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Choice of alkali element for DPAL scaling, a numerical study
Optics Communications 296 (2013) 101–105
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Choice of alkali element for DPAL scaling, a numerical study Hongyan Wang, Zining Yang n, Weihong Hua, Xiaojun Xu, Qisheng Lu College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
a r t i c l e i n f o
abstract
Article history: Received 5 September 2012 Received in revised form 15 January 2013 Accepted 17 January 2013 Available online 1 February 2013
In this paper, from the efficiency point of view, a systematic comparison of Cesium, Rubidium and Potassium lasers is made. The different properties for the three types of lasers mainly arise from their energy structure, especially the difference of fine-structure energy gap. At a realistic pump intensity of several kW/cm2, the Cesium laser shows a best performance. Some other considerations for choice are also discussed. & 2013 Elsevier B.V. All rights reserved.
Keywords: Alkali vapor laser DPAL Fluorescence suppression Atomic gas laser
1. Introduction Diode pumped alkali vaporlaser (DPAL), which combines advantages of solid-state laser’s compactness and gas laser’s convective cooling ability, have developed rapidly since its invention by Krupke et al. in 2003 [1] and first demonstration by Page et al. in 2005 [2]. Recently, an efficient CW kW-level Cesium DPAL was successfully realized, which represented a significant progress in power scaling of DPALs [3]. Up to now, Cesium, Rubidium and Potassium DPALs have all been demonstrated, and each possesses different properties. For Rubidium laser, it was the firstly demonstrated alkali laser and has reached hundred Watts CW output power [4]; for Cesium laser, it has reached the highest record of optical conversion efficiency [5,6] and kilowatt CW output [3]; while for Potassium laser, it was realized much later with relatively poor performance [7,8]. But Potassium laser was still recognized as a promising competitor due to two main reasons: the first is the extremely high quantum efficiency (K 99.56%, Rb 98.1%, Cs 95.3%); the second is the large fine-structure mixing cross-section between Potassium and Helium, and an atmosphere of Helium could provide sufficient population transfer rate between 2P1/2 and 2 P3/2 states. For Rubidium and Cesium DPALs, to obtain the required fine-structure mixing rate, hydrocarbons (Methane or Ethane) are usually needed, which have shown chemical instability under strong CW pumping conditions [6]. Another way for Rubidium laser is to add a high pressure (10–20 atm) Helium to
n
Corresponding author. Fax: þ86 731 84514127. E-mail address: [email protected] (Z. Yang).
0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.01.025
compensate for the small fine-structure mixing cross-section, which also allows for weak spectrally controlled diode pumps [9]; but for Cesium laser the hydrocarbons are necessary. A natural question arises since the beginning of alkali laser development: which element will be the best choice for DPAL scaling? Zweiback made a comparitive study of the three DPAL types, assuming an capillary gain structure with pump intensity of nearly 40 kW/cm2 [10]. The results showed Potassium laser’s potential advantage as compared with Rubidium and Cesium, mainly on aspect of its low waste heat due to the extremely small quantum defect. In this paper, we push this study forward by considering: (1) Due to the diode lasers’ poor beam quality, damage threshold of optical elements, available heat deposition density and some other engineering issues, a reasonable focused diode pump intensity should be much lower, usually in a range of 5–10 kW/cm2 for DPALs. For example, the recently realized kW-level Cs laser has used pump intensity of 3.5 kW/cm2. Under this pump intensity level, we get some different conclusions. (2) For the large atomic cross-sections of alkali D lines, the strong spontaneous emission (fluorescence) becomes an important issue, which may seriously decrease the optical conversion efficiency and increase the additional heat deposition. In Zweiback’s analysis [10], the fluorescence influence is not specially discussed, which is complemented in this paper. It should be noticed that, an advantage of Potassium and Rubidium DPALs, as compared with Cesium DPAL, is their ability for chemically stable hydrocarbon-free operation. But recent studies including pulsed alkali lasers [11], actively-conductive [4] and convective [3] cooling CW DPALs, all have shown good performance without any reports of chemical reaction between alkalis and hydrocarbons. As a result, we could infer that, under
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good thermal management, a low temperature rise may avoid the chemical reaction in DPALs with hydrocarbon additions, so this issue is not specially considered in this paper.
