Modeling of pulsed K diode pumped alkali laser - OSA Publishing

Modeling of pulsed K diode pumped alkali laser: Analysis of the experimental results Ilya Auslender,1 Boris Barmashenko,1,* Salman Rosenwaks,1 Boris Zhdanov,2 Matthew Rotondaro,2 and Randall J. Knize2 1

Department of Physics, Ben-Gurion University of the Negev, Ben-Gurion Blvd. 1, Beer-Sheva, 84105, Israel US Air Force Academy, Laser and Optics Research Center, 2354 Fairchild Dr., Ste. 2A31, USAF Academy, Colorado 80840, USA * [email protected]

2

Abstract: A simple optical model of K DPAL, where Gaussian spatial shapes of the pump and laser intensities in any cross section of the beams are assumed, is reported. The model, applied to the recently reported highly efficient static, pulsed K DPAL [Zhdanov et al, Optics Express 22, 17266 (2014)], shows good agreement between the calculated and measured dependence of the laser power on the incident pump power. In particular, the model reproduces the observed threshold pump power, 22 W (corresponding to pump intensity of 4 kW/cm2), which is much higher than that predicted by the standard semi-analytical models of the DPAL. The reason for the large values of the threshold power is that the volume occupied by the excited K atoms contributing to the spontaneous emission is much larger than the volumes of the pump and laser beams in the laser cell, resulting in very large energy losses due to the spontaneous emission. To reduce the adverse effect of the high threshold power, high pump power is needed, and therefore gas flow with high gas velocity to avoid heating the gas has to be applied. Thus, for obtaining high power, highly efficient K DPAL, subsonic or supersonic flowing-gas device is needed. ©2015 Optical Society of America OCIS codes: (140.1340) Atomic gas lasers; (140.3480) Lasers, diode-pumped; (140.3430) Laser theory.

References and links 1.

W. F. Krupke, “Diode pumped alkali lasers (DPALs) — A review (rev1),” J. Prog. Quantum Electron. 36(1), 4– 28 (2012). 2. B. V. Zhdanov and R. J. Knize, “Review of alkali laser research and development,” Opt. Eng. 52(2), 021010 (2012). 3. B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Efficient potassium diode pumped alkali laser operating in pulsed mode,” Opt. Express 22(14), 17266–17270 (2014). 4. G. D. Hager and G. P. Perram, “A three-level analytic model for alkali metal vapor lasers: part I. Narrowband optical pumping,” Appl. Phys. B 101(1-2), 45–56 (2010). 5. G. D. Hager and G. P. Perram, “A three-level model for alkali metal vapor lasers. Part II: broadband optical pumping,” Appl. Phys. B 112(4), 507–520 (2013). 6. B. D. Barmashenko and S. Rosenwaks, “Detailed analysis of kinetic and fluid dynamic processes in diodepumped alkali lasers,” J. Opt. Soc. Am. B 30(5), 1118–1126 (2013). 7. 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). 8. A. M. Komashko and J. Zweiback, “Modeling laser performance of scalable side-pumped alkali laser,” Proc. SPIE 7581, 75810H (2010). 9. R. J. Knize, B. V. Zhdanov, and M. K. Shaffer, “Photoionization in alkali lasers,” Opt. Express 19(8), 7894– 7902 (2011). 10. B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: model calculations,” Appl. Phys. Lett. 102(14), 141108 (2013). 11. B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Power degradation due to thermal effects in Potassium Diode Pumped Alkali Laser,” Opt. Commun. 341, 97–100 (2015).

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Received 1 Jul 2015; revised 29 Jul 2015; accepted 29 Jul 2015; published 3 Aug 2015 10 Aug 2015 | Vol. 23, No. 16 | DOI:10.1364/OE.23.020986 | OPTICS EXPRESS 20986

12. H. Wang, P. L. Gould, and W. C. Stwalleya, “Long-range interaction of the 39K(4s)+ 39K(4p) asymptote by photoassociative spectroscopy. I. The 0 g pure long-range state and the long-range potential constants,” J. Chem. Phys. 106(19), 7899–7912 (1997). 13. Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011). 14. J. Ciuryelo and L. Krause, “42P1/2 → 42P3/2 mixing in potassium induced in collisions with noble gas atoms,” J. Quant. Spectrosc. Radiat. Transf. 28(6), 457–461 (1982). 15. P. Ya. Kantor, N. P. Penkin, and L. N. Shabanov, “Broadening of the K I 769.9 and 766.5-nm lines by inert gases,” Opt. Spectrosc. (USSR) 59(2), 151–156 (1985). 16. K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “CFD assisted simulation of temperature distribution and laser power in pulsed and CW pumped static gas DPALs,” Proc. SPIE (to be published). 17. B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Study of potassium DPAL operation in pulsed and CW mode,” Proc. SPIE 9251, 92510Y (2014).

