A kinetic model for diode pumped Rubidium vapor laser

Optics Communications 284 (2011) 4045–4048

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Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m

A kinetic model for diode pumped Rubidium vapor laser Wang Ya-Juan ⁎, Pan Bai-Liang, Zhu Qi, Yang Jing Department of Physics, Zhejiang University, Hangzhou, 310027, China

a r t i c l e

i n f o

Article history: Received 20 January 2011 Received in revised form 8 April 2011 Accepted 11 April 2011 Available online 27 April 2011 Keywords: DPAL Diode pump Rubidium laser Physical model

a b s t r a c t A physical model is established to describe the kinetic processes and laser mechanism of diode pumped rubidium vapor laser. Influences of some parameters such as the output coupler reflectivity, the cell length, the temperature and the buffer gases on the output power and the optical–optical efficiency are calculated and analyzed. The simulation results agree well with the experiments. A set of optimization parameters is obtained for designing an efficient diode pumped Rb vapor laser. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Since the first optically pumped alkali vapor laser was proposed by Schcwlow and Townes in 1958 [1], there had been decades until Krupke et al. first reported the end-pumped rubidium laser using a titanium sapphire laser as pump source in 2003 [2]. After that, it attracted a gaining attention as efficient and high power diode laser pump sources were developed [3–6]. Diode pumped alkali vapor lasers (DPAL) have many desirable features such as high quantum efficiency (e.g., 95.3% for Cs, 98.1% for Rb and 99.6% for K) which is very important for increasing the laser efficiency and minimizing the thermal effect, good optical quality of gain medium and the narrow line-width (several MHZ) [7]. Additionally, the output wavelengths for these lasers (795 nm for Rb and 895 nm for Cs) exhibit excellent atmospheric propagation with minimal attenuation due to molecular absorption. These lasers also have many potential applications from laser cooling to material processing and directional energy transmission [8]. Various experiments on DPALs have been conducted with very promising results. In 2007, Perschbacher et al. presented a narrowline (~1 MHz) diode pumped rubidium laser with an optical slope efficiency of 69% [8]. Zhdanov et al. reported a continuous wave narrowband laser diode array pumped cesium vapor laser with 10 W output power and a laser diode array pumped rubidium laser with 8 W output power, the slope efficiency is 68% and 60%, respectively [9,10]. The demonstration of a transverse pumped Cs laser of 49 W output power and 43% slope efficiency opened new possibilities in power scaling of alkali lasers [11]. ⁎ Corresponding author. E-mail addresses: [email protected] (W. Ya-Juan), [email protected] (P. Bai-Liang). 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.04.027

Compare to the experiments, only rare report on the kinetic processes and laser mechanism of DPAL [12,13]. In this paper, we establish a physical model to describe the kinetics and laser mechanism of diode pumped Rb vapor laser. In reference to the parameters in experiments [14], we analyze the influence of parameters of the pump laser, the output coupler reflectivity, the cell length, the temperature and the buffer gases on the output power and the optical–optical efficiency. The simulation results agree well with the experiments. A set of optimization parameters is obtained for designing an efficient diode pumped Rb vapor laser.

2. Description of the model Fig. 1 outlined the energy level of Rb used for pump excitation and laser extraction. The Rb laser is pumped on the D2 transition from the 52S1/2 to the 52P3/2 state using diode laser excitation. By means of spin-orbit coupling and fine-structure relaxation accelerated by collision with helium and ethane molecules between the 52P3/2 and 52P1/2 levels, the 52P3/2 state relax faster to the upper laser 52P1/2 level than spontaneous radiative decay to the ground 52S1/2 level. And then laser is achieved on the D1 transition between the 52P1/2 and 52S1/2 levels. Considering the impacts of the pump laser, the cavity, the finestructure mixing, the buffer gases and so on to the number density of Rb atomic energy levels, the rate equations of Rb atomic levels in the cell can be described below [15]:

dn1 n n = −Γp + Γl + 2 + 3 dt τ D1 τD2

ð1Þ

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52P3/2

Considering the mismatch between the pump beam (which had an elliptical cross-section) and the laser cavity mode, ηmod e is modified by

52P1/2

2

η mode =

52S1/2 Fig. 1. Energy level diagram of Rb showing pump excitation and laser extraction.


    dn2 ΔE n = −Γl + γ2 P3 = 2− 2 P1 = 2 ðn3 −n2 Þ− 2 exp − −1 n2 − 2 kB T dt τ D1 ð2Þ 
    dn3 ΔE n = Γp −γ2 P3 = 2− 2 P1 = 2 ðn3 −n2 Þ− 2 exp − −1 n2 − 3 ð3Þ kB T dt τ D2 Where n1,n2 and n3 are the number density of Rb atomic energy levels 52S1/2, 52P1/2, 52P3/2 separately. ΔE is the energy difference between states 2P1/2 and 2P3/2, T is Kelvin temperature, τD1 and τD2 are the lifetime of levels 52P1/2 and 52P3/2. The fine-structure mixing rate is written as