2. Numerical studies and discussions Based on the models [12,13], we first compared the optical conversion efficiency among Cesium, Rubidium and Potassium DPALs, see Fig. 1(a) and (b). Here, the efficiency is calculated under ‘‘optimal conditions’’, which means that the temperature (alkali density) and output coupler are both adjusted for a maximal optical conversion efficiency. The length of gain medium was set as 8 cm, the single-pass transmission of the cavity was 98%, and the back reflector was 99%. The pump intensity was assumed to be as realistic as 5 kW/cm2 with a linewidth of 0.1 nm centered on alkali D2 lines. For Cesium and Rubidium lasers, the buffer gases contained 200 torr Methane and 560 torr Helium, and for Potassium laser only 760 torr Helium was added. All the atomic interaction coefficients, including alkali D-line broadening and shifting rates, fine-structure mixing and collisional quenching cross-sections etc., were quoted from the published literatures [14–17]. We can see that the Cesium laser obtains the highest optical conversion efficiency (86.2%) while the Potassium laser gets the lowest (52.7%). A more detailed comparison is shown in Fig. 2.
where Zlaser, Zfluorescence and Zheat (10 Zheat in Fig. 2 for a more clear illustration) are the optical conversion, fluorescence and heat efficiencies (relatively to total pump power), respectively. Zabs is the pump absorption fraction, Roc and T are the optimal output coupler and operation temperature. It is worthy to be noticed that, in order to eliminate the influence of different atomic interaction coefficients of DPALs, we have assumed all the interaction coefficients for Potassium and Cesium to be the same with Rubidium, and the results were as similar as in Fig. 2. Thus different characteristics for Cesium, Rubidium and Potassium lasers arise from their natural energy structure and physical properties. From the results, we can get some conclusions:
(1) From Cesium to Potassium, the optimal alkali density is changing as 0.98 1013-1.39 1013-2.29 1013 cm3, and the optimal output coupler is changing as 4%-17%-64%, which implies highest gain level for Cesium and lowest for Potassium. The reason is mainly due to the difference of energy gap DE (Cs 554.1 cm 1, Rb 237.5 cm 1, K 57.7 cm 1) between fine-structure energy levels (2P1/2 and 2P3/2). According to the law of detailed balance, the collisional induced population transition rates g23 (2P1/2-2P3/2) and g32 (2P3/2 -2P1/2) satisfies the relationship g23 =g32 ¼ 2expðDE=kTÞ,
Fig. 1. The maximal optical conversion efficiencies for DPALs (left) at optimal output coupler and temperature conditions (right).
Fig. 2. A comparison of Cesium, Rubidium and Potassium DPALs under optimal conditions.
