Photoionization in alkali lasers

R.J. Knize; B.V. Zhdanov; M.K. Shaffer

doi:10.1364/OE.19.007894

1. Introduction

There has been renewed interest in alkali vapor lasers in the last decade [1] because of their potential to generate high power in a high quality beam. Lasers have been demonstrated for Potassium (n = 4), Rubidium (n = 5) and Cesium (n = 6) vapors. These lasers are pumped from the ground nS_1/2 state to the nP_3/2 state using D2 resonant light (see Fig. 1 with energy level diagram for Rb atom). In a standard alkali laser, a buffer gas is used to transfer population from the nP_3/2 state to the nP_1/2 state and to broaden the alkali vapor absorption line. If the pumping and mixing are rapid enough, a population inversion between the nP_1/2 state and the nS_1/2 state occurs and lasing is possible at the D1 transition.

Fig. 1 An abbreviated energy diagram of Rb, shows the lower levels important for pumping, lasing and photoionization. K and Cs have similar energy diagrams.

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There are several approaches in designing an efficient high power alkali lasers. One approach is to use multi-atmospheres (10 atmospheres) of helium buffer gas to mix the Rb nP states [2] and broaden the Rb absorption line to match it to a pump diode laser emission line. Another approach is to use approximately one atmosphere or less of buffer gas [3–5] for nP states mixing. In this case a narrowbanding of the pump laser linewidth to about 10 GHz is required to match it to the alkali vapor absorption line. A different approach is to pump a Cs exciplex and either lase 6P_3/2 to 6S_1/2 directly or use a buffer gas and lase 6P_1/2 to 6S_1/2 [6–8]. This approach allows the use of commercial broadband pump diode lasers. There is one problem, existing in all types of alkali lasers, which is that the nD_5/2, nD_3/2 and (n + 2)S_1/2 states can also be populated by either photon excitation from the nP states or energy pooling collisions of two nP states. The intense pump and lasing radiation can then photoionize atoms in these excited S and D states, leading to loss of neutral alkali atoms in the laser gain medium. In this paper we have calculated this photoionization rate for several types of alkali lasers and have found that this rate can be quite severe for the high pressure Rb laser and the exciplex laser. To replenish the loss of neutral alkali atoms because of photoionization, a flow of the gain medium is required with a fast, possibly supersonic, speed.

2. Model and calculations

The energy diagram for a standard three-level alkali laser shown in Fig. 1 and includes the relevant excited S and D states and the ionization limit. In each of the considered alkali systems, the nD_5/2, nD_3/2 and (n + 2)S_1/2 states can be populated by photon excitation from the nP_3/2 and nP_1/2 states by means of either D1 or D2 light and, then, ionized by the same D1 or D2 light. Table 1 lists the wavelengths (λ), lifetimes (τ), absorption cross- sections (σ) and detunings (∆) between upper level transitions for K, Rb and Cs and either D1 or D2 light. For example, the detuning ∆_D1 in the block of the table corresponding to the nP_3/2→nD_5/2 transition refers to the detuning in MHz between the frequency of nP_3/2 → nD_5/2 transition and the D1 light frequency (nP_1/2 – nS_1/2). Similar detunings are defined for other states and for D1 or D2 light or the pump wavelength of the exciplex laser.

Table 1. Tabulated are the Relevant Values for the Wavelengths λ, Fractional Population η, Lifetime τ, Absorption Cross Sections σ and Detunings Δ from the D1 and D2 Light for the K, Rb, and Cs.

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The stationary isolated atom cross section σ_o can be calculated using Eq. (1)

σ_{o} = λ_{21}^{2} A_{21} g_{2} / (2 π A_{Total} g_{1})

where λ is wavelength of the transition, A is the Einstein coefficient for the relevant transition, A_Total is the sum of Einstein coefficients (includes both relevant states, i.e. P_3/2 and D_5/2, decay rates) and g₁ and g₂ are the degeneracies for the lower and upper states respectively [9]. This can be calculated for each of the relevant alkali transitions in Cs, Rb or K [10–13]. In these laser systems, a buffer gas will pressure broaden the transition and the excitation rate from state j to i, E_ij, due to D2 light can be expressed by Eq. (2)

