Abstract

A physical model combining rate, power propagation, and transient heat conduction equations for diode-pumped alkali vapor lasers (DPAL) is applied to a pulsed Rb-CH4 DPAL, which agrees well with the time evolution of laser power and temperature measured by K absorption spectroscopy. The output feature and temperature rise of a multi-pulse DPAL are also calculated in the time domain, showing that if we energize the pump light when the temperature rise decays to 1/2, rather than 1/e of its maximum, we can increase the duty cycle and obtain more output energy. The repetition rate of >100Hz is high enough to achieve QCW (quasi-continuous-wave) laser pulses.

© 2017 Optical Society of America

1. Introduction

Diode-pumped alkali lasers (DPALs) are a new type of high-power laser system with many advantages. These include high quantum efficiencies (for K, Rb, and Cs are 99.6%, 98.1%, and 95.3%, respectively), the capability to convert low-quality unphased pump light into a coherent laser beam with near diffraction-limited beam quality [1], a narrow linewidth of ~10 GHz, and the nonuse of hazardous expendable chemicals. As a result, DPALs have undergone extensive research and development since the first successful realization of an optically pumped 795 nm Rb vapor laser in 2003 [2], and of a diode-pumped 894 nm Cs vapor laser in 2005 [3]. Several groups have published demonstrations of lasing of various atomic species [2–4], pumping in longitudinal and transverse directions [5,6], and cooling by a flowing procedure [7,8]. Especially, the potential for scaling DPALs to high powers was preliminarily demonstrated in 2012 with an output power exceeding 1 kW [7]. In addition, the steady-state temperature was measured in 2015 [9] and subsequently in 2017 [10], showing a practical way to achieve diagnostics of DPALs. Meanwhile, many theoretical models of DPALs have been established [11–21], of which the focus has recently concentrated on beam size fitting [20,21] and temperature evaluation [16,17,21].

Recently, two teams proposed and demonstrated the real-time temperature measurement methods. Zhdanov et al. employed a camera with a ~1 kHz frame rate to nonperturbatively probe the distortion in the interferometric fringes caused by the variation in the refractive index, and experimentally measured the time evolution of temperatures in the gain medium of a Cs DPAL [22]. Wang et al. used a photo detector with a 14 ns rise time to directly detect the absorption signal of the K atoms added as non-disturbing tracing atoms, and demonstrated a tracing-atom-based absorption spectroscopy method for temperature measurement inside a Rb DPAL cell [23]. The limiting effects revealed by the experiments, such as output power degradation in time, require comprehensive research of the time-dependent characteristics of an alkali vapor laser. Additionally, knowledge of the temperature distribution inside the cell is essential for computation of thermal phase shift, thermal lensing, and thermally induced birefringence. Thus, study of the time evolutions of temperature and output features is very important for high-power DPAL development. In this paper, we propose a computational method to model the time-dependent three-dimensional temperature distribution in a DPAL cell. The axial distribution of beam radius and the radial distribution of intensity are both taken into account. The density distribution of alkali atoms and buffer gases, the collisional broadening rate of D1 and D2 lines, and the relaxation and quenching rates are all temperature-dependent. The rate equations of population densities, the power propagation equations, and the three-dimensional thermal conduction equation are combined to obtain the time evolution of power and temperature of both single-pulse and multi-pulses diode-pumped alkali vapor lasers.

2. Description of the model

The temporal and spatial divisions of a vapor cell with radius R and length L are shown in Fig. 1, with each divided volume element having dimensions of Δx×Δy×Δz. The minimum time difference of the same volume element is Δt.

 figure: Fig. 1

Fig. 1 Schematic illustration of the spatial and temporal division of the alkali vapor cell.

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2.1. Rate equations and power calculation

The rate equations of population density of energy levels of alkali atoms in a volume element at time t are given by

dn2dt=(n2n1)σD1fl(Pl++Pl)hvl+γ32[n32n2exp(ΔEkT)]γ21n2A21n2,
 dn3dt=(n112n3)σD2(λ)fpPp(λ)hvpdλγ32[n32n2exp(ΔEkT)]γ31n3A31n3,
n1=NoTo/Tn3n2,
where nj (j=1, 2, 3) are the respective population density of the alkali atomic energy levels nS 21/2, nP 21/2, nP 23/2, respectively. hvp and hvl are the pump and laser photon energy, respectively. No is the total density of alkali vapor at the operating temperature To (The density of buffer gas is also temperature-dependent). The spontaneous emission coefficients A31 (P 23/2S 21/2) and A21 (P 21/2S 21/2) are 3.81×107s1 and 3.61×107s1, respectively.

The ratio of the forward and the reverse spin-orbit relaxation rates must obey the principle of detailed balance γ23 (P 21/23/2)=2γ32exp(ΔE/kT), where γ32, as well as the quenching rates, γ31 (P 23/2S 21/2) and γ21 (P 21/2S 21/2), are calculated by

γij=133.3PCH4σij(T)kT8kTπmr,.
where σij is the temperature-dependent collisional cross section for the transition ij given by [24], k is Boltzmann’s constant, mr is the reduced mass between the alkali atom and the CH4 molecule, and PCH4 is the CH4 pressure in Torr.

To fit the real pump and laser intensity and beam radius inside the cell, fp,l and wp,  l are expressed in the xy plane:

fp(x,y,z)=c2πwpx(z)wpy(z)exp{c2[x2wpx(z)2+y2wpy(z)2]},
fl(x,y,z)=c2πwl(z)2exp[c2(x2+y2)wl(z)2],
wpx,py,l(z)=w0,px,py,l[(zz0,px,py,l)cpx,py,lλp,lπw0,px,py,l2]2+1,
where wpx, and wpy are the pump beam radiii in the x and y directions, respectively, whereas wl is the laser beam radius. z0,px,py,l are the z-coordinates of the pump and laser beam waists w0,px,py,l. The coefficients cpx,py,l determined by focal lengths and positions of the lens can be solved by substituting the measured beam radius at z=0 and the beam waist into Eq. (7). The Gaussian coefficient c2=2, 2, ln2 depending on Pwaist/Ptotal, i.e., the ratio of the power inside the beam waist to the total power (c2=2 with Pwaist/Ptotal>90%, c2=2 with Pwaist/Ptotal~86%, and c2=ln2 with Pwaist/Ptotal~63%).