H. Wang et al. / Optics Communications 296 (2013) 101–105
where k and T are Boltzmann constant and temperature. For different DE values, g23/g32 for Cesium, Rubidium and Potassium are 0.23, 0.83 and 1.65 respectively, and the temperature influence is much less significant. A low g23/g32 value means that the population is much easier to be collisionally relaxed from pump upper level 2P3/2 to laser upper level 2P1/2, which directly leads to a high gain property and a low laser threshold. (2) Although the quantum defect for Potassium is extremely low (0.44%), as compared with Rubidium and Cesium lasers, the pump absorption fraction of Potassium laser is lower (84.2%) and the fluorescence loss is higher (26.4%), which lead to a much lower optical conversion efficiency (52.7%). The unabsorbed pump power and strong fluorescence could dramatically heat the surroundings, and a large fraction of fluorescence may finally turns into heat deposition by alkali ground state reabsorption. These problems counteract the advantage of Potassium’s low quantum defect, and also lead to cooling and many other engineering issues. The reason is still due to the difference of energy gap DE. For DPALs, three population transition rates decide the performance: the stimulated pump absorption rate G13(m 3 s 1), the finestructure mixing rate G32 and the stimulated laser emission rate G21. The subscripts 1,2,3 represents 2S1/2, 2P1/2, and 2P3/2 levels, and all the three rates are net values that contain both up and down population transfer processes. These rates satisfy the relationship of G13 ¼ G32 þn3A31, G32 ¼ G21 þn2A21, where ni(i¼1,2,3) is the population density and A21(A31) the spontaneous emission coefficient. The rates are tightly correlated to form a cycle G13-G32-G21-G13. As a three-level laser system, if any one of the rates is bottlenecked, the other two are also affected to slow down the overall cycling rate. The fine-structure mixing rate G32 is related with the energy gap DE, which is expressed as G32 ¼ g32 ½n3 2n2 expðDE=kTÞ. Although G32 is also the function of population densities, the calculation shows that, at the same conditions, a low DE always leads to a low G32. In this example, the value of G32 for Potassium, Rubidium and Cesium lasers are 0.93 1011, 8.88 1011 and 9.38 1011 cm 3 s 1, and the corresponding atomic cycling time t ¼nalkali/G21 are 16.5, 7.2 and 4.0 ns. Because the spontaneous emission coefficients are constant, a long atomic cycling time means a weak competition of
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stimulated process as compared with spontaneous process, thus leads to a strong fluorescence. Because the optimal temperature (alkali density) is a balance between pump absorption and spontaneous emission processes, a strong fluorescence leads to low pump absorption, as well as the optical conversion efficiency, as illustrated in Fig. 2. According to the analysis above, we can see that the effective fluorescence suppression becomes an important issue for design of DPALs. The stimulated transition coefficient is W¼ sI/hn, where s is the atomic emission (absorption) cross-section, I the laser (pump) intensity and hn the laser (pump) photon energy. An effective fluorescence suppression requires the stimulated transition coefficient W dominant over the spontaneous emission coefficient A. Two ways are available:
(1) Increase the atomic cross-section s by decreasing the buffer gas pressure. This method needs a narrower pump linewidth for spectral match to get a sufficient pump absorption. Fig. 3 shows the results with 200 torr Methane for Cesium and Rubidium, and 200 torr Helium for Potassium. The pump linewidth is correspondingly narrowed to an ideal value of 0.01 nm with intensity of 5 kW/cm2. The result shows that, a better fluorescence suppression significantly enhances the pump absorption fraction and optical conversion efficiency. And the performance of Rubidium laser is nearly the same with Cesium, for their fluorescence difference ( 3.7%) compensates for the difference of heat efficiency ( 2.8%). (2) Increase pump intensity I to suppress the fluorescence. Figs. 4–6 shows the intensity influence on performance of Cesium, Rubidium and Potassium lasers, and all the results are given under optimal conditions. We can see that a higher pump intensity can effectively suppress the fluorescence, enhance the pump absorption and finally leads to higher optical conversion efficiency. These results, which are calculated under high pump intensity, are as similar as Zweiback’s analysis [10]. It is also shown that, the sensitivity of optical conversion efficiency relative to the pump intensity is K4Rb4Cs. To get an optical conversion efficiency of 80%, the required pump
Fig. 3. A comparison of Cesium, Rubidium and Potassium DPALs under conditions of 200 torr buffer gas pressure and 0.01 nm pump linewidth.
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Fig. 4. Pump intensity influence on performance of Potassium laser (left) at optimal conditions (right).
Fig. 5. Pump intensity influence on performance of Rubidium laser (left) at optimal conditions (right).