E_{ij}^{} = I_{D2} σ_{o} (f_{n} / f_{b}) / (1 + 4 Δ_{i}^{2} / f_{b}^{2})

where I_D2 is the intensity of D2 pumping light, f_n is the natural linewidth and f_b is the FWHM pressure broadened linewidth. The pressure broadening for the nD_5/2, nD_3/2 and (n + 2)S_1/2 states have not yet been determined for Cs, Rb, and K in the presence of helium or ethane. In a number of references [14–17], however, this broadening rate has been measured in transitions and atmospheres similar to those of interest here .These values tend to lie between 40 and 80 MHz/torr, the majority of which can be included in the range of 55 ± 15 MHz/Torr. For the purpose of this paper, we have chosen to use the mean value of 55 MHz/Torr for the different alkalis.

Once the upper excited state j is populated, the photoionization rate, P_j, from that state can be written as Eq. (3)

P_{j} = (I_{D2 +} I_{D1}) σ_{i}

where I_D1 and I_D2 are the intensities of the D1 lasing light and D2 pumping light respectively, σ_i is the photoionization cross section [18]. The photoionization cross section is weakly dependent on the wavelength and will be similar for the (n + 2)S_1/2, nD_3/2, and nD_5/2 states in all alkalis considered. For the purposes of this paper we use the value for Rb of σ_i = 2 x 10⁻¹⁷ cm² for all the alkalis [18]. The effective ionization or loss rate per alkali atom in D1 light, R_L(D1), is shown in Eq. (4).

\begin{matrix} R (D1) = η_{P3 / 2} (E_{P3 / 2, D5 / 2} P_{D5 / 2} τ_{D5 / 2} + E_{P3 / 2, D3 / 2} P_{D3 / 2} τ_{D3 / 2} + E_{P3 / 2, S1 / 2} P_{S1 / 2} τ_{S1 / 2}) \\ + η_{P1 / 2} (E_{P3 / 2, D5 / 2} P_{D5 / 2} τ_{D5 / 2} + E_{P3 / 2, D3 / 2} P_{D3 / 2} τ_{D3 / 2} + E_{P3 / 2, S1 / 2} P_{S1 / 2} τ_{S1 / 2}) \end{matrix}

where η_P1/2 and η_P3/2 are the fractions of atoms in the nP_1/2 and nP_3/2 states, respectively, and τ is the lifetime of the relevant nD_j or (n + 2)S_1/2 state. Then Eq. (5) is the total loss rate from both the D1 and D2 light.

R_{Total} = R (D1) + R (D2)

Two different classes of standard alkali lasers have been demonstrated: K, Rb and Cs lasers with a low (≤1 atmosphere) buffer gas pressure and a Rb laser with a high (close to 10 atmospheres) helium gas pressure. Helium is not a very efficient buffer gas for nP state mixing in Rb, which is why a pressure of about 10 atmospheres is required. Helium is, however, efficient at mixing the nP states in K such that less than 1 atmosphere is sufficient [19]. A low pressure Rb or Cs laser will require another buffer gas such as ethane or methane for rapid mixing. The D1 and D2 transitions are broadened by about 20 MHz/Torr for common buffer gasses. η will be determined by the pumping rate, the nP mixing rate, the laser intensity, the relevant cross sections and the relative statistical weight factors g_i, which equal to 1, 2, 1, respectively for the S_1/2, P_3/2 and P_1/2 states. In the limit of strong pumping, rapid P state mixing and without lasing, η_p3/2 equals to 0.47, 0.36 and 0.17, respectively for K, Rb and Cs at a temperature of 373K. During laser operation, η_p3/2 will be increased as lasing will tend to equilibrate the S_1/2 and P_1/2 levels so that η_p3/2 will approach 0.5 and η_p1/2 will approach 0.25. For the exciplex laser, where there is no P state mixing, η is greater than 2/3. For calculations in this paper, we use η_p3/2 = 0.5 and η_p1/2 = 0.25 for a standard operating alkali laser with fast P state mixing.