The propagation of pump and laser power in the longitudinal dimensions, modified from [20], can be given by

Pp(z+Δz,λ)=Pp(z,λ)Rx,yRfp(x,y,z)exp[(n1n32)σD2(x,y,λ)Δz]ΔxΔy,
Pl±(z+Δz)=Pl±(z)Rx,yRfl(x,y,z)exp[±(n2n1)σD1(x,y)Δz]ΔxΔy,

Appointing an initial value of output laser power as Pl[0,Pp), then the boundary conditions for the two way laser powers are given by Pl+(0)=PltwRoc/(1Roc) and Pl(0)=Pl/tw(1Roc). The solution for the output laser flux is found by iterating on Pl until Pl+(L)tw2ts2Rl=Pl(L) (<1%), where Roc is the reflectivity of the output coupler, tw is the window transmission, and ts is the single-pass scattered transmission that is assumed to be located at the end of the laser reflector with reflectivity Rl.

2.2. 3D thermal conduction and temperature calculation

Combining the thermal conduction equation given by Eq. (56).5) from [25] and the heat source density Ω, the Tuation of heat transfer is

Cρ(Tt+υT)=[KT]+Ω,
where C, ρ, and K are the specific heat in J·kg−1·K−1, the mass density in kg·m−3, and the thermal conductivity in W·m−1·K−1, respectively. The thermal conductivity of methane can be calculated by KCH4=0.05+0.039/200×(T400), derived from the measured data [26]. The appearance of internal currents in the gain medium caused by the absence of mechanical equilibrium due to non-uniform temperature in a gravitational field is known as free convection. For the pulsed laser, the convection speed υ is negligibly small on a time scale of ~ms level during temperature rise. With respect to the fact that gases show isotropic properties, we expand Eq. (10) in rectangular coordinates as

CρTt=KT[(Tx)2+(Ty)2+(Tz)2]+K(2Tx2+2Ty2+2Tz2)+Ω(x,y,z,t).

This transient heat conduction formulation includes a general temperature distribution varying both with time and position. The first term in the right-hand-side of Eq. (11) is far smaller than the second term (<0.01%) and hence is negligible. According to Fig. 1(c), we continue our treatment by making a discretization on Eq. (11) using T(x,y,z,t)Ti,j,kt and

{Tt=Ti,j,kt+1Ti,j,ktΔt,2Tx2=Ti,+1j,kt2Ti,j,kt+Ti,1j,ktΔx2,2Ty2=Ti,j+1,kt2Ti,j,kt+Ti,j1,ktΔy2,2Tz2=Ti,j,k+1t2Ti,j,kt+Ti,j,k1tΔz2.

Therefore, the momentary three-dimensional heat equation will appear as

CρTi,j,kt+1Ti,j,ktΔt=K(Ti+1,j,kt+Ti1,j,kt2Ti,j,ktΔx2+Ti,j+1,kt+Ti,j1,kt2Ti,j,ktΔy2+Ti,j,k+1t+Ti,j,k1t2Ti,j,ktΔz2)+Ωi,j,kt,
or, on rearranging,
Ti,j,kt+1=(14α2β)Ti,j,kt+ΔtCρΩi,j,kt+α(Ti+1,j,kt+Ti1,j,kt+Ti,j+1,kt+Ti,j1,kt)+β(Ti,j,k+1t+Ti,j,k1t),
where α=δΔt/Δx2 (Δy=Δx) and β=δΔt/Δz2; δ=K/Cρ is the thermal diffusivity (m2/s). For meeting the stability condition of the explicit difference scheme (14α2β>0), including >99% of pump and laser energy in the cross section, and increasing the iteration speed as much as possible, parameters are set as: Δx=Δy=0.15mm, Δz=0.4mm and Δt=12.5μs. The superscript t (t=0, 1, 2, ) is an index of the real time.

The volume density of generated heat power Ω is given by

Ω=γ32[n32n2exp(ΔEkT)]ΔE+hνpγ31n3+hνlγ21n2,
where ΔE is the energy gap between level P 23/2 and P 21/2.

The product of C and ρ can be calculated by

Cρ=CpCH4(T)mCH4NAmCH4nCH4(T)=CpCH4(T)nCH4(T)/NA,
where the isobaric molar heat capacity CpCH4(T)=40.652+11.857/200×(T400) (unit: J·mol−1·K−1), derived from the measured data [26]. nCH4 is the number density of CH4, and NA is the Avogadro constant.

At each t, using the current temperature distribution Ti,j,kt (Ti,j,k0=To) to solve the rate Eqs. (1)–(3) and the power propagation Eqs. (8)–(9), we can obtain the laser power Pl and the 3D distribution of heat power density Ωi,j,kt. Substituting Ωi,j,kt into the heat Eq. (14) obtains the temperature of the next moment Ti,j,kt+1. These iterative processes are executed repeatedly via using multiple nested “for” loops in MATLAB to obtain both the spatial distribution and the temporal evolution of power and temperature.

3. Results and discussion

Due to the reason that the response time of a photodiode (for detecting the absorption signal of the K atoms) is usually much faster than CMOS or CCD sensors (for acquiring the interferometric fringes), and the error value is lower, the tracing-atom-based absorption spectroscopy method for temperature measurement is much faster and more accurate than the interference measuring method. Therefore, we applied our model to the recently-reported pulsed Rb-CH4 DPAL of which the real-time temperature was obtained by the absorption spectroscopy method [23]. The main experimental parameters are listed in Table 1.

Tables Icon

Table 1. Experimental parameters of the Rb DPAL.

It should be noted that because the power inside the beam waist was 86% of the total power, i.e., Pwaist/Ptotal~86% [23], that c2=2. The alkali cell contained Rb for lasing and CH4 for pressure broadening and relaxation, and K as tracing atoms. However, the number density of Rb and K (~1019m3) is much smaller than that of CH4 (~1025m3), and hence the average thermal conductivity and the average heat capacity of the mixture are completely dominated by CH4. The probe laser, precisely tuned to the central wavelength of the K D1 line so as to be absorbed by K atoms, was a single frequency DBR diode laser with a narrow linewidth of ~1 MHz, rather less than the alkali D1 line of ~10 GHz. The photo detector had a sufficiently large active area of 13 mm2 to receive the total probe power, and had a sufficiently fast rise time of 14 ns to realize the real-time measurement.