Fig. 6. Pump intensity influence on performance of Cesium laser (left) at optimal conditions (right).
intensity for Potassium is over 20 kW/cm2, for Rubidium 7 kW/cm2 and for Cesium much less than 5 kW/cm2. A high pump intensity will not only increase the engineering difficulty of the laser design, but also also counteract the advantage of low quantum defect, thus may lead to a similar heat deposition density for the three DPALs. In a realistic pump focusing condition of several kW/cm2, Cesium laser will get a highest efficiency. Some other considerations of choice of DPAL species include:
Pump linewidth induced parasitic excitation: For Potassium,
Available power of diode pumps at DPAL wavelengths: Research at DILAS Diodenlaser GmbH shows that the available power from a single bar for Potassium (766 nm), Rubidium (780 nm) and Cesium (852 nm) lasers are 40 W, 60 W and 100 W respectively [18], which means that at the same pump power, the Cesium DPAL will have the smallest weight and volume.
the close pump (776.7 nm) and laser (770.11 nm) wavelengths is easily to be simultaneity excited by the red wing of pump light, which will degrade the laser performance. For Rubidium, the blue wing of pump light may excite the 5P3/2-5D5/2 (776 nm) transition and induce photoionization phenomenon [19]. And for Cesium, no such wing excitation exists due to its energy structure. Atmosphere propagation property: Research has showed that, for Rubidium laser, the D1 line will interact with one water absorption line under an atmosphere buffer gas pressure, and interact with more than 6 water lines at pressures approaching 7 atm [20]; for Cesium laser, the D1 line also interacts with some water lines under an atmosphere buffer gas pressure [21]; and the atmosphere propagation property for Potassium is much better. In design for DPALs, many factors, e.g. the
H. Wang et al. / Optics Communications 296 (2013) 101–105
buffer gas mixture, resonator design and line selective technology, should be considered to focus the energy into the required spectral lines.
3. Conclusions From the efficiency point of view, a systematic comparison of Cesium, Rubidium and Potassium DPALs was made. The different properties for the three DPALs mainly arise from their energy structure, especially the fine-structure energy gap. At reasonable pump intensity of several kW/cm2, the Cesium laser shows a best performance, including low laser threshold, sufficient pump absorption and effective fluorescence suppression, which leads to a highest optical conversion efficiency. And the Potassium laser shows a relatively poor performance although with extremely low quantum defect. The Rubidium laser will get a similar optical conversion efficiency with Cesium if the fluorescence can be effectively suppressed. According to the current development stage of high power line-narrowed diode pumps, the Rubidium laser with high pressure Helium (10–20atm) is nearly realistic. Combined with the consideration of the efficiency advantage, available pump power for DPAL wavelengths and pump wing parasitic excitation effects, Cesium laser will be a much better choice in future DPAL scaling, if the possible chemical reaction with hydrocarbons could be surely to be eliminated under good thermal management, and line-control technology be used for a good atmosphere propagation.
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References [1] W.F. Krupke, R.J. Beach, V.K. Kanz, S.A. Payne., Optics Letters 28 (2003) 2336. [2] R.H. Page, R.J. Beach, V.K. Kanz, W.F. Krupke., Optics Letters 31 (2006) 353. [3] A.V. Bogachev, S.G. Garanin, A.M. Dudov, V.A. Yeroshenko, S.M. Kulikov, G.T. Mikaelian, V.A. Panarin, V.O. Pautov, A.V. Rus, S.A. Sukharev., Quantum Electronics 42 (2012) 95. [4] J. Zweiback, A. Komashko, W.F. Krupke, SPIE 7581 (2010) 75810G. [5] B.V. Zhdanov, T. Ehrenreich, R.J. Knize., Optics Communications 260 (2006) 696. [6] B.V. Zhdanov, R.J. Knize., Optics Letters 32 (2007) 2167. [7] B. Zhdanov, C. Maes, T. Ehrenreich, A. Havko, N. Koval, T. Meeker, B. Worker, B. Flusche, R.J. Knize, Optics Communications 270 (2007) 353. [8] B.V. Zhdanov, M.K. Shaffer, R.J. Knize, SPIE 7915 (2011) 791506. [9] S.S.Q. Wu. Ph. D. Thesis, University of California, San Diego. 