Results

The results of calculations for various types of alkali lasers are shown in Table 2 , where the calculated total effective alkali atom loss rates and the loss rate contributions from relevant transitions driven by either D1 or D2 light are presented. Included in the table are the buffer gas pressures for each alkali laser and the associated pump laser (or D2) light intensity. Here, the Rb 10 atm Diode Pumped Alkali Laser (DPAL) has an increased pump intensity compared with its 1 atm counterpart due to the fact that the cross sections and saturation intensities decrease with increasing of the buffer gas pressure. Thus, a higher pump intensity is necessary for laser operation as compared to the 1 atm alkali laser. The large pump intensity for the Cs exciplex laser (XPAL) arises from the large saturation intensity associated with pumping off resonance and typical operation uses ~5ns, 5mJ 837nm pulses [7]. For a standard alkali laser, the loss rate scales as I²P/∆², where P is the buffer gas pressure and I is the average intensity. The operating intensity is linear with pressure, so that the loss rate scales as P³/∆². Since ∆ is much smaller and σ_o larger for Rb, the loss rate is much higher than the one for K under similar operating conditions and pressures. The Rb laser operating at 10 atmospheres of helium has a loss rate increased by three orders of magnitude as compared with a 1 atmosphere Rb laser.

Table 2. The Total Loss Rate Due to Photoionization, R_Total, for the Considered Alkali Lasers are Summarized Along with the Contributions to the Loss Rate From Various Transitions. All Loss Rate Values are in Inits of s⁻¹. Z⁺ Denotes the Alkali Ion.

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A different approach is that of the exciplex laser. In this case, pumping occurs away from the D2 transition. The Cs-Ar exciplex laser operates at a typical temperature of 464 K, which corresponds to a density of 1.3 x 10¹⁵ cm⁻³.The transmission at the 837 nm pump wavelength is about 80%, which yields an effective absorption cross section per ground state Cs atom of σ = 1.2 x 10⁻¹⁷ cm². The effective saturation intensity, I_sat = 1/(σ τ), where τ is the 6P_3/2 lifetime, is calculated to be 610 kW/cm². In the exciplex laser, the D and upper S states can also be populated by energy pooling collisions between P states, shown by Eq. (6),

{6P}_{3 / 2} + {6P}_{3 / 2} \to {6S}_{1 / 2} + {6D}_{3 / 2}

with similar processes to populate the 6D_5/2 and other upper states, as well as processes involving the 6P_1/2 state. The reaction rate, k, for energy pooling has been measured for Cs [20], Rb [21] and K [22]. The high pump and lasing intensities (>1MW/cm²) in the exciplex laser will rapidly ionize the 6D states in less than 100 nsec. The energy pooling excitation rate to the (n + 2)S_1/2, nD_3/2 or nD_5/2 states is given by Eq. (7).

E_{ij} = η_{i} k_{ij} N

where η_i is the fraction of atoms in the relevant state i, N is the alkali density and k_ij is the reaction rate for populating any higher state j from state i, which will then be rapidly ionized. The loss rate per alkali atom via energy pooling, R, will be given by Eqs. (8a) and (8b).

R = η_{i} E_{i j} P_{j} τ_{j}

R = η_{i} {^{2}}_{} k_{ij} N (I_{D2 +} I_{D1}) σ_{i} τ_{j}

For exciplex lasers, the loss rate per Cs atom due to multi-step ionization is about 10⁶ sec⁻¹. In the case of the exciplex Cs laser, the sum of the energy pooling rates, k, for populating the (n + 2)S_1/2, nD_3/2 or nD_5/2 states, is k_total≈2 x 10⁻⁹ cm³/s. This corresponds to an ionization rate of 10⁴, an increase of ~0.5% to the total loss rate. Additionally, this loss rate scales linearly with density so it will be correspondingly larger at higher temperatures. Energy pooling will also occur in standard alkali lasers. However in these cases, the rates are lower than in the exciplex laser because the intensities and densities are much lower. Ionization rates associated with energy pooling are slow and the contribution to the total loss rate by energy pooling collisions are insignificant when compared with the three-step photoionization considered above.