The average pump (or laser) power discussed in [23] is obtained by dividing the pump pulse energy Ep by the pulse duration τp: P¯p=Ep/τp. The incident spectrally resolved pump power at z=0 and time t can be given by

Ppt(0,λ)=Pp¯τp0τpSp(t)dtSp(t)ηln2π2Δλpexp[4ln2Δvp2(cλcλp)2],
where η is the total transmission of the coupled lens and the cell window, c is the speed of light, Δλp and Δvp are the linewidths (FWHM) of the pump light, and λp is its central wavelength. The pump pulse signal Sp(t) is given by the experiment. Under the experimental condition of P¯p=92 W and τp=2 ms (FWHM), we can transform Sp(t) into the pump power and calculate the temperature and power evolution as shown in Fig. 2. It can be seen that the simulation results are in good agreement with the experiment. Both laser power (signal) and temperature increase with time until they reach the maximum values, and then subsequently decrease. The reason why the laser power is not maximal at the beginning of the temperature growth, where the thermal effect appears to be the weakest, is that the pump power requires a rising process. Before the pump power reaches its maximum, because the heat deposited from spin-orbit relaxation and quenching is too large, the laser power starts to decrease linearly (in fact it should decrease exponentially if the pump signal is a square wave [27], but the still-increasing pump power has compensated part of the downward trend). The average laser power calculated by
Pl¯=0τpPl(t)dt/τp
is 10.3 W, which is basically consistent with the measured 10 W value. The maximum temperature of 633 K (corresponding to a temperature rise of 225K) achieved at ~3 ms is also in good agreement with the experimental value of ~630 K. According to Zhdanov’s team [22] and our previous work [28], the high temperature rise can be mainly attributed to quenching. In addition, the quenching cross sections from [29] are also used to calculate temperature for comparison. The maximum temperature rise obtained by the smaller value of quenching cross sections [29] is 109K, nearly 50% lower than the experimental result, showing that different choices of collisional cross sections of quenching affect the temperature calculation a lot, which is worth of further research. The increase and decrease of temperature is not symmetric, the heat deposition is faster than the heat dissipation, and a long time is needed for temperature to return to the original value after the pump beam is turned off.

 figure: Fig. 2

Fig. 2 Experimental and simulated signals of time evolution of pump, laser, and temperature with Pp¯=92 W and τp=2 ms (FWHM).

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At time = 3 ms after pump light is on, the three-dimensional distribution of temperature in the cell is shown in Fig. 3.

 figure: Fig. 3

Fig. 3 The 3D temperature distribution in the cell of a DPAL at time = 3 ms after pump light is on (the whole time-dependent temperature distribution can be seen in Visualization 1).

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The experimental and simulated results of temperature rise and average laser power under different pulse durations are shown in Fig. 4(a) with To=408 K and Pp¯=85.3 W. We can see that when the pump pulse width varies from 1 ms to 5 ms, the temperature rise increases from ~130 K to ~300 K owing to the longer heat deposition time, while the average laser power decreases from 10.4 W to 9.1 W because of a more serious drop of the instant laser power induced by more accumulated heat, which can be seen in Fig. 4(b). The experimental pump pulse signal is fitted by a trapezoid function. At a pulse duration of 5 ms, the instant laser power decreases exponentially, drops to below half of its maximum before the pump light is turned off, which results in a lower average laser power than those of shorter pulse duration.

 figure: Fig. 4

Fig. 4 (a) Temperature rise and average laser power as functions of pump pulse duration. (b) Time evolution of pump and laser signals. The gas cell is heated to 408 K and the average pump power is 85.3 W.

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It is well known that high-power lasers operating in CW mode will suffer from power degradation owing to thermal effects in the gain medium, hence a QCW (quasi-continuous-wave) mode occurs, which has various important applications in material processing, communications, medicine, and science. In order to shorten the time required by heat dissipation, we investigate the time evolution of laser power and of temperature rise in multiple-pulse DPALs. In Fig. 5, the pump pulse is assumed to have a nearly rectangular shape [27] with an average power of 90 W. When the laser power reduces from its maximal to 1/2 of this value, the pump light is turned off; and when the temperature rise decays to 1/e (a) or 1/2 (b) of its maximum (the corresponding thermal relaxation times are indicated as te and t2), it is turned on. The average laser powers achieved in Figs. 5(a) and 5(b) are 11.2 W and 10.7 W for a single pulse (in fact they should be higher in the first pulse). The maximal temperature rises are both 224 K, and the thermal relaxation times te=~5.3 ms and t2=~3.8 ms. QCW operation requires a short break time between two pump pulses and more excited pulses to achieve higher output energy. At a time range of 22 ms, for te there are only 4 pulses, the duty factor is 38% and the total output energy is 84 mJ; for t2 there are 5 pulses, the duty factor is 44% and the total output power is 91 mJ. This means that we can shorten the thermal relaxation time to increase the duty cycle and obtain higher output energy. The repetition rates for Figs. 5(a) and 5(b) exceeded 100 Hz, which is high enough to achieve QCW laser pulses.

 figure: Fig. 5

Fig. 5 Time evolution of power and temperature rise of multi-pulses DPALs, where the pump signal is assumed to be an ideal rectangular shape. (a) The pump power is turned on when the temperature rise decays to 1/e of its maximum. (b) The pump power is turned on when the temperature rise decays to 1/2 of its maximum.

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However, unlike the rectangular pump pulse used in [27], the pulse measured by [23] had a rise and fall time, which means that when the pump light was turned on, it took some time to increase, and when it was turned off, it also took some time to decrease. Therefore, we assume the pump signal to be trapezoidal with a rise and fall time of 0.5 ms, as shown in Fig. 6. The average laser powers of 9.3 W and 8.9 W achieved respectively in Figs. 6(a) and 6(b) are smaller than those of Fig. 5 owing to the higher temperature rise of 260 K. The descent of pump power resists the temperature fall, which is in agreement with experiment that even during the fast drop of pump signal, the mixed gases still experience elevated temperature. The thermal relaxation times te and t2 are 4.2 ms and 3.2 ms, respectively, which are smaller than that of Fig. 5. This is because higher temperature will result in faster heat dissipation; hence, the time the temperature takes to fall back to a certain ratio of its maximum is shorter. However, at the given time range, owing to the rising and falling processes of the pump pulse, the number of pulses for te and for t2 are 3 and 4, respectively. The total output energy of 81 mJ for Fig. 6(a) is less than that for Fig. 5(a) owing to the fewer pulses. Nevertheless, the energy for Fig. 6(b) is 100 mJ, which is even higher than Fig. 5(b). This is because, in spite of less pulses, the DPAL is still lasing during the rising and falling processes of pump power, and the pulse width is 40% larger than that in Fig. 5. However, the repetition rates of >100 Hz in Fig. 6 are still high enough for realization of QCW operation.

 figure: Fig. 6

Fig. 6 Time evolution of power and temperature rise of multi-pulses DPALs, where the pump signal is assumed to be trapezoidal with a rise and fall time of 0.5 ms. (a) The pump power is turned on when the temperature rise decays to 1/e of its maximum. (b) The pump power is turned on when the temperature rise decays to 1/2 of its maximum.