2009. [10] J. Zweiback, W.F. Krupke, SPIE 6874 (2008) 68740G. [11] J. Zweiback, J.B. Krupke, B. SPIE 7005 (2008) 700525. [12] R.J. Beach, W.F. Krupke, V.K. Kanz, S.A. Payne, M.A. Dubinskii, L.D. Merkle., Journal of the Optical Society of America B 21 (2004) 2151. [13] Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, J. Chen., Journal of Physics B: Atomic, Molecular and Optical Physics 44 (2011) 085401. [14] G.A. Pitz, A.J. Sandoval, N.D. Zameroski, W.L. Klennert, D.A. Hostutler., Journal of Quantitative Spectroscopy and Radiative Transfer 112 (2011) 59. [15] M.D. Rotondaro, G.P. Perram., J. Quant., Journal of Quantitative Spectroscopy and Radiative Transfer 57 (1997) 497. [16] G.A. Pitz, D.E. Wertepny, G.P. Perram., Physical Review A 80 (2009) 062718. [17] E.S. Hrycyshyn, L. Krause., Canadian Journal of Physics 48 (1970) 2761. ¨ [18] H. Kissel, B. Kohler, J. Biesenbach., SPIE 8241 (2012) 82410Q. [19] R.J. Knize, B.V. Zhdanov, M.K. Shaffer., Optics Express 19 (2011) 7894. [20] G.A. Pitz, S. Glass, B. Kamer, W.L. Klennert, D.A. Hostutler, SPIE 8380 (2012) 83800V. [21] C.A. Rice, G. Perram, SPIE 8238 (2012) 82380I.
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Choice of alkali element for DPAL scaling, a numerical study Hongyan Wang, Zining Yang n, Weihong Hua, Xiaojun Xu, Qisheng Lu College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
a r t i c l e i n f o
abstract
Article history: Received 5 September 2012 Received in revised form 15 January 2013 Accepted 17 January 2013 Available online 1 February 2013
In this paper, from the efficiency point of view, a systematic comparison of Cesium, Rubidium and Potassium lasers is made. The different properties for the three types of lasers mainly arise from their energy structure, especially the difference of fine-structure energy gap. At a realistic pump intensity of several kW/cm2, the Cesium laser shows a best performance. Some other considerations for choice are also discussed. & 2013 Elsevier B.V. All rights reserved.
Keywords: Alkali vapor laser DPAL Fluorescence suppression Atomic gas laser
1. Introduction Diode pumped alkali vaporlaser (DPAL), which combines advantages of solid-state laser’s compactness and gas laser’s convective cooling ability, have developed rapidly since its invention by Krupke et al. in 2003 [1] and first demonstration by Page et al. in 2005 [2]. Recently, an efficient CW kW-level Cesium DPAL was successfully realized, which represented a significant progress in power scaling of DPALs [3]. Up to now, Cesium, Rubidium and Potassium DPALs have all been demonstrated, and each possesses different properties. For Rubidium laser, it was the firstly demonstrated alkali laser and has reached hundred Watts CW output power [4]; for Cesium laser, it has reached the highest record of optical conversion efficiency [5,6] and kilowatt CW output [3]; while for Potassium laser, it was realized much later with relatively poor performance [7,8]. But Potassium laser was still recognized as a promising competitor due to two main reasons: the first is the extremely high quantum efficiency (K 99.56%, Rb 98.1%, Cs 95.3%); the second is the large fine-structure mixing cross-section between Potassium and Helium, and an atmosphere of Helium could provide sufficient population transfer rate between 2P1/2 and 2 P3/2 states. For Rubidium and Cesium DPALs, to obtain the required fine-structure mixing rate, hydrocarbons (Methane or Ethane) are usually needed, which have shown chemical instability under strong CW pumping conditions [6]. Another way for Rubidium laser is to add a high pressure (10–20 atm) Helium to
n
Corresponding author. Fax: þ86 731 84514127. E-mail address: [email protected] (Z. Yang).
