temperature, pump energy and buffer gas on the output laser pulses are presented and analyzed in detail, which reveal the unique properties of nanosecond-pulse XPCsL.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Diode-pumped atomic alkali vapor laser (DPAL) has grown as an indispensable light source in modern scientific research since it has dual advantages of solid-state and gas-phase lasers, which mainly includes high outputting power, efficient energy conversion, good beam quality and excellent thermal management [1]. The concept of alkali vapor laser was proposed by Schawlow and Townes in 1958 [2]. However, due to the limitation of the pump source, it did not attract widespread attention until the realizations of Ti: Sapphire pumped Rb vapor laser in 2003 [3] and diode-pumped Cs vapor laser in 2005 [4], respectively. So far, the outputting power of DPAL has been increased from mW to kW through the applications of efficient pump configurations, high-power pump sources and cooling systems [1,3,5–9], proving its potential in high-power laser region.
However, the mismatching between alkali atomic absorption and laser diodes array (LDA) emission leads not only a low energy conversion efficiency but also a severe thermal accumulation in the vapor cell [10]. In general, the linewidth of LDA is two orders of magnitude greater than that of alkali atomic absorption, which means thousands of torr of noble gas is required as a broadening medium in an efficient high-power DAPL [10]. In 2008, Readle et al. experimentally reported a new class of alkali laser, excimer pumped alkali vapor laser (XPAL), whose laser-active medium is excimer pair of alkali atom and noble gas [11]. Especially, its resonance absorption linewidth is broadened to nanometer scale [12]. Palla et al. presented a theoretical model for XPAL systems and compared it with the experimental results, and further simulated its operating performance [13–15]. The results showed that XPAL has the potential of high-power laser in CW (continuous-wave) operation [15]. However, the severe heat accumulation in the operation process hindered the experimental research of XPAL [16]. Therefore, the method of introducing a super-fast gas flow into the vapor cell has been proposed, and the results showed that the sonic-level gas flow is required to control the thermal effects in a CW XPAL, which is difficult in experiment t [16–21]. On the other hand, the operation mode of QCW (quasi-continuous-wave) pulse pumped can effectively suppress the thermal effect [22,23]. Thus, the research of nanosecond-pulse pumped XPAL is very significant for the development of high-power XPAL.
Inspired from the methodology of “ab initio” and “ray tracing”, a physical model for the time evolution of kinetic processes and laser beam propagation are established in this paper, in which the non-stationary rate equations is solved by ordinary differential equation (ODE). On basis of the validation of our simulation result by comparing with experimental data, we further depict the microphysical picture in the ignition process of short-pulse pumped XPAL system, providing an insight into the influence of pump energy, cell temperature and buffer gas on its output characteristics.
2. Description of model
2.1 Laser kinetic processes and rate equations in the high-power XPCsL systems
An energy diagram of high-power XPCsL is depicted in Fig. 1, giving a clear physical picture of the kinetic processes of XPCsL: the laser-active state, ${X^2}\Sigma _{1/2}^ + $, is formed due to the gradient force of intermolecular potential between Cs and Ar gases (thermal equilibrium), providing a resonance with blue-shifted D2 line of Cs. Afterwards, the excited excimer trends to dissociate into unbounded Cs and Ar atoms, respectively. Cs atom at ${6^2}P_{3/2}^{}$ state can decay to the ground state directly with emitting a photon at 852.3 nm, or with the help of relaxation medium, Cs can relax to ${6^2}P_{1/2}^{}$ state firstly and return to ground state with releasing a photon at 894.6 nm (Fig. 1, left-bottom). However, as described in the rate equations, excited Cs can be further pumped to higher excited states by secondary photoexcitation, and photoionization occurs. It should be noted that the cross-sections for secondary photoexcitation and photoionization are reduced to constants since their enegry gaps are both off-resonant with incident frequency, and the three higher excited states (${6^2}D_{3/2}^{},\textrm{ }{6^2}D_{5/2}^{},\textrm{ }{8^2}S_{1/2}^{}$) are merged to one whose degeneracy coefficient is also reduced to a constant (the summation of three levels) [12,15]. Based on the atom physics, the simplifications here can be without loss of generality but improve the efficiency of simulation calculations.