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4. Conclusion

A spatiotemporal model for diode-pumped alkali vapor lasers is established by combining the rate equations, the power propagation equations, and the transient thermal conduction equation. The model shows good agreement between the calculated and measured time evolution of laser power and temperature when applied to a pulsed Rb-CH4 DPAL of which the temperature was obtained by using photodiode to detect the absorption signal of the K atoms added as non-disturbing tracing atoms. When the pump pulse width increases from 1 ms to 5 ms, the temperature rise increases by ~170 K, while the average laser power decreases by about 1.3 W owing to the larger heat deposition. The time-dependent output feature and temperature rise of the multi-pulses DPALs are also calculated, showing that at a time range of 22 ms, if we turn on the pump light when the temperature rise decays to half of its maximum, rather than 1/e of its maximum or lower, we are able to achieve shorter thermal relaxation time, higher duty cycle, and higher output energy. The repetition rate we investigate is higher than 100 Hz, which is enough to achieve QCW laser pulses.

Funding

Zhejiang Provincial Natural Science Foundation (LY14A040005).

References and links

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2. 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]   [PubMed]  

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4. B. V. 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]  

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27. 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). [CrossRef]  

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References

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  1. B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Thermal effects in Cs DPAL and alkali cell window damage,” SPIE 9990, 99900C (2016).
  2. 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] [PubMed]
  3. T. Ehrenreich, B. V. Zhdanov, T. Takekoshi, S. P. Phipps, and R. J. Knize, “Diode pumped caesium laser,” Electron. Lett. 41(7), 415–416 (2005).
    [Crossref]
  4. B. V. 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]
  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] [PubMed]
  6. B. V. Zhdanov, M. K. Shaffer, J. Sell, and R. J. Knize, “Cesium vapor laser with transverse pumping by multiple laser diode arrays,” Opt. Commun. 281(23), 5862–5863 (2008).
    [Crossref]
  7. 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]
  8. B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “‘Potassium diode pumped alkali laser demonstration using a closed cycle flowing system,” Opt. Commun. 354, 256–258 (2015).
    [Crossref]
  9. M. K. Shaffer, T. C. Lilly, B. V. Zhdanov, and R. J. Knize, “In situ non-perturbative temperature measurement in a Cs alkali laser,” Opt. Lett. 40(1), 119–122 (2015).
    [Crossref] [PubMed]
  10. R. Wang, Z. Yang, H. Wang, and X. Xu, “Methane-based in situ temperature rise measurement in a diode-pumped rubidium laser,” Opt. Lett. 42(4), 667–670 (2017).
    [Crossref] [PubMed]
  11. 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]
  12. Q. Zhu, B. Pan, L. Chen, Y. Wang, and X. Zhang, “Analysis of temperature distributions in diode-pumped alkali vapor lasers,” Opt. Commun. 283(11), 2406–2410 (2010).
    [Crossref]
  13. Z. Yang, H. Wang, Q. Lu, Y. Li, W. Hua, X. Xu, and J. Chen, “Modeling, numerical approach, and power scaling of alkali vapor lasers in side-pumped configuration with flowing medium,” J. Opt. Soc. Am. B 28(6), 1353–1364 (2011).
    [Crossref]
  14. B. Q. Oliker, J. D. Haiducek, D. A. Hostutler, G. A. Pitz, W. Rudolph, and T. J. Madden, “Simulation of deleterious processes in a static-cell diode pumped alkali laser,” Proc. SPIE 8962, 89620B (2014).
    [Crossref]
  15. B. Shen, B. Pan, J. Jiao, and C. Xia, “Kinetic and fluid dynamic modeling, numerical approaches of flowing-gas diode-pumped alkali vapor amplifiers,” Opt. Express 23(15), 19500–19511 (2015).
    [Crossref] [PubMed]
  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 9650, 96500C (2015).
    [Crossref]
  17. J. Han, Y. Wang, H. Cai, W. Zhang, L. Xue, and H. Wang, “Algorithm for evaluation of temperature distribution of a vapor cell in a diode-pumped alkali laser system: part I,” Opt. Express 22(11), 13988–14003 (2014).
    [Crossref] [PubMed]
  18. W. Huang, R. Tan, Z. Li, and X. Lu, “Theoretical model and simulations for a cw exciplex pumped alkali laser,” Opt. Express 23(25), 31698–31715 (2015).
    [Crossref] [PubMed]
  19. B. Shen, X. Xu, C. Xia, and B. Pan, “Theoretical analysis of the semi-ring and trapezoid LD side-pumped alkali vapor lasers,” Opt. Commun. 380, 28–34 (2016).
    [Crossref]
  20. I. Auslender, B. Barmashenko, S. Rosenwaks, B. Zhdanov, M. Rotondaro, and R. J. Knize, “Modeling of pulsed K diode pumped alkali laser: Analysis of the experimental results,” Opt. Express 23(16), 20986–20996 (2015).
    [Crossref] [PubMed]
  21. K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Laser power, cell temperature and beam quality dependence on cell length of static Cs DPAL,” J. Opt. Soc. Am. B 34(2), 279–286 (2017).
    [Crossref]
  22. B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Measurements of the gain medium temperature in an operating Cs DPAL,” Opt. Express 24(17), 19286–19292 (2016).
    [Crossref] [PubMed]
  23. X. Zhao, Z. Yang, W. Hua, H. Wang, and X. Xu, “Real-time measurement of temperature rise in a pulsed diode pumped rubidium vapor laser by potassium tracing atom based absorption spectroscopy,” Opt. Express 25(6), 5841–5851 (2017).
    [Crossref] [PubMed]
  24. E. S. Hrycyshyn and L. Krause, “Inelastic collisions between excited alkali atoms and molecules. VII. Sensitized fluorescence and quenching in mixtures of rubidium with H2, HD, D2, N2, CH4, CD4, C2H4, and C2H6,” Can. J. Phys. 48(22), 2761–2768 (1970).
    [Crossref]
  25. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Course of Theoretical Physics, Vol. 6 (Pergamon, Elmsford, 1989), Chap. 5.
  26. E. W. Lemmon, M. O. McLinden, and D. G. Friend, Thermophysical properties of fluid systems (NIST Chemistry Webbook, NIST Standard Reference Database, 2005), Available: http://webbook.nist.gov/chemistry/fluid .
  27. 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).
    [Crossref]
  28. B. Shen, J. Huang, X. Xu, C. Xia, and B. Pan, “Modeling of steady-state temperature distribution in diode-pumped alkali vapor lasers: analysis of the experimental results,” IEEE J. Quantum Electron. 53(3), 1–7 (2017).
    [Crossref]
  29. N. D. Zameroski, W. Rudolph, G. D. Hager, and D. A. Hostutler, “A study of collisional quenching and radiation-trapping kinetics for Rb(5p) in the presence of methane and ethane using time-resolved fluorescence,” J. Phys. B 42(24), 245401 (2009).
    [Crossref]

2017 (4)

2016 (3)

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Measurements of the gain medium temperature in an operating Cs DPAL,” Opt. Express 24(17), 19286–19292 (2016).
[Crossref] [PubMed]

B. Shen, X. Xu, C. Xia, and B. Pan, “Theoretical analysis of the semi-ring and trapezoid LD side-pumped alkali vapor lasers,” Opt. Commun. 380, 28–34 (2016).
[Crossref]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Thermal effects in Cs DPAL and alkali cell window damage,” SPIE 9990, 99900C (2016).