γ2 P3 = 2− 2 P1 = 2 = nc2 H4  σðc2 H4 Þ 2  σðHeÞ 2 P

P3 = 2− 2 P1 = 2

3 = 2−

2

P1 = 2

 VrðCs−C2 H4 Þ + nHe

ð4Þ

 VrðCs−HeÞ

where nC2H4 and nHe are the number densities of ethane and helium in the cell, respectively, Vr is the rms thermally averaged relative velocity between alkali atoms and ethane (or helium) molecules, σC2H2 and σHe are the cross-sectional values for Rb 52P3/2 to 52P1/2 population transfer by collisions with ethane and helium, respectively. Γp and Γl are the transition rates associated with pump photon absorption and laser photon emission, respectively. They can be expressed as

η  ηdel 1 dPp Γp = mode ∫dλ hc = λ dλ VL f1− exp½−ðn1 −0:5  n3 Þσ D2 ðλÞlg

ð5Þ

n o  1 + Rp exp½−ðn1 −0:5  n3 ÞσD2 ðλÞl

0 10 sffiffiffiffiffiffiffiffi1 1 PL ROC B 1 t2 A C@ Γl = @qffiffiffiffiffiffiffiffiffiffiffiffi −1A 1 + VL hvL 1−ROC ROC t 2 ROC

ð6Þ

Where ηmode is the mode match parameter, ηdel is the delivery efficiency from the source power to the gain medium, VL is the volume of the laser mode that intercepts the gain medium, dPp/dλ is the spectrally resolved pump power, σD2(λ) is the absorption crosssection, l is the gain cell length, PL is the output laser power, t is the one-way cavity transmission.

ω2l

ωl V ⋅ L + ω2p VP

ð7Þ

Where ωl and ωp are the beam waists of the laser and pump light respectively, VP is the volume of the pump mode. With the energetics model established above and main parameters listed in Table 1, we calculate the influence of parameters on the laser output performance using the Matlab program, and analyze the optimized parameters to get the high efficient diode pumped Rb lasers. 3. Simulation results 3.1. Influence of the output coupler reflectivity We can see from Eq. (6) that the output coupler reflectivity has important influence on output laser power. Fig. 2 displays the laser power rises with the input pump power under different output coupler reflectivities with 378 K cell temperature and 2 cm cell length. The optical–optical efficiency is somewhat lower with larger coupler reflectivity. For the optimal output coupler reflectivity of 11%, the calculation result shows 58% optical to optical slope efficiency in lower pump power (b100 W), which is very close to the experimental data [14]. And we can see that the simulation result agrees well with the experimental date in the lower pump power. When the pump power grows even higher, the slope efficiency delines to 8%. This may be caused by the thermal lensing effect in higher pump power that changes the laser cavity configuration, and reduces the optical–optical efficiency. And the higher pump power needs higher temperature to provide enough Rb vapor density, so under the same temperature, it also causes the lower efficiency in higher pump power. The point of infection changes with the cell temperature, and it would increase

Table 1 Model parameters for Rb laser. Parameter description

Parameter value

Source of parameter value

Transition energy level difference ΔE D1 transition wavelength D1 radiative lifetime D1 natural line-width D1 atomic cross-section D1 line collisionally broadened cross-section D2 transition wavelength D2 radiative lifetime D2 natural line-width D2 atomic cross-section D2 line collisionally broadened cross-section He–Rb relative velocity Mixing cross-section for He σHe Ethane pressure at room temperature Ethane–Rb relative velocity Mixing cross-section for ethane σC2H2 Fine-structure mixing rate mode match parameter ηmode Laser beam waist ωl Pump light beam waist ωp Volume of the laser mode VL Volume of the pump mode VP Length of gain medium One-way transmission through cavity

4.71 * 10− 21 J 795.0 nm 27.7 ns 0.036 GHz 1.08 * 10− 9 cm2 5.59 * 10− 13 cm2

Ref. [15] Ref. [16] Ref. [16] Ref. [16] Ref. [16] Calculated

780.2 nm 26.3 ns 0.038 GHz 1.94 * 10− 9 cm2 10.49 * 10− 13 cm2

Ref. [16] Ref. [16] Ref. [16] Ref. [16] Calculated

1634 m/s 1.03 * 10− 17 cm2 600 Torr 678 m/s 7.7 * 10− 15 cm2 1.63 * 109/s 0.754 300 μm 275 μm 1.0436 * 10− 8 m3 0.752 * 10−8 m3 2 cm 0.82

Calculated Ref. [18] Ref. [14] Calculated Ref. [17] Eq.(4) Eq.(7) Ref. [14] Ref. [14] Calculated Calculated Ref. [14] Ref. [15]

W. Ya-Juan et al. / Optics Communications 284 (2011) 4045–4048

3.3. Influence of the temperature

60

44% 33% 21% 11% experiment

50

Laser Power(w)

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40 30 20 10 0 0

20

40

60

80

100

120

140

160

180

Pump power(W) Fig. 2. Output power of the Rb laser as a function of input pump power for different output couplers (44%, 33%, 21% and 11%).