The rate equations for high-power XPCsL can be written as
In short pulse-duration, laser oscillation in the cavity is not as stable as in CW operation, so that spontanesous emission has an important influence on the short pulse laser system, the rates, ${A_{30}}$ and ${A_{40}}$ are determined by
where V is the volume of a segment, $\nu $ and $\tau $ are the frequency and lifetime of corresponding energy levels, respectively. $\phi (\nu )$ is the uniformed Lorentzian profile of the pressure broadening. $s(\nu )$ is a function of state density, indicating the mode number in a longitudinal frequency scale, which can be expressed as where c is the vaccum speed of light.${\alpha _{pass}}$ denotes the coefficient of single-pass loss in the cavity,
where ${R_{OC}}$ and ${R_{HR}}$ are the reflectivities of output coupler and high reflector.Secondary photoexcitation and ionization in high-power XPCsL can severely influence the lasing power and energy conversion efficiency, and promote the formation of low-temperture plasma. In the non-stationary rate equations, Eqs. (1)–(8), the rates of pump-induced excitation, $F_p^{(35,45)}$, laser-induced exciatation, $F_{D1,D2}^{(35,45)}$, and ionization processes, ${F_{ion}}$ can be computed as follow,
2.2 Algorithm methods
The sketch of optical resonator is presented in Fig. 2. The length of cavity L = 1 m and the Cs-Ar cell placed in the center has a length of 6 cm and a diameter of 2.5 cm. The Gaussian pump pulse whose spectral and pulse linewidths are 7 GHz and 4.3 ns respectively are introduced from the output coupler (OC), and then propagate along the x-axis. Unlike continuous-wave (CW) or quasi-CW operation alkali vapor laser, the non-stationary rate equations for XPCsL have to be solved by the methodology of ordinary differential equation (ODE). By using the “Runge-Kutta” method, we are allowed to obtain a series of numerical results. Specifically, in our simulation, $\Delta t\textrm{ = }0.02$ ns is chosen as time accuracy, since it is much longer than the typical time of light–matter interaction(${10^{ - 18}}$s).
The propagation of the laser beam in the cavity (without gain medium) is described as
The propagation of the pump beam in the cavity is described by
The iterative calculating flow chart is shown in Fig. 3.
As shown in the flowchart, the latest coordinate x of the pump and laser beam can be attained by the calculation of time t. If the coordinate x is in the cell, the ode function in the MATLAB can be used to solve the rate equations with the initial values of the number density of energy levels and photons of D1 and D2 transitions at time $t - \Delta t$. After getting the particle number density of the energy levels and photons at time t, the laser intensity at t and the pump intensity at $t + \Delta t$ are obtained; Otherwise, the propagation equation and boundary conditions was used to simulate the propagation of pump and laser beams. In summary, the evolution of the laser intensity over time can be obtained by multiple iterative loops.
3. Results and discussion
Figure 4 is the comparison between experimental (a) [11] and simulation (b) results, which can verify the accuracy of the model. With the parameters shown in Table 2, a good agreement of simulation results with experiment is shown up with a ∼7.5 ns of time delay between pump and laser pulse. However, there is a ∼0.9 ns of difference in the FWHM of the lasing signal between simulation and experimental result. The lasing condition is ideal in the simulation while inevitable perturbation in the experiment can decay the density inversion rapidly. As a result, the simulated laser pulse appears earlier and its rising curve was smoother.
Figure 5 calculates the effect of cell temperature on output laser pulse. It can be seen from Fig. 5(a) that the peak of laser pulse and the delay time between pump and laser peaks increase with rising the cell temperature. Higher temperature means higher particle number density of Cs, which leads to a higher laser pulse power. However, the time to establish the inversion of the number density between energy levels of Cs also increases. Figure 5(b) shows the peak of each laser pulse first rises and then decreases as the temperature increases, which means, there is an optimum temperature of Cs-Ar cell for a specific pump energy.
Figures 6(a) and 6(b) presents the effect of pump energy on laser pulses. As shown in Fig. 6(a), the peak of lasing pulse increases with the pump energy while the delay time between pump and laser pulses decreases with it. When the temperature is fixed, the number density of particles of Cs in the cell is constant. The pump light all have a profile of Gaussian. Based on the above reasons, rising the pump energy can increase the intensity of output laser pulse while make the pump pulse reach the pump threshold earlier in time, resulting in the laser output pulse appearing earlier. In Fig. 6(b), for each specific temperature, the peak of laser pulse increases with increasing pump energy, and then gradually approaches saturation.