2015 (7)

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “‘Potassium diode pumped alkali laser demonstration using a closed cycle flowing system,” Opt. Commun. 354, 256–258 (2015).
[Crossref]

M. K. Shaffer, T. C. Lilly, B. V. Zhdanov, and R. J. Knize, “In situ non-perturbative temperature measurement in a Cs alkali laser,” Opt. Lett. 40(1), 119–122 (2015).
[Crossref] [PubMed]

B. Shen, B. Pan, J. Jiao, and C. Xia, “Kinetic and fluid dynamic modeling, numerical approaches of flowing-gas diode-pumped alkali vapor amplifiers,” Opt. Express 23(15), 19500–19511 (2015).
[Crossref] [PubMed]

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 9650, 96500C (2015).
[Crossref]

I. Auslender, B. Barmashenko, S. Rosenwaks, B. Zhdanov, M. Rotondaro, and R. J. Knize, “Modeling of pulsed K diode pumped alkali laser: Analysis of the experimental results,” Opt. Express 23(16), 20986–20996 (2015).
[Crossref] [PubMed]

W. Huang, R. Tan, Z. Li, and X. Lu, “Theoretical model and simulations for a cw exciplex pumped alkali laser,” Opt. Express 23(25), 31698–31715 (2015).
[Crossref] [PubMed]

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).
[Crossref]

2014 (2)

J. Han, Y. Wang, H. Cai, W. Zhang, L. Xue, and H. Wang, “Algorithm for evaluation of temperature distribution of a vapor cell in a diode-pumped alkali laser system: part I,” Opt. Express 22(11), 13988–14003 (2014).
[Crossref] [PubMed]

B. Q. Oliker, J. D. Haiducek, D. A. Hostutler, G. A. Pitz, W. Rudolph, and T. J. Madden, “Simulation of deleterious processes in a static-cell diode pumped alkali laser,” Proc. SPIE 8962, 89620B (2014).
[Crossref]

2012 (1)

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]

2011 (1)

2010 (1)

Q. Zhu, B. Pan, L. Chen, Y. Wang, and X. Zhang, “Analysis of temperature distributions in diode-pumped alkali vapor lasers,” Opt. Commun. 283(11), 2406–2410 (2010).
[Crossref]

2009 (1)

N. D. Zameroski, W. Rudolph, G. D. Hager, and D. A. Hostutler, “A study of collisional quenching and radiation-trapping kinetics for Rb(5p) in the presence of methane and ethane using time-resolved fluorescence,” J. Phys. B 42(24), 245401 (2009).
[Crossref]

2008 (2)

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] [PubMed]

B. V. Zhdanov, M. K. Shaffer, J. Sell, and R. J. Knize, “Cesium vapor laser with transverse pumping by multiple laser diode arrays,” Opt. Commun. 281(23), 5862–5863 (2008).
[Crossref]

2007 (1)

B. V. 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]

2005 (1)

T. Ehrenreich, B. V. Zhdanov, T. Takekoshi, S. P. Phipps, and R. J. Knize, “Diode pumped caesium laser,” Electron. Lett. 41(7), 415–416 (2005).
[Crossref]

2004 (1)

2003 (1)

1970 (1)

E. S. Hrycyshyn and L. Krause, “Inelastic collisions between excited alkali atoms and molecules. VII. Sensitized fluorescence and quenching in mixtures of rubidium with H2, HD, D2, N2, CH4, CD4, C2H4, and C2H6,” Can. J. Phys. 48(22), 2761–2768 (1970).
[Crossref]

Auslender, I.

Barmashenko, B.

Barmashenko, B. D.

K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Laser power, cell temperature and beam quality dependence on cell length of static Cs DPAL,” J. Opt. Soc. Am. B 34(2), 279–286 (2017).
[Crossref]

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 9650, 96500C (2015).
[Crossref]

Beach, R. J.

Bogachev, A. V.

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]

Boyadjian, G.

Cai, H.

Chen, J.

Chen, L.

Q. Zhu, B. Pan, L. Chen, Y. Wang, and X. Zhang, “Analysis of temperature distributions in diode-pumped alkali vapor lasers,” Opt. Commun. 283(11), 2406–2410 (2010).
[Crossref]

Dubinskii, M. A.

Dudov, A. M.

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]

Ehrenreich, T.

B. V. 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]

T. Ehrenreich, B. V. Zhdanov, T. Takekoshi, S. P. Phipps, and R. J. Knize, “Diode pumped caesium laser,” Electron. Lett. 41(7), 415–416 (2005).
[Crossref]

Eroshenko, V. A.

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]

Flusche, B.

B. V. 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]

Garanin, S. G.

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]

Hager, G. D.

N. D. Zameroski, W. Rudolph, G. D. Hager, and D. A. Hostutler, “A study of collisional quenching and radiation-trapping kinetics for Rb(5p) in the presence of methane and ethane using time-resolved fluorescence,” J. Phys. B 42(24), 245401 (2009).
[Crossref]

Haiducek, J. D.

B. Q. Oliker, J. D. Haiducek, D. A. Hostutler, G. A. Pitz, W. Rudolph, and T. J. Madden, “Simulation of deleterious processes in a static-cell diode pumped alkali laser,” Proc. SPIE 8962, 89620B (2014).
[Crossref]

Han, J.

Havko, A.

B. V. 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]

Hostutler, D. A.

B. Q. Oliker, J. D. Haiducek, D. A. Hostutler, G. A. Pitz, W. Rudolph, and T. J. Madden, “Simulation of deleterious processes in a static-cell diode pumped alkali laser,” Proc. SPIE 8962, 89620B (2014).
[Crossref]

N. D. Zameroski, W. Rudolph, G. D. Hager, and D. A. Hostutler, “A study of collisional quenching and radiation-trapping kinetics for Rb(5p) in the presence of methane and ethane using time-resolved fluorescence,” J. Phys. B 42(24), 245401 (2009).
[Crossref]

Hrycyshyn, E. S.

E. S. Hrycyshyn and L. Krause, “Inelastic collisions between excited alkali atoms and molecules. VII. Sensitized fluorescence and quenching in mixtures of rubidium with H2, HD, D2, N2, CH4, CD4, C2H4, and C2H6,” Can. J. Phys. 48(22), 2761–2768 (1970).
[Crossref]

Hua, W.

Huang, J.

B. Shen, J. Huang, X. Xu, C. Xia, and B. Pan, “Modeling of steady-state temperature distribution in diode-pumped alkali vapor lasers: analysis of the experimental results,” IEEE J. Quantum Electron. 53(3), 1–7 (2017).
[Crossref]

Huang, W.