0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.01.025
compensate for the small fine-structure mixing cross-section, which also allows for weak spectrally controlled diode pumps [9]; but for Cesium laser the hydrocarbons are necessary. A natural question arises since the beginning of alkali laser development: which element will be the best choice for DPAL scaling? Zweiback made a comparitive study of the three DPAL types, assuming an capillary gain structure with pump intensity of nearly 40 kW/cm2 [10]. The results showed Potassium laser’s potential advantage as compared with Rubidium and Cesium, mainly on aspect of its low waste heat due to the extremely small quantum defect. In this paper, we push this study forward by considering: (1) Due to the diode lasers’ poor beam quality, damage threshold of optical elements, available heat deposition density and some other engineering issues, a reasonable focused diode pump intensity should be much lower, usually in a range of 5–10 kW/cm2 for DPALs. For example, the recently realized kW-level Cs laser has used pump intensity of 3.5 kW/cm2. Under this pump intensity level, we get some different conclusions. (2) For the large atomic cross-sections of alkali D lines, the strong spontaneous emission (fluorescence) becomes an important issue, which may seriously decrease the optical conversion efficiency and increase the additional heat deposition. In Zweiback’s analysis [10], the fluorescence influence is not specially discussed, which is complemented in this paper. It should be noticed that, an advantage of Potassium and Rubidium DPALs, as compared with Cesium DPAL, is their ability for chemically stable hydrocarbon-free operation. But recent studies including pulsed alkali lasers [11], actively-conductive [4] and convective [3] cooling CW DPALs, all have shown good performance without any reports of chemical reaction between alkalis and hydrocarbons. As a result, we could infer that, under
102
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good thermal management, a low temperature rise may avoid the chemical reaction in DPALs with hydrocarbon additions, so this issue is not specially considered in this paper.
2. Numerical studies and discussions Based on the models [12,13], we first compared the optical conversion efficiency among Cesium, Rubidium and Potassium DPALs, see Fig. 1(a) and (b). Here, the efficiency is calculated under ‘‘optimal conditions’’, which means that the temperature (alkali density) and output coupler are both adjusted for a maximal optical conversion efficiency. The length of gain medium was set as 8 cm, the single-pass transmission of the cavity was 98%, and the back reflector was 99%. The pump intensity was assumed to be as realistic as 5 kW/cm2 with a linewidth of 0.1 nm centered on alkali D2 lines. For Cesium and Rubidium lasers, the buffer gases contained 200 torr Methane and 560 torr Helium, and for Potassium laser only 760 torr Helium was added. All the atomic interaction coefficients, including alkali D-line broadening and shifting rates, fine-structure mixing and collisional quenching cross-sections etc., were quoted from the published literatures [14–17]. We can see that the Cesium laser obtains the highest optical conversion efficiency (86.2%) while the Potassium laser gets the lowest (52.7%). A more detailed comparison is shown in Fig. 2.
where Zlaser, Zfluorescence and Zheat (10 Zheat in Fig. 2 for a more clear illustration) are the optical conversion, fluorescence and heat efficiencies (relatively to total pump power), respectively. Zabs is the pump absorption fraction, Roc and T are the optimal output coupler and operation temperature. It is worthy to be noticed that, in order to eliminate the influence of different atomic interaction coefficients of DPALs, we have assumed all the interaction coefficients for Potassium and Cesium to be the same with Rubidium, and the results were as similar as in Fig. 2. Thus different characteristics for Cesium, Rubidium and Potassium lasers arise from their natural energy structure and physical properties. From the results, we can get some conclusions:
(1) From Cesium to Potassium, the optimal alkali density is changing as 0.98 1013-1.39 1013-2.29 1013 cm3, and the optimal output coupler is changing as 4%-17%-64%, which implies highest gain level for Cesium and lowest for Potassium. The reason is mainly due to the difference of energy gap DE (Cs 554.1 cm 1, Rb 237.5 cm 1, K 57.7 cm 1) between fine-structure energy levels (2P1/2 and 2P3/2). According to the law of detailed balance, the collisional induced population transition rates g23 (2P1/2-2P3/2) and g32 (2P3/2 -2P1/2) satisfies the relationship g23 =g32 ¼ 2expðDE=kTÞ,
Fig. 1. The maximal optical conversion efficiencies for DPALs (left) at optimal output coupler and temperature conditions (right).