1. Introduction Among the different Diode pumped alkali lasers (DPALs), extensively studied during the last decade [1,2], the K DPAL is of special interest. It has very high quantum efficiency (99.6%) and can operate with low pressure He buffer gas [1]. Cs and Rb DPALs on the other hand operate with hydrocarbon buffer (usually with some He added), and Rb also with high pressure (several atmospheres) He. Recently a highly efficient static, pulsed K DPAL with slope efficiency of 52% was demonstrated in USAFA [3]. In spite of the high efficiency, its threshold power was rather high, 22 W. As shown below this value cannot be fitted by simple standard models [1,4–6] assuming uniform intensities of the pump and laser beams in the transverse direction. In this paper we report on a model of K DPAL where Gaussian spatial shapes of the pump and laser intensities in any cross section of the beams are assumed and show that these assumptions can explain the measured dependence of the lasing power on the pump power. In addition, the influence of the spatial distribution of the spontaneous emission across the beam on the threshold power is studied in detail. 2. Description of the model K DPAL operates at frequency νl of the D1(4 2P1/2 → 42S1/2) transition of K. It is pumped via absorption of radiation of diode laser at frequency νp of the D2(42S1/2 → 42P3/2) transition, followed by rapid relaxation (by He) of the upper to the lower fine-structure level, 42P3/2 to 42P1/2 (designated as levels 3 and 2, respectively; the ground state 4 2S1/2 is designated as 1). The model considers typical configuration of a DPAL with end-pump geometry studied in [3] and shown in Fig. 1. A pump beam with total power Pp ,0 enters a cylindrical laser cell of length l through windows with transmission t. The lasing medium consists of a mixture of alkali vapor K and He for broadening the D2 transition and mixing between the fine-structure levels 3 and 2. The walls of the cell are heated to the temperature T ~180-190 C. The laser resonator of length L consists of a concave reflector of radius R and a plane output coupler with reflectivity r1 (close to 100%) and r2, respectively, located outside the laser cell. Both the pump and laser beams propagate along the optical axis Z of the resonator. Unlike our previous models [6,7] the pump and laser intensities, I p and I l± , respectively, are not assumed to be uniform in the beam cross section xy and their spatial distributions have the form:

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I p ( x, y, z,ν ) = Pp ( z,ν ) f p ( x, y, z ),

(1)

I l± ( x, y, z ) = Pl ± ( z ) fl ( x, y, z ),

(2)


where Pp ( z,ν ) is the spectral density of the pump power per unite frequency, Pl ± ( z ) is the total laser power and f p ,l ( x, y, z ) are the normalized spatial distributions of the pump and laser intensity over the beam cross section xy, slightly dependent of z, so that



dxdyf p ,l ( x, y, z ) = 1.

(3)

−∞< x , y rl , π rl 2

(18)

(19)

where wx , y ,l are wx , y ,l averaged over z inside the cell. Such pump and laser beams were studied in the standard semi-analytical models of DPALs [4–6]. As shown in Fig. 5, the calculated Plase in this case are larger than the experimental values, whereas Pth = 5 W was much smaller than the measured 22 W value. Thus, agreement between the calculated and measured Plase can be reached only assuming Gaussian spatial distributions of the intensity (Eqs. (14) and (15)) in both the pump and laser beams.

Fig. 4. Calculated and measured small signal transmission of the K vapor cell for the pump wavelength at different temperatures. Pump intensity is 1 W/cm2.

Fig. 5. Measured [3] and calculated dependence of the output laser power Plase on the incident pump power Pp,0 for different temperatures and pump and laser beams spatial distributions in the transverse direction.

3.2. Influence of the spatial distribution of the spontaneous emission on the threshold power The high threshold power Pth = 22 W shown in Fig. 5 cannot be explained by standard semianalytical models of the DPAL [4–6]. Actually, according to these models Pth is given by

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(

Pth = hν pV n2 / τ D1 + n3 / τ D2

)

(ηabs t ) ,

(20)

where ηabs = 1 − Tr is the fraction of the pump energy absorbed in the laser cell and V is the volume occupied by the excited K atoms contributing to the spontaneous emission and assumed to be equal to the volume occupied by the pump beam. At T = 193 C the saturated K vapor density n0 = 1014 cm −3 , assuming n3 = 0.5n0 and n2 = 0.25n0 [4,9], and for ηabs = 1 and V = 5x10−3 cm3 (found from Fig. 3 showing the size of the pump beam) we found from Eq. (20) that Pth is about 4 W. This value is close to Pth = 5W found for cylindrical hat-top pump and laser beams with uniform transverse distributions of the intensity, both values being much lower that the measured Pth = 22 W. The only possible reason for the difference between the

estimated and measured values of Pth could be that the assumption that V is close to the volume occupied by the pump beam is not correct. To check this possibility the spatial distribution of the spontaneous emission intensity l

 hν ( n p

I sp ( x, y ) =

2

)