Jiao, J.

Kanz, V. K.

Knize, R. J.

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Thermal effects in Cs DPAL and alkali cell window damage,” SPIE 9990, 99900C (2016).

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Measurements of the gain medium temperature in an operating Cs DPAL,” Opt. Express 24(17), 19286–19292 (2016).
[Crossref] [PubMed]

I. Auslender, B. Barmashenko, S. Rosenwaks, B. Zhdanov, M. Rotondaro, and R. J. Knize, “Modeling of pulsed K diode pumped alkali laser: Analysis of the experimental results,” Opt. Express 23(16), 20986–20996 (2015).
[Crossref] [PubMed]

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).
[Crossref]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “‘Potassium diode pumped alkali laser demonstration using a closed cycle flowing system,” Opt. Commun. 354, 256–258 (2015).
[Crossref]

M. K. Shaffer, T. C. Lilly, B. V. Zhdanov, and R. J. Knize, “In situ non-perturbative temperature measurement in a Cs alkali laser,” Opt. Lett. 40(1), 119–122 (2015).
[Crossref] [PubMed]

B. V. Zhdanov, M. K. Shaffer, J. Sell, and R. J. Knize, “Cesium vapor laser with transverse pumping by multiple laser diode arrays,” Opt. Commun. 281(23), 5862–5863 (2008).
[Crossref]

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] [PubMed]

B. V. 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]

T. Ehrenreich, B. V. Zhdanov, T. Takekoshi, S. P. Phipps, and R. J. Knize, “Diode pumped caesium laser,” Electron. Lett. 41(7), 415–416 (2005).
[Crossref]

Koval, N.

B. V. 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]

Krause, L.

E. S. Hrycyshyn and L. Krause, “Inelastic collisions between excited alkali atoms and molecules. VII. Sensitized fluorescence and quenching in mixtures of rubidium with H2, HD, D2, N2, CH4, CD4, C2H4, and C2H6,” Can. J. Phys. 48(22), 2761–2768 (1970).
[Crossref]

Krupke, W. F.

Kulikov, S. M.

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]

Li, Y.

Li, Z.

Lilly, T. C.

Lu, Q.

Lu, X.

Madden, T. J.

B. Q. Oliker, J. D. Haiducek, D. A. Hostutler, G. A. Pitz, W. Rudolph, and T. J. Madden, “Simulation of deleterious processes in a static-cell diode pumped alkali laser,” Proc. SPIE 8962, 89620B (2014).
[Crossref]

Maes, C.

B. V. 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]

Meeker, T.

B. V. 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]

Merkle, L. D.

Mikaelian, G. T.

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]

Oliker, B. Q.

B. Q. Oliker, J. D. Haiducek, D. A. Hostutler, G. A. Pitz, W. Rudolph, and T. J. Madden, “Simulation of deleterious processes in a static-cell diode pumped alkali laser,” Proc. SPIE 8962, 89620B (2014).
[Crossref]

Pan, B.

B. Shen, J. Huang, X. Xu, C. Xia, and B. Pan, “Modeling of steady-state temperature distribution in diode-pumped alkali vapor lasers: analysis of the experimental results,” IEEE J. Quantum Electron. 53(3), 1–7 (2017).
[Crossref]

B. Shen, X. Xu, C. Xia, and B. Pan, “Theoretical analysis of the semi-ring and trapezoid LD side-pumped alkali vapor lasers,” Opt. Commun. 380, 28–34 (2016).
[Crossref]

B. Shen, B. Pan, J. Jiao, and C. Xia, “Kinetic and fluid dynamic modeling, numerical approaches of flowing-gas diode-pumped alkali vapor amplifiers,” Opt. Express 23(15), 19500–19511 (2015).
[Crossref] [PubMed]

Q. Zhu, B. Pan, L. Chen, Y. Wang, and X. Zhang, “Analysis of temperature distributions in diode-pumped alkali vapor lasers,” Opt. Commun. 283(11), 2406–2410 (2010).
[Crossref]

Panarin, V. A.

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]

Pautov, V. O.

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]

Payne, S. A.

Phipps, S. P.

T. Ehrenreich, B. V. Zhdanov, T. Takekoshi, S. P. Phipps, and R. J. Knize, “Diode pumped caesium laser,” Electron. Lett. 41(7), 415–416 (2005).
[Crossref]

Pitz, G. A.

B. Q. Oliker, J. D. Haiducek, D. A. Hostutler, G. A. Pitz, W. Rudolph, and T. J. Madden, “Simulation of deleterious processes in a static-cell diode pumped alkali laser,” Proc. SPIE 8962, 89620B (2014).
[Crossref]

Rosenwaks, S.

Rotondaro, M.

Rotondaro, M. D.

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Measurements of the gain medium temperature in an operating Cs DPAL,” Opt. Express 24(17), 19286–19292 (2016).
[Crossref] [PubMed]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Thermal effects in Cs DPAL and alkali cell window damage,” SPIE 9990, 99900C (2016).

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “‘Potassium diode pumped alkali laser demonstration using a closed cycle flowing system,” Opt. Commun. 354, 256–258 (2015).
[Crossref]

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).
[Crossref]

Rudolph, W.

B. Q. Oliker, J. D. Haiducek, D. A. Hostutler, G. A. Pitz, W. Rudolph, and T. J. Madden, “Simulation of deleterious processes in a static-cell diode pumped alkali laser,” Proc. SPIE 8962, 89620B (2014).
[Crossref]

N. D. Zameroski, W. Rudolph, G. D. Hager, and D. A. Hostutler, “A study of collisional quenching and radiation-trapping kinetics for Rb(5p) in the presence of methane and ethane using time-resolved fluorescence,” J. Phys. B 42(24), 245401 (2009).
[Crossref]

Rus, A. V.

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]

Sell, J.

B. V. Zhdanov, M. K. Shaffer, J. Sell, and R. J. Knize, “Cesium vapor laser with transverse pumping by multiple laser diode arrays,” Opt. Commun. 281(23), 5862–5863 (2008).
[Crossref]

Shaffer, M. K.

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Thermal effects in Cs DPAL and alkali cell window damage,” SPIE 9990, 99900C (2016).

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Measurements of the gain medium temperature in an operating Cs DPAL,” Opt. Express 24(17), 19286–19292 (2016).
[Crossref] [PubMed]

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).
[Crossref]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “‘Potassium diode pumped alkali laser demonstration using a closed cycle flowing system,” Opt. Commun. 354, 256–258 (2015).
[Crossref]

M. K. Shaffer, T. C. Lilly, B. V. Zhdanov, and R. J. Knize, “In situ non-perturbative temperature measurement in a Cs alkali laser,” Opt. Lett. 40(1), 119–122 (2015).
[Crossref] [PubMed]

B. V. Zhdanov, M. K. Shaffer, J. Sell, and R. J. Knize, “Cesium vapor laser with transverse pumping by multiple laser diode arrays,” Opt. Commun. 281(23), 5862–5863 (2008).
[Crossref]

Shen, B.