Fig. 2. A comparison of Cesium, Rubidium and Potassium DPALs under optimal conditions.
H. Wang et al. / Optics Communications 296 (2013) 101–105
where k and T are Boltzmann constant and temperature. For different DE values, g23/g32 for Cesium, Rubidium and Potassium are 0.23, 0.83 and 1.65 respectively, and the temperature influence is much less significant. A low g23/g32 value means that the population is much easier to be collisionally relaxed from pump upper level 2P3/2 to laser upper level 2P1/2, which directly leads to a high gain property and a low laser threshold. (2) Although the quantum defect for Potassium is extremely low (0.44%), as compared with Rubidium and Cesium lasers, the pump absorption fraction of Potassium laser is lower (84.2%) and the fluorescence loss is higher (26.4%), which lead to a much lower optical conversion efficiency (52.7%). The unabsorbed pump power and strong fluorescence could dramatically heat the surroundings, and a large fraction of fluorescence may finally turns into heat deposition by alkali ground state reabsorption. These problems counteract the advantage of Potassium’s low quantum defect, and also lead to cooling and many other engineering issues. The reason is still due to the difference of energy gap DE. For DPALs, three population transition rates decide the performance: the stimulated pump absorption rate G13(m 3 s 1), the finestructure mixing rate G32 and the stimulated laser emission rate G21. The subscripts 1,2,3 represents 2S1/2, 2P1/2, and 2P3/2 levels, and all the three rates are net values that contain both up and down population transfer processes. These rates satisfy the relationship of G13 ¼ G32 þn3A31, G32 ¼ G21 þn2A21, where ni(i¼1,2,3) is the population density and A21(A31) the spontaneous emission coefficient. The rates are tightly correlated to form a cycle G13-G32-G21-G13. As a three-level laser system, if any one of the rates is bottlenecked, the other two are also affected to slow down the overall cycling rate. The fine-structure mixing rate G32 is related with the energy gap DE, which is expressed as G32 ¼ g32 ½n3 2n2 expðDE=kTÞ. Although G32 is also the function of population densities, the calculation shows that, at the same conditions, a low DE always leads to a low G32. In this example, the value of G32 for Potassium, Rubidium and Cesium lasers are 0.93 1011, 8.88 1011 and 9.38 1011 cm 3 s 1, and the corresponding atomic cycling time t ¼nalkali/G21 are 16.5, 7.2 and 4.0 ns. Because the spontaneous emission coefficients are constant, a long atomic cycling time means a weak competition of
103
stimulated process as compared with spontaneous process, thus leads to a strong fluorescence. Because the optimal temperature (alkali density) is a balance between pump absorption and spontaneous emission processes, a strong fluorescence leads to low pump absorption, as well as the optical conversion efficiency, as illustrated in Fig. 2. According to the analysis above, we can see that the effective fluorescence suppression becomes an important issue for design of DPALs. The stimulated transition coefficient is W¼ sI/hn, where s is the atomic emission (absorption) cross-section, I the laser (pump) intensity and hn the laser (pump) photon energy. An effective fluorescence suppression requires the stimulated transition coefficient W dominant over the spontaneous emission coefficient A. Two ways are available:
(1) Increase the atomic cross-section s by decreasing the buffer gas pressure. This method needs a narrower pump linewidth for spectral match to get a sufficient pump absorption. Fig. 3 shows the results with 200 torr Methane for Cesium and Rubidium, and 200 torr Helium for Potassium. The pump linewidth is correspondingly narrowed to an ideal value of 0.01 nm with intensity of 5 kW/cm2. The result shows that, a better fluorescence suppression significantly enhances the pump absorption fraction and optical conversion efficiency. And the performance of Rubidium laser is nearly the same with Cesium, for their fluorescence difference ( 3.7%) compensates for the difference of heat efficiency ( 2.8%). (2) Increase pump intensity I to suppress the fluorescence. Figs. 4–6 shows the intensity influence on performance of Cesium, Rubidium and Potassium lasers, and all the results are given under optimal conditions. We can see that a higher pump intensity can effectively suppress the fluorescence, enhance the pump absorption and finally leads to higher optical conversion efficiency. These results, which are calculated under high pump intensity, are as similar as Zweiback’s analysis [10]. It is also shown that, the sensitivity of optical conversion efficiency relative to the pump intensity is K4Rb4Cs. To get an optical conversion efficiency of 80%, the required pump
Fig. 3. A comparison of Cesium, Rubidium and Potassium DPALs under conditions of 200 torr buffer gas pressure and 0.01 nm pump linewidth.