Figure 7 shows the outputting laser of the D1(894.6nm) and D2(852.3nm) lines with different concentration of buffer gas (${C_2}{H_6}$). We can see that D1 line is positively proportioned to the pressure of ethane, and further reaches simultaneously with D2 line when 10-15 Torr of ethane is added. Besides, the D2 line always appears earlier than the D1 line, and the time interval between the peak of D1 and D2 pulses decreases with the addition of ethane. It can be seen in Fig. 7(d), the slope of the curve representing the number density of ${6^2}{P_{1/2}}$ grows with the concentration of ethane, suggesting the promoting effect of buffer gas in the relaxation process. It is worth mentioning that the laser pulses shown in Figs. 7(a)–7(c) are measured at $x = 0$ while the number density in Fig. 7(d) is at $x = {x_1}$, where a 1.6 ns of time difference exists between the two coordinates.
4. Summary
In this article, we established a dynamical model for a short–pulse XPAL system with a nanosecond pump pulse. By solving the non-stationary differential rate equations including higher excited and ionized energy levels, we simulated the laser kinetics properties of a nanosecond-pulse XPCsL and figured out the temporal behavior of laser pulses and the dependences of outputting laser performances on buffer gas, cell temperature and pump energy. The stimulation results were consistent with the experiment data and showed unique properties of a short-pulse XPAL. Increasing the temperature of cell and pump energy can both increase the energy of output laser pulse, but the former causes the laser pulse relatively delay in time domain, whereas the latter makes it appear earlier. Moreover, there is an optimal temperature for a specific pump energy while the outputting energy has its maximum limit for a specific cell temperature. Besides, the output characteristics of the double-line laser with different concentration of ethane are also shown in detail. This work can help to understand the laser dynamics and characteristics of a nanosecond-pulsed XPAL system and facilitate the design of an efficient short-pulse XPAL in experiment.
Funding
China Aerospace Science and Technology Corporation (KM20170269).
Disclosures
The authors declare no conflicts of interest.
References
1. B. Zhdanov and R. Knize, Diode pumped alkali lasers (SPIE, 2011).
2. A. L. Schawlow and C. H. Townes, “Infrared and Optical Masers,” Phys. Rev. 112(6), 1940–1949 (1958). [CrossRef]
3. W. F. Krupke, R. J. Beach, V. K. Kanz, and S. A. Payne, “Resonance transition 795-nm rubidium laser,” Opt. Lett. 28(23), 2336–2338 (2003). [CrossRef]
4. R. J. Beach, W. F. Krupke, V. K. Kanz, S. A. Payne, M. A. Dubinskii, and L. D. Merkle, “End-pumped continuous-wave alkali vapor lasers: experiment, model, and power scaling,” J. Opt. Soc. Am. B 21(12), 2151–2163 (2004). [CrossRef]
5. B. V. Zhdanov, A. Stooke, G. Boyadjian, A. Voci, and R. J. Knize, “Rubidium vapor laser pumped by two laser diode arrays,” Opt. Lett. 33(5), 414–415 (2008). [CrossRef]
6. T. Ehrenreich, B. Zhdanov, T. Takekoshi, S. P. Phipps, and R. J. Knize, “Diode pumped caesium laser,” Electron. Lett. 41(7), 415–416 (2005). [CrossRef]
7. B. Zhdanov, C. Maes, T. Ehrenreich, A. Havko, N. Koval, T. Meeker, B. Worker, B. Flusche, and R. J. Knize, “Optically pumped potassium laser,” Opt. Commun. 270(2), 353–355 (2007). [CrossRef]
8. A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Eroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” Quantum Electron. 42(2), 95–98 (2012). [CrossRef]
9. G. Pitz, G. Hager, T. Tafoya, J. Young, G. Perram, and D. Hostutler, An experimental high pressure line shape study of the rubidium D1 and D2 transitions with the noble gases, methane, and ethane (SPIE, 2014).