B. Shen, J. Huang, X. Xu, C. Xia, and B. Pan, “Modeling of steady-state temperature distribution in diode-pumped alkali vapor lasers: analysis of the experimental results,” IEEE J. Quantum Electron. 53(3), 1–7 (2017).
[Crossref]

B. Shen, X. Xu, C. Xia, and B. Pan, “Theoretical analysis of the semi-ring and trapezoid LD side-pumped alkali vapor lasers,” Opt. Commun. 380, 28–34 (2016).
[Crossref]

B. Shen, B. Pan, J. Jiao, and C. Xia, “Kinetic and fluid dynamic modeling, numerical approaches of flowing-gas diode-pumped alkali vapor amplifiers,” Opt. Express 23(15), 19500–19511 (2015).
[Crossref] [PubMed]

Stooke, A.

Sukharev, S. A.

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]

Takekoshi, T.

T. Ehrenreich, B. V. Zhdanov, T. Takekoshi, S. P. Phipps, and R. J. Knize, “Diode pumped caesium laser,” Electron. Lett. 41(7), 415–416 (2005).
[Crossref]

Tan, R.

Voci, A.

Waichman, K.

K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Laser power, cell temperature and beam quality dependence on cell length of static Cs DPAL,” J. Opt. Soc. Am. B 34(2), 279–286 (2017).
[Crossref]

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 9650, 96500C (2015).
[Crossref]

Wang, H.

Wang, R.

Wang, Y.

J. Han, Y. Wang, H. Cai, W. Zhang, L. Xue, and H. Wang, “Algorithm for evaluation of temperature distribution of a vapor cell in a diode-pumped alkali laser system: part I,” Opt. Express 22(11), 13988–14003 (2014).
[Crossref] [PubMed]

Q. Zhu, B. Pan, L. Chen, Y. Wang, and X. Zhang, “Analysis of temperature distributions in diode-pumped alkali vapor lasers,” Opt. Commun. 283(11), 2406–2410 (2010).
[Crossref]

Worker, B.

B. V. 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]

Xia, C.

B. Shen, J. Huang, X. Xu, C. Xia, and B. Pan, “Modeling of steady-state temperature distribution in diode-pumped alkali vapor lasers: analysis of the experimental results,” IEEE J. Quantum Electron. 53(3), 1–7 (2017).
[Crossref]

B. Shen, X. Xu, C. Xia, and B. Pan, “Theoretical analysis of the semi-ring and trapezoid LD side-pumped alkali vapor lasers,” Opt. Commun. 380, 28–34 (2016).
[Crossref]

B. Shen, B. Pan, J. Jiao, and C. Xia, “Kinetic and fluid dynamic modeling, numerical approaches of flowing-gas diode-pumped alkali vapor amplifiers,” Opt. Express 23(15), 19500–19511 (2015).
[Crossref] [PubMed]

Xu, X.

Xue, L.

Yang, Z.

Zameroski, N. D.

N. D. Zameroski, W. Rudolph, G. D. Hager, and D. A. Hostutler, “A study of collisional quenching and radiation-trapping kinetics for Rb(5p) in the presence of methane and ethane using time-resolved fluorescence,” J. Phys. B 42(24), 245401 (2009).
[Crossref]

Zhang, W.

Zhang, X.

Q. Zhu, B. Pan, L. Chen, Y. Wang, and X. Zhang, “Analysis of temperature distributions in diode-pumped alkali vapor lasers,” Opt. Commun. 283(11), 2406–2410 (2010).
[Crossref]

Zhao, X.

Zhdanov, B.

Zhdanov, B. V.

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Measurements of the gain medium temperature in an operating Cs DPAL,” Opt. Express 24(17), 19286–19292 (2016).
[Crossref] [PubMed]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Thermal effects in Cs DPAL and alkali cell window damage,” SPIE 9990, 99900C (2016).

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “‘Potassium diode pumped alkali laser demonstration using a closed cycle flowing system,” Opt. Commun. 354, 256–258 (2015).
[Crossref]

M. K. Shaffer, T. C. Lilly, B. V. Zhdanov, and R. J. Knize, “In situ non-perturbative temperature measurement in a Cs alkali laser,” Opt. Lett. 40(1), 119–122 (2015).
[Crossref] [PubMed]

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).
[Crossref]

B. V. Zhdanov, M. K. Shaffer, J. Sell, and R. J. Knize, “Cesium vapor laser with transverse pumping by multiple laser diode arrays,” Opt. Commun. 281(23), 5862–5863 (2008).
[Crossref]

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] [PubMed]

B. V. 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]

T. Ehrenreich, B. V. Zhdanov, T. Takekoshi, S. P. Phipps, and R. J. Knize, “Diode pumped caesium laser,” Electron. Lett. 41(7), 415–416 (2005).
[Crossref]

Zhu, Q.

Q. Zhu, B. Pan, L. Chen, Y. Wang, and X. Zhang, “Analysis of temperature distributions in diode-pumped alkali vapor lasers,” Opt. Commun. 283(11), 2406–2410 (2010).
[Crossref]

Can. J. Phys. (1)

E. S. Hrycyshyn and L. Krause, “Inelastic collisions between excited alkali atoms and molecules. VII. Sensitized fluorescence and quenching in mixtures of rubidium with H2, HD, D2, N2, CH4, CD4, C2H4, and C2H6,” Can. J. Phys. 48(22), 2761–2768 (1970).
[Crossref]

Electron. Lett. (1)

T. Ehrenreich, B. V. Zhdanov, T. Takekoshi, S. P. Phipps, and R. J. Knize, “Diode pumped caesium laser,” Electron. Lett. 41(7), 415–416 (2005).
[Crossref]

IEEE J. Quantum Electron. (1)

B. Shen, J. Huang, X. Xu, C. Xia, and B. Pan, “Modeling of steady-state temperature distribution in diode-pumped alkali vapor lasers: analysis of the experimental results,” IEEE J. Quantum Electron. 53(3), 1–7 (2017).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. B (1)

N. D. Zameroski, W. Rudolph, G. D. Hager, and D. A. Hostutler, “A study of collisional quenching and radiation-trapping kinetics for Rb(5p) in the presence of methane and ethane using time-resolved fluorescence,” J. Phys. B 42(24), 245401 (2009).
[Crossref]

Opt. Commun. (6)