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Fig. 4. Pump intensity influence on performance of Potassium laser (left) at optimal conditions (right).
Fig. 5. Pump intensity influence on performance of Rubidium laser (left) at optimal conditions (right).
Fig. 6. Pump intensity influence on performance of Cesium laser (left) at optimal conditions (right).
intensity for Potassium is over 20 kW/cm2, for Rubidium 7 kW/cm2 and for Cesium much less than 5 kW/cm2. A high pump intensity will not only increase the engineering difficulty of the laser design, but also also counteract the advantage of low quantum defect, thus may lead to a similar heat deposition density for the three DPALs. In a realistic pump focusing condition of several kW/cm2, Cesium laser will get a highest efficiency. Some other considerations of choice of DPAL species include:
Pump linewidth induced parasitic excitation: For Potassium,
Available power of diode pumps at DPAL wavelengths: Research at DILAS Diodenlaser GmbH shows that the available power from a single bar for Potassium (766 nm), Rubidium (780 nm) and Cesium (852 nm) lasers are 40 W, 60 W and 100 W respectively [18], which means that at the same pump power, the Cesium DPAL will have the smallest weight and volume.
the close pump (776.7 nm) and laser (770.11 nm) wavelengths is easily to be simultaneity excited by the red wing of pump light, which will degrade the laser performance. For Rubidium, the blue wing of pump light may excite the 5P3/2-5D5/2 (776 nm) transition and induce photoionization phenomenon [19]. And for Cesium, no such wing excitation exists due to its energy structure. Atmosphere propagation property: Research has showed that, for Rubidium laser, the D1 line will interact with one water absorption line under an atmosphere buffer gas pressure, and interact with more than 6 water lines at pressures approaching 7 atm [20]; for Cesium laser, the D1 line also interacts with some water lines under an atmosphere buffer gas pressure [21]; and the atmosphere propagation property for Potassium is much better. In design for DPALs, many factors, e.g. the
H. Wang et al. / Optics Communications 296 (2013) 101–105
buffer gas mixture, resonator design and line selective technology, should be considered to focus the energy into the required spectral lines.
3. Conclusions From the efficiency point of view, a systematic comparison of Cesium, Rubidium and Potassium DPALs was made. The different properties for the three DPALs mainly arise from their energy structure, especially the fine-structure energy gap. At reasonable pump intensity of several kW/cm2, the Cesium laser shows a best performance, including low laser threshold, sufficient pump absorption and effective fluorescence suppression, which leads to a highest optical conversion efficiency. And the Potassium laser shows a relatively poor performance although with extremely low quantum defect. The Rubidium laser will get a similar optical conversion efficiency with Cesium if the fluorescence can be effectively suppressed. According to the current development stage of high power line-narrowed diode pumps, the Rubidium laser with high pressure Helium (10–20atm) is nearly realistic. Combined with the consideration of the efficiency advantage, available pump power for DPAL wavelengths and pump wing parasitic excitation effects, Cesium laser will be a much better choice in future DPAL scaling, if the possible chemical reaction with hydrocarbons could be surely to be eliminated under good thermal management, and line-control technology be used for a good atmosphere propagation.
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