The cell temperature plays an important role in DPALs. The temperature could produce an effect on the alkali vapor density, which is essential to improve the laser output power. The lower temperature couldn't provide the proper rubidium vapor density while the higher temperature has a higher probability of the cell contamination by products of chemical reactions between the rubidium atoms and the buffer gas, which will prevent the laser output power from further increasing. Fig. 4 presents the laser output power changes with the cell temperature for various output couplers, when the input pump power is 17.8 W and the cell length is 2 cm. It is obvious that as the temperature goes up, the output power keep growing until to a maximum value and then start falling. The optimized temperature is different for each output coupler reflectivity. When reach to their maximum output power, the diode pumped rubidium laser with the output couplers of 10% has the highest cell temperature (about 404 K) while 80% output couplers has the lowest temperature (about 399 K). 3.4. Influence of buffer gas

slightly when improve the temperature. But the improving of the cell temperature will also cause other problems (such as the cell contamination and so on), that limit the increase of the laser power. With the restrictions of the pump source power, the cell size, the buffer gas and the thermal effect, the highest laser output power reported so far is 28 W [19]. The simulation results provide a scientific prevision for further improving the output power.

3.2. Influence of the cell length Fig. 3 shows the dependence of the overall optical to optical efficiency on the input pump power with different cell length under 405 K cell temperature and 10% output coupler reflectivity. It can be seen that the optical efficiency raises dramatically as the pump power growing at the beginning and then tends to keep stabilization. At the relatively lower pump power, the cell length of 1.5 cm appearing highest gaining. But as the pump power growing. The cell length of 2 cm gets the highest optical efficiency under the same circumstance. It agrees well with the experiments as 2 cm long cell always gets higher output power at much lower temperature [14]. It is reasonable that the gain medium absorption is non-linear along the cell length and the mismatching of the pump-to-cavity mode beam size also creates losses at the lasing wavelength, so the longer cell cannot bring higher optical efficiency.

In the experiment on diode pumped rubidium laser, the gain medium Rb is usually sealed in cell with some ratio of helium and ethane as buffer gas. Ethane has been turned out to be the efficient element to promote rapid fine-structure mixing between the terminal pump level 2P3/2 and the initial laser level 2P1/2, and helium is used to homogenously broaden the alkali vapor absorption spectrum. The different ethane and helium pressures could produce a great effect on the output power, so it is important to get the optimized combination. With a better parametric combination of 405 K temperature, 10% output coupler and 2 cm cell length, we calculate the influence of pump power on the optical efficiency with varying ethane and helium pressures, which is plotted in Fig. 5. According to Fig. 5, increasing the ethane pressure improves performance substantially even in the absence of helium. The buffer gas combination 600 Torr of ethane with no helium gets the highest optical–optical efficiency (about 57%). This is most likely due to more rapid spin–orbit quenching with higher amounts of ethane. And besides that, ethane also has the effect on the subsequent pressure broadening of the rubidium absorption transition. 4. Conclusion In this paper, we have established a physical model to describe the kinetics and laser mechanism of diode pumped Rb vapor laser. The 10 0.1 0.3 0.6 0.8

8

0.5

Output power(w)

optical-optical efficiency

0.6

0.4 0.3 0.2

6

4

2 0.1 0

0.0 0

20

40

60

80

100

Pump power(W) Fig. 3. Optical–optical slope efficiencies versus input pump power with different cell length.

380

390

400

410

420

430

Temperature(T) Fig. 4. Laser output power for various output couplers(10%, 30%, 60% and 80%) plotted against cell temperature when Pp = 17.8 W and cell length l = 2 cm.

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Acknowledgments

optical-optical efficiency

0.60 0.55

This work was supported by the National Natural Science Foundation of China under Grant No. 10974176 and the Zhejiang Provincial Natural Science Foundation under Grant No. Y1090087.

0.50 0.45 500/100 600/0 50/600

0.40 0.35

References

0.30 0.25 0.20 0.15 0.10 10

20

30

40

50

60

Pump power(W) Fig. 5. Optical–optical slope efficiencies versus input pump power with 500 Torr of ethane and 100 Torr of helium, 600 Torr of ethane with no helium, 50 Torr of ethane and 600 Torr of helium.

influences of parameters of the output coupler reflectivity, the cell length, the temperature and the buffer gases on the output power and the optical–optical efficiency have been calculated and analyzed. With a set of optimization parameters of 405 K cell temperature, 10% output coupler, 2 cm cell length and 600 Torr ethane pressure in the Rb vapor cell, 34 W output power can be obtained under 60 W pump power. The model can provide an effective way for designing an efficient diode pumped Rb vapor laser.

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