Though the aforementioned photoionization processes are of great significance to high power CW alkali laser operation, there are several mechanisms (recombination, diffusion, convection and flow) which can aid in restoring the neutral alkali density in the gain medium of alkali lasers. Radiative two-body and three-body recombination mechanisms [23,24] have relatively slow rates of ~10⁻¹² cm³s⁻¹ for alkalis under conditions similar to ours. Molecular recombination, on the other hand, may be a large contributing factor to the replenishment of neutral alkali density in alkali lasers. After an alkali ion A⁺ is formed, it will quickly covert to a dimer ion in the reaction described by Eq. (9),

A^{+} + A + M \to A_{2}^{+} + M

where M is a third body, either being an alkali atom or a buffer gas atom. This rapid reaction removes two neutral alkali atoms for each ion formed. The dominant neutralization occurs via dissociative recombination shown in Eq. (10),

A_{2}^{+} + e^{-} \to A + A^{*}

The recombination coefficient α_M for this reaction has been measured [25–27] under different experimental conditions for Cs at elevated temperatures with values in the range of 10⁻⁸ to 10⁻⁶ cm³ s⁻¹. Considering this range of α_M, a 10 atm Rb-He DPAL a with a neutral Rb density of 10¹⁴ cm⁻³, where the ionization rate, R_Total, is about 2 x 10⁵ s⁻¹, has a steady state alkali neutral atom density in the range of ~54-93% of the original alkali density. One unknown of this mechanism is the effect the states of the newly dissociated atoms have on the behavior of the system. Upon dissociation, at least one if not both atoms can be in an excited state. With ionization occurring ~1µsec and relatively long lifetimes for some states (i.e. the 5D states in Rb with τ~235ns), ionization can occur again before the atom can decay to a state where it will be useful to the lasing system. This effect could potentially reduce the effective α_M, leading to a lower fraction of neutral alkali atoms in the steady state. In addition, ambipolar diffusion and electron thermalization can also play a role in reducing recombination rates [28]. These results show that photoionization may be a serious neutral atom loss mechanism in this case and that the value of α_M can play a critical role in the operation of alkali lasers. Also to be considered are other deleterious effects such as those seen by Tam [29] and Happer [30], where laser induced plasma demonstrated an avalanche/ hysteresis characteristic that may lead to increased or sustained plasma as well as cell degradation. Plasma formation leads to a loss of neutral atom density and also can contribute to heating and to the broadening and shifting of atomic lines. Further measurements and calculations are required to better understand dissociation, recombination and other effects induced by the laser plasma.

Convection, a circulatory motion established in a fluid with a non-uniform temperature distribution, is driven by a difference in densities of the medium. Zhanga et. al [31] has recently modeled the temperature profiles in an alkali laser cell and state that temperatures in a Cs laser operating at a pump intensity of 2000W/cm² can rise to 500-800 °K, while typical ambient Cs cell temperatures are ~373 °K. As temperature is increased by ~50%, the alkali density is reduced by ~50% establishing a slow convective flow of the gain medium, replenishing the neutral alkali density. Details of convection will be geometry and operating parameter dependent and will require further analysis.

Another mechanism is diffusion of neutral alkali atoms into the gain medium mode volume from the ambient neutral surrounding vapors. We suspect that low power alkali lasers can operate CW due to diffusion of neutral alkali atoms to the gain medium, because of the ionization rates being on the same order of magnitude of the diffusion rate. A simple estimate for the diffusion time, τ_D, is given by Eq. (11).

τ_{D} = L^{2} / D

where L is the mode radius and D is the diffusion coefficient. For Cs in ethane, D has not been experimentally determined, however, W. Happer [32] compiled a table of values of D for Cs in the gases He, Ne, Ar, and N₂. A trend of decreasing values of D with increasing atomic mass of the buffer gas is apparent in the table and with N₂ having roughly the same mass as an ethane molecule, we crudely estimate the value of D for Cs in ethane will be near that of N₂, which is estimated to be 0.07 cm²/sec at one atmosphere. This gives a diffusion time of τ_D~35ms for a typical L of 0.05cm. For the laser described in [33], there is an observed exponential decay of 26 msec in the laser output performance as a function of time. The calculated ionization rate of this laser system which is about R_L = 50 s⁻¹, or a decay time of τ = 20ms. The observed decay time is very similar to both the ionization decay time and the diffusion time. Degradation of laser performance can occur due to both photoionization and heating. Beyond these first approximations, the solutions for both of these replenishing mechanisms, convection and diffusion, in an alkali laser can become quite involved and merit further investigation to fully understand their role in the operation of an alkali laser.