10. G. A. Pitz, C. D. Fox, and G. P. Perram, “Pressure broadening and shift of the cesium D-2 transition by the noble gases and N-2, H-2, HD, D-2, CH4, C2H6, CF4, and He-3 with comparison to the D-1 transition,” Phys. Rev. A 82(4), 042502 (2010). [CrossRef]
11. J. D. Readle, C. J. Wagner, J. T. Verdeyen, D. A. Carroll, and J. G. Eden, “Lasing in Cs at 894.3 nm pumped by the dissociation of CsAr excimers,” Electron. Lett. 44(25), 1466–1467 (2008). [CrossRef]
12. J. D. Readle, C. J. Wagner, J. T. Verdeyen, T. M. Spinka, D. L. Carroll, and J. G. Eden, Excimer-pumped alkali vapor lasers: a new class of photoassociation lasers (SPIE, 2010).
13. A. D. Palla, J. T. Verdeyen, and D. L. Carroll, Exciplex pumped alkali laser (XPAL) modeling and theory (SPIE, 2010).
14. A. D. Palla, D. L. Carroll, J. T. Verdeyen, and M. C. Heaven, XPAL modeling and theory (SPIE, 2011).
15. A. D. Palla, D. L. Carroll, J. T. Verdeyen, J. D. Readle, T. M. Spinka, C. J. Wagner, J. G. Eden, M. C. Heaven, S. J. Davis, and J. T. Schriempf, “Multi-dimensional modeling of the XPAL system,” Proc. SPIE 7581, 75810L (2010). [CrossRef]
16. X. Xu, B. Shen, C. Xia, and B. Pan, “Modeling of Kinetic and Thermodynamic Processes in a Flowing Exciplex Pumped Alkali Vapor Laser,” IEEE J. Quantum Electron. 53(2), 1–7 (2017). [CrossRef]
17. K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Computational fluid dynamics modeling of subsonic flowing-gas diode-pumped alkali lasers: comparison with semi-analytical model calculations and with experimental results,” J. Opt. Soc. Am. B 31(11), 2628–2637 (2014). [CrossRef]
18. E. Yacoby, K. Waichman, O. Sadot, B. D. Barmashenko, and S. Rosenwaks, “Modeling of supersonic diode pumped alkali lasers,” J. Opt. Soc. Am. B 32(9), 1824–1833 (2015). [CrossRef]
19. E. Yacoby, K. Waichman, O. Sadot, B. D. Barmashenko, and S. Rosenwaks, “Flowing-gas diode pumped alkali lasers: theoretical analysis of transonic vs supersonic and subsonic devices,” Opt. Express 24(5), 5469–5477 (2016). [CrossRef]
20. X. Xu, B. Shen, J. Huang, C. Xia, and B. Pan, “Theoretical investigation on exciplex pumped alkali vapor lasers with sonic-level gas flow,” J. Appl. Phys. 122(2), 023304 (2017). [CrossRef]
21. X. Xu, B. Shen, J. Huang, C. Xia, and B. Pan, “Detailed computation on exciplex pumped alkali vapor laser with supersonic flow,” Opt. Express 25(26), 32745–32756 (2017). [CrossRef]
22. B. Shen, J. Huang, X. Xu, C. Xia, and B. Pan, “Modeling of time evolution of power and temperature in single-pulse and multi-pulses diode-pumped alkali vapor lasers,” Opt. Express 25(12), 13396–13407 (2017). [CrossRef]
23. C. Su, B. Shen, X. Xu, C. Xia, and B. Pan, “Simulation and analysis of the time evolution of laser power and temperature in static pulsed XPALs,” High Power Laser Sci. Eng. 7, e44 (2019). [CrossRef]
24. G. A. Pitz, C. D. Fox, and G. P. Perram, “Transfer between the cesium 6 2 P 1/2 and 6 2 P 3/2 levels induced by collisions with H 2, HD, D 2, CH 4, C 2 H 6, CF 4, and C 2 F 6,” Phys. Rev. A 84(3), 032708 (2011). [CrossRef]
25. M. Mahmoud and Y. Gamal, “Effect of energy pooling collisions in formation of a cesium plasma by continuous wave resonance excitation,” Opt. Appl. 40, 129–141 (2010).
26. E. Hinnov and J. G. Hirschberg, “Electron-ion recombination in dense plasmas,” Phys. Rev. 125(3), 795–801 (1962). [CrossRef]