B. Shen, X. Xu, C. Xia, and B. Pan, “Theoretical analysis of the semi-ring and trapezoid LD side-pumped alkali vapor lasers,” Opt. Commun. 380, 28–34 (2016).
[Crossref]

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).
[Crossref]

Q. Zhu, B. Pan, L. Chen, Y. Wang, and X. Zhang, “Analysis of temperature distributions in diode-pumped alkali vapor lasers,” Opt. Commun. 283(11), 2406–2410 (2010).
[Crossref]

B. V. 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]

B. V. Zhdanov, M. K. Shaffer, J. Sell, and R. J. Knize, “Cesium vapor laser with transverse pumping by multiple laser diode arrays,” Opt. Commun. 281(23), 5862–5863 (2008).
[Crossref]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “‘Potassium diode pumped alkali laser demonstration using a closed cycle flowing system,” Opt. Commun. 354, 256–258 (2015).
[Crossref]

Opt. Express (6)

Opt. Lett. (4)

Proc. SPIE (2)

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 9650, 96500C (2015).
[Crossref]

B. Q. Oliker, J. D. Haiducek, D. A. Hostutler, G. A. Pitz, W. Rudolph, and T. J. Madden, “Simulation of deleterious processes in a static-cell diode pumped alkali laser,” Proc. SPIE 8962, 89620B (2014).
[Crossref]

Quantum Electron. (1)

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]

SPIE (1)

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Thermal effects in Cs DPAL and alkali cell window damage,” SPIE 9990, 99900C (2016).

Other (2)

L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Course of Theoretical Physics, Vol. 6 (Pergamon, Elmsford, 1989), Chap. 5.

E. W. Lemmon, M. O. McLinden, and D. G. Friend, Thermophysical properties of fluid systems (NIST Chemistry Webbook, NIST Standard Reference Database, 2005), Available: http://webbook.nist.gov/chemistry/fluid .

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (3922 KB)      Visualization 1 the whole time-dependent temperature distribution

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Figures (6)

Fig. 1
Fig. 1 Schematic illustration of the spatial and temporal division of the alkali vapor cell.
Fig. 2
Fig. 2 Experimental and simulated signals of time evolution of pump, laser, and temperature with P p ¯ =92 W and τ p =2 ms (FWHM).
Fig. 3
Fig. 3 The 3D temperature distribution in the cell of a DPAL at time = 3 ms after pump light is on (the whole time-dependent temperature distribution can be seen in Visualization 1).
Fig. 4
Fig. 4 (a) Temperature rise and average laser power as functions of pump pulse duration. (b) Time evolution of pump and laser signals. The gas cell is heated to 408 K and the average pump power is 85.3 W.
Fig. 5
Fig. 5 Time evolution of power and temperature rise of multi-pulses DPALs, where the pump signal is assumed to be an ideal rectangular shape. (a) The pump power is turned on when the temperature rise decays to 1/e of its maximum. (b) The pump power is turned on when the temperature rise decays to 1/2 of its maximum.
Fig. 6
Fig. 6 Time evolution of power and temperature rise of multi-pulses DPALs, where the pump signal is assumed to be trapezoidal with a rise and fall time of 0.5 ms. (a) The pump power is turned on when the temperature rise decays to 1/e of its maximum. (b) The pump power is turned on when the temperature rise decays to 1/2 of its maximum.

Tables (1)

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Table 1 Experimental parameters of the Rb DPAL.

Equations (18)

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d n 2 d t = ( n 2 n 1 ) σ D 1 f l ( P l + + P l ) h v l + γ 32 [ n 3 2 n 2 exp ( Δ E k T ) ] γ 21 n 2 A 21 n 2 ,
  d n 3 d t = ( n 1 1 2 n 3 ) σ D 2 ( λ ) f p P p ( λ ) h v p d λ γ 32 [ n 3 2 n 2 exp ( Δ E k T ) ] γ 31 n 3 A 31 n 3 ,
n 1 = N o T o / T n 3 n 2 ,
γ ij = 133.3 P C H 4 σ ij (T) kT 8kT π m r ,.
f p (x,y,z)= c 2 π w px (z) w py (z) exp{ c 2 [ x 2 w px (z) 2 + y 2 w py (z) 2 ] },
f l (x,y,z)= c 2 π w l (z) 2 exp[ c 2 ( x 2 + y 2 ) w l (z) 2 ],
w px,py,l (z)= w 0, p x , p y ,l [ (z z 0,px,py,l ) c px,py,l λ p,l π w 0,px,py,l 2 ] 2 +1 ,
P p (z+Δz,λ)= P p (z,λ) Rx,yR f p (x,y,z)exp[ ( n 1 n 3 2 ) σ D2 (x,y,λ)Δz ] ΔxΔy,
P l ± (z+Δz)= P l ± (z) Rx,yR f l (x,y,z)exp[ ±( n 2 n 1 ) σ D1 (x,y)Δz ] ΔxΔy,
Cρ( T t +υT )=[ KT ]+Ω,
Cρ T t = K T [ ( T x ) 2 + ( T y ) 2 + ( T z ) 2 ]+K( 2 T x 2 + 2 T y 2 + 2 T z 2 )+Ω(x,y,z,t).
{ T t = T i,j,k t+1 T i,j,k t Δt , 2 T x 2 = T i,+1j,k t 2 T i,j,k t + T i,1j,k t Δ x 2 , 2 T y 2 = T i,j+1,k t 2 T i,j,k t + T i,j1,k t Δ y 2 , 2 T z 2 = T i,j,k+1 t 2 T i,j,k t + T i,j,k1 t Δ z 2 .
Cρ T i,j,k t+1 T i,j,k t Δt = K( T i+1,j,k t + T i1,j,k t 2 T i,j,k t Δ x 2 + T i,j+1,k t + T i,j1,k t 2 T i,j,k t Δ y 2 + T i,j,k+1 t + T i,j,k1 t 2 T i,j,k t Δ z 2 )+ Ω i,j,k t ,
T i,j,k t+1 =( 14α2β ) T i,j,k t + Δt Cρ Ω i,j,k t +α( T i+1,j,k t + T i1,j,k t + T i,j+1,k t + T i,j1,k t )+β( T i,j,k+1 t + T i,j,k1 t ),
Ω= γ 32 [ n 3 2 n 2 exp( ΔE kT ) ]ΔE+h ν p γ 31 n 3 +h ν l γ 21 n 2 ,
Cρ= C pC H 4 (T) m C H 4 N A m C H 4 n C H 4 (T)= C pC H 4 (T) n C H 4 (T)/ N A ,
P p t ( 0,λ )= P p ¯ τ p 0 τ p S p ( t )d t S p (t)η ln2 π 2 Δ λ p exp[ 4ln2 Δ v p 2 ( c λ c λ p ) 2 ],
P l ¯ = 0 τ p P l ( t )d t / τ p

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