Similar to the convective process, the effective loss of neutral alkali atoms can also be mitigated by force flowing the gain medium, so that new alkali atoms enter the pumping region. Typical pumping regions for an alkali laser has a transverse dimension of about d = 0.1 – 1 cm. For a transverse flow speed of v = R_L d, and neglecting recombination effects, the alkali density will decrease by 1/e from the upstream to downstream side, assuming flat top beams. A laser will probably require a more uniform alkali density than this, so that the flow speed will have to be several times v. Table 3 shows the calculated flow speed v for the different cases of alkali lasers with different transverse.

Table 3. For the total photoionization loss rates for each alkali laser, the nominal flow rates of neutral alkali are tabulated for 1/e replenishment of the gain medium. This is done for a mode diameter of 0.1 and 1.0 cm, neglecting recombination effects.

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These results show that very high, nearly supersonic flow speeds, will be required for a 10 atmosphere Rb-He laser and for an exciplex laser. These fast flow speeds will be problematic in these lasers, especially in maintaining good optical quality and in power requirements to maintain the flow. A one atmosphere alkali laser will require flow speeds of less than 1 m/sec or less. The effect of photoionization, required alkali density uniformity and flow speed will require detailed modeling.

Conclusion

Photoionization rates have been calculated for standard alkali lasers and for an exciplex alkali laser. For standard alkali lasers, photon excitation to the nD or (n + 2)S states with subsequent photoionization is the dominant loss mechanism of neutral alkali atoms in the gain medium. For an exciplex alkali laser, energy pooling slightly contributes to the populating of nD or (n + 2)S states, however photo excitation and photoionization remains the dominant neutral atom loss mechanism. In certain cases, such as the 10 atmosphere Rb laser, where the pressures and intensities are higher and 5P→5D transitions are nearly resonant with the D2 pump light, the loss rates can approach 10⁵ sec⁻¹, which may require supersonic flow of the gain medium to replenish the neutral atoms for high power CW operation of the laser.

Acknowledgements

We acknowledge support of the Air Force Office of Scientific Research, the Joint Technology Office for High Energy Lasers, and the National Science Foundation.

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	States and transitions	K	Rb	Cs
λ (nm)	nS_1/2→nP_1/2	770	795	894
η	nP_1/2	0.25	0.25	0.25
λ (nm)	nS_1/2→nP_3/2	766	780	852
η	nP_3/2	0.5	0.5	0.5
λ (nm)	nP_3/2→nD_5/2	696	776	917
τ _nlj (ns)		283	235	60
σ (cm²)		1.5 x 10⁻¹²	9.0 x 10⁻¹¹	6.4 x 10⁻¹⁰
Δ _D1 (MHz)		4.1 x 10⁷	9.2 x 10⁶	−8.4 x 10⁶
Δ _D2 (MHz)		3.9 x 10⁷	2.0 x 10⁶	−2.5 x 10⁷
λ (nm)	nP_3/2→nD_3/2	696	776	921
τ _nlj (ns)		283	235	60
σ (cm²)		1.5 x 10⁻¹²	1.0 x 10⁻¹¹	7.0 x 10⁻¹¹
Δ _D1 MHz)		4.1 x 10⁷	9.2 x 10⁶	−9.8 x 10⁶
Δ _D2 (MHz)		3.9 x 10⁷	2.0 x 10⁶	−2.6 x 10⁷
λ (nm)	nP_1/2→nD_3/2	694	762	876
τ _nlj (ns)		283	235	60
σ (cm²)		1.5 x 10⁻¹²	9.8 x 10⁻¹¹	7.0 x 10⁻¹⁰
Δ _D1 (MHz)		4.3 x 10⁷	1.6 x 10⁶	6.9 x 10⁶
Δ _D2 (MHz)		4.1 x 10⁷	9.1 x 10⁶	−9.6 x 10⁶
λ (nm)	nP_3/2→ (n + 2)S_1/2	694	741	795
τ _nlj (ns)	nP_3/2→ (n + 2)S_1/2	90	86	48
σ (cm²)		3.3 x 10⁻¹¹	3.5 x 10⁻¹¹	4.3 x 10⁻¹¹
Δ _D1 (MHz)		4.3 x 10⁷	2.8 x 10⁷	4.2 x 10⁷
Δ _D2 (MHz)		4.1 x 10⁷	2.0 x 10⁷	2.5 x 10⁷
λ (nm)	nP_1/2→ (n + 2)S_1/2	691	728	761
τ _nlj (ns)	nP_1/2→ (n + 2)S_1/2	90	86	48
σ (cm²)		3.4 x 10⁻¹¹	3.7 x 10⁻¹¹	4.9 x 10⁻¹¹
Δ _D1 (MHz)		4.4 x 10⁷	3.5 x 10⁷	5.9 x 10⁷
Δ _D2 (MHz)		4.2 x 10⁷	2.8 x 10⁷	4.2 x 10⁷