/ τ D1 + n3 / τ D2 dz

0

l

(21)

averaged over z was calculated. Figure 6 shows I sp ( y ) and the spatial distributions of the pump and laser beams f p ( y ) f p ( y = 0) and f l ( y ) f l ( y = 0) , respectively, at x = 0. It is seen that the width of the spontaneous emission region is more than three times larger than the widths of the pump and laser beams. That means that the volume V occupied by K atoms contributing to the spontaneous emission is much larger than the volume of the pump beam which contradicts our initial assumption. The large width of the spontaneous emission region is due to strong excitation of K atoms in the wings of the Gaussian pump and laser beams. In spite of the relatively low light intensity of the beams in the wings, the excitation rates of levels 2 and 3 is still much higher than the spontaneous emission rate. As a result, the steady state populations of these states, established mainly due to the balance between the processes of the absorption/stimulated emission on the D1 and D2 transitions and the very fast relaxation of level 3 to 2, are almost the same as in the optical axis. We note that the large values of n2 in the wings do not result in lasing on the high order transverse modes which have big size in the transverse direction. Actually, our calculations show that the saturated population inversion on this transition, n2-n1, is positive only near the optical axis at the region with y < 0.6 mm where the fundamental transverse mode oscillates and is negative in the wings and hence hindering the lasing on the high order transverse modes. The last statement is in line with the aforementioned assumption that only the fundamental Gaussian transverse mode participates in the lasing. As follows from Eq. (20) large value of V results in the high threshold power Pth observed in the K DPAL. High Pth is the main obstacle for obtaining high Plase and optical-to-optical efficiency of the K DPAL. It is very difficult to decrease Pth which depends on n2 and n3 , proportional to the K atoms density n0 (see Eqs. (10)–(12)) and on the volume and shape of the pump and laser modes (see Eq. (20)). Decrease of n0 by decreasing T results in the decrease of absorption on the D2 transition and of the slope efficiency, as shown in Fig. 5 where it is seen that the slope efficiency at 180 C is lower than that at 193 C. It is also very difficult to decrease the volume and shape of the pump and laser modes since the pump beam diameter is already < 1 mm. So taking into account the fact that spontaneous emission does not affect the slope efficiency of the DPALs [4–6] we conclude that for increasing Plase and the optical-to-optical efficiency it

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is necessary to increase Pp ,0 which should be several times larger than Pth , i.e., > 100 W. To avoid the heating of the medium at such high Pp ,0 gas flow with high gas velocity should be applied. Hence, the only possible way for obtaining high power, highly efficient K DPAL, subsonic [17] or supersonic [10] flowing-gas device has to be employed. For example, as calculated in [10], at Pp ,0 = 10 kW and gas velocity of 20 m/s the optical-to-optical efficiency of the subsonic K DPAL is as high as 63%. Supersonic mode of operation has an additional advantage since the flowing gas also cools down due to the supersonic expansion [10]. We have recently carried out further calculations (unpublished) where we compared subsonic, transonic and supersonic modes of operation and the advantage of supersonic operation was corroborated.

Fig. 6. Spatial distribution of the spontaneous emission, pump and laser intensities in the y direction at x = 0 and Pp,0 = 45 W. The vertical axis shows Ip/Ip(y = 0), Il/Il(y = 0) and Isp(103 W/cm3).

4. Summary

A simple optical model of K DPAL, where Gaussian spatial shapes of the pump and laser intensities in any cross section of the beams are assumed, is reported. The model, applied to the static, pulsed K DPAL with high slope efficiency of 52% demonstrated in [3], shows good agreement between the calculated and measured dependence of Plase on the incident pump power Pp ,0 . In particular, the model calculates correct value of the threshold pump power Pth of 22 W (corresponding to pump intensity of 4 kW/cm2) which is much higher than that predicted by the standard semi-analytical models of the DPAL [4–6]. Other assumed spatial distributions of the pump and lasing intensities, in particular those with the hat-top pump and Gaussian laser beams and with cylindrical hat-top pump and laser beams, are unable to calculate the observed values of Plase . It is shown that the reason for the large values of Pth is that the volume occupied by the excited K atoms contributing to the spontaneous emission is much larger than the volumes of the pump and laser beams, resulting in very large energy losses due to the spontaneous emission. The large volume of the spontaneous emission region is due to strong excitation of K atoms in the wings of the Gaussian pump and laser beams. High Pth is the main obstacle for obtaining high Plase and optical-to-optical efficiency of the K

DPAL. Since it is very difficult to decrease Pth , it turns out that for increasing Plase and the optical-to-optical efficiency it is necessary to increase Pp ,0 and to apply gas flow with high

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gas velocity to avoid heating the gas. Hence, for obtaining high power, highly efficient K DPAL, employment of subsonic [16] or supersonic [10] flowing-gas device is needed. Acknowledgment

Effort sponsored by the High Energy Laser Joint Technology Office (HEL JTO) and the European Office of Aerospace Research and Development (EOARD) under grant FA865513-1-3072.

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