		K DPAL	Cs DPAL	Rb DPAL	Rb DPAL	Cs XPAL
Buffer Gas Pressure (atm)		1	1	1	10	1
Pump Intensity (kW/cm²)		2	2	2	40	500
Total Loss R_Total (s⁻¹)		7.7 x 10⁻²	5.0 x 10¹	5.4 x 10¹	2.2 x 10⁵	2.7 x 10⁶

Loss Contributions (s⁻¹) Transition & Light
nP_3/2 →nD_5/2 →Z⁺	D1	9.4 x 10⁻⁴	2.0 x 10¹	2.1 x 10⁰	8.3 x 10³	1.3 x 10⁶
	D2	1.1 x 10⁻³	2.3 x 10⁰	4.5 x 10¹	1.8 x 10⁵	9.3 x 10⁴
nP_3/2 →nD_3/2 →Z⁺	D1	1.0 x 10⁻⁴	1.8 x 10⁰	2.3 x 10⁻¹	9.2 x 10²	1.1 x 10⁵
	D2	1.1 x 10⁻⁴	2.4 x 10⁻¹	5.0 x 10⁰	2.0 x 10⁴	9.9 x 10³
nP_1/2 →nD_3/2 →Z⁺	D1	4.9 x 10⁻⁴	1.7 x 10¹	3.5 x 10⁻¹	1.4 x 10³	1.0 x 10⁶
	D2	5.3 x 10⁻⁴	8.6 x 10⁰	1.1 x 10⁰	4.5 x 10³	2.0 x 10⁵
nP_3/2 →n + 2)S_1/2 →Z⁺	D1	2.2 x 10⁻²	2.8 x 10⁻²	4.5 x 10⁻²	1.8 x 10²	1.7 x 10³
	D2	2.0 x 10⁻²	7.7 x 10⁻²	8.3 x 10⁻²	3.3 x 10²	8.5 x 10³
nP_1/2 →n + 2)S_1/2 →Z⁺	D1	1.5 x 10⁻²	1.6 x 10⁻²	2.9 x 10⁻²	1.2 x 10²	1.0 x 10³
	D2	1.7 x 10⁻²	3.1 x 10⁻²	4.7 x 10⁻²	1.9 x 10²	2.7 x 10³

		Nominal Flow Rate (cm/sec)
Alkali Laser	Rloss	d = 0.1cm	d = 1.0cm
K DPAL 1 atm	7.7 x 10⁻²	7.7 x 10⁻³	7.7 x 10⁻²
Cs DPAL 1 atm	5.0 x 10¹	5.0 x 10⁰	5.0 x 10¹
Rb DPAL 1 atm	5.4 x 10¹	5.4 x 10⁰	5.4 x 10¹
Rb DPAL 10 atm	2.2 x 10⁵	2.2 x 10⁴	2.2 x 10⁵
Cs XPAL 1 atm	2.7 x 10⁶	2.7 x 10⁵	2.7 x 10⁶

	States and transitions	K	Rb	Cs
λ (nm)	nS_1/2→nP_1/2	770	795	894
η	nP_1/2	0.25	0.25	0.25
λ (nm)	nS_1/2→nP_3/2	766	780	852
η	nP_3/2	0.5	0.5	0.5
λ (nm)	nP_3/2→nD_5/2	696	776	917
τ _nlj (ns)		283	235	60
σ (cm²)		1.5 x 10⁻¹²	9.0 x 10⁻¹¹	6.4 x 10⁻¹⁰
Δ _D1 (MHz)		4.1 x 10⁷	9.2 x 10⁶	−8.4 x 10⁶
Δ _D2 (MHz)		3.9 x 10⁷	2.0 x 10⁶	−2.5 x 10⁷
λ (nm)	nP_3/2→nD_3/2	696	776	921
τ _nlj (ns)		283	235	60
σ (cm²)		1.5 x 10⁻¹²	1.0 x 10⁻¹¹	7.0 x 10⁻¹¹
Δ _D1 MHz)		4.1 x 10⁷	9.2 x 10⁶	−9.8 x 10⁶
Δ _D2 (MHz)		3.9 x 10⁷	2.0 x 10⁶	−2.6 x 10⁷
λ (nm)	nP_1/2→nD_3/2	694	762	876
τ _nlj (ns)		283	235	60
σ (cm²)		1.5 x 10⁻¹²	9.8 x 10⁻¹¹	7.0 x 10⁻¹⁰
Δ _D1 (MHz)		4.3 x 10⁷	1.6 x 10⁶	6.9 x 10⁶
Δ _D2 (MHz)		4.1 x 10⁷	9.1 x 10⁶	−9.6 x 10⁶
λ (nm)	nP_3/2→ (n + 2)S_1/2	694	741	795
τ _nlj (ns)	nP_3/2→ (n + 2)S_1/2	90	86	48
σ (cm²)		3.3 x 10⁻¹¹	3.5 x 10⁻¹¹	4.3 x 10⁻¹¹
Δ _D1 (MHz)		4.3 x 10⁷	2.8 x 10⁷	4.2 x 10⁷
Δ _D2 (MHz)		4.1 x 10⁷	2.0 x 10⁷	2.5 x 10⁷
λ (nm)	nP_1/2→ (n + 2)S_1/2	691	728	761
τ _nlj (ns)	nP_1/2→ (n + 2)S_1/2	90	86	48
σ (cm²)		3.4 x 10⁻¹¹	3.7 x 10⁻¹¹	4.9 x 10⁻¹¹
Δ _D1 (MHz)		4.4 x 10⁷	3.5 x 10⁷	5.9 x 10⁷
Δ _D2 (MHz)		4.2 x 10⁷	2.8 x 10⁷	4.2 x 10⁷

		K DPAL	Cs DPAL	Rb DPAL	Rb DPAL	Cs XPAL
Buffer Gas Pressure (atm)		1	1	1	10	1
Pump Intensity (kW/cm²)		2	2	2	40	500
Total Loss R_Total (s⁻¹)		7.7 x 10⁻²	5.0 x 10¹	5.4 x 10¹	2.2 x 10⁵	2.7 x 10⁶

Loss Contributions (s⁻¹) Transition & Light
nP_3/2 →nD_5/2 →Z⁺	D1	9.4 x 10⁻⁴	2.0 x 10¹	2.1 x 10⁰	8.3 x 10³	1.3 x 10⁶
	D2	1.1 x 10⁻³	2.3 x 10⁰	4.5 x 10¹	1.8 x 10⁵	9.3 x 10⁴
nP_3/2 →nD_3/2 →Z⁺	D1	1.0 x 10⁻⁴	1.8 x 10⁰	2.3 x 10⁻¹	9.2 x 10²	1.1 x 10⁵
	D2	1.1 x 10⁻⁴	2.4 x 10⁻¹	5.0 x 10⁰	2.0 x 10⁴	9.9 x 10³
nP_1/2 →nD_3/2 →Z⁺	D1	4.9 x 10⁻⁴	1.7 x 10¹	3.5 x 10⁻¹	1.4 x 10³	1.0 x 10⁶
	D2	5.3 x 10⁻⁴	8.6 x 10⁰	1.1 x 10⁰	4.5 x 10³	2.0 x 10⁵
nP_3/2 →n + 2)S_1/2 →Z⁺	D1	2.2 x 10⁻²	2.8 x 10⁻²	4.5 x 10⁻²	1.8 x 10²	1.7 x 10³
	D2	2.0 x 10⁻²	7.7 x 10⁻²	8.3 x 10⁻²	3.3 x 10²	8.5 x 10³
nP_1/2 →n + 2)S_1/2 →Z⁺	D1	1.5 x 10⁻²	1.6 x 10⁻²	2.9 x 10⁻²	1.2 x 10²	1.0 x 10³
	D2	1.7 x 10⁻²	3.1 x 10⁻²	4.7 x 10⁻²	1.9 x 10²	2.7 x 10³

Photoionization in alkali lasers

Abstract

1. Introduction

2. Model and calculations

Results

Conclusion

Acknowledgements

References and links

Cited By

Figures (1)

Tables (3)

Equations (12)

Optics Express