Abstract

Diode pumped alkali vapor amplifier (DPAA) is a potential candidate in high power laser field. In this paper, we set up a model for the diode double-side-pumped alkali vapor amplifier. For the three-dimensional volumetric gain medium, both the longitudinal and transverse amplified spontaneous emission (ASE) effects are considered and coupled into the rate equations. An iterative numerical approach is proposed to solve the model. Some important influencing factors are simulated and discussed. The results show that in the case of saturated amplification, the ASE effect can be well suppressed rather than a limitation in power scaling of a DPAA.

©2011 Optical Society of America

1. Introduction

As first demonstrated in 2006 [1], diode pumped alkali vapor lasers (DPALs) have gained much attention and fast development in recent years. As a new kind of optically pumped gas laser, DPAL offers a new way to high-power, high-efficiency, high-brightness and compact laser systems due to its many significant characteristics. The quantum efficiency is high (95.3% for Cs, 98.1% for Rb and 99.6% for K), which is important for increasing the optical to optical efficiency and minimizing thermal problems. And the thermal problems can be further reduced since the gaseous gain medium can be flowed to remove the heat. Good thermal management as well as the stability at high pump intensity [2] provides no significant single aperture power scaled limitation for DPALs. For the fast recycling time of alkali atoms in the lasing process [3], it is promising to extract high power from small gain volumes. These advantages make DPAL a potential candidate in the future high power laser field. Till now, a great number of DPAL experiments have demonstrated high efficiency and good beam quality [411].

As compared with a single oscillator, another power scaled method is to use the MOPA (master oscillator power amplifier) configuration, by adding a single or chain of diode-pumped alkali vapor amplifiers (DPAAs). As being successfully applied in solid-state lasers, the MOPA configuration can simplify the pump arrangement, disperse the thermal effect and keep good beam quality. Till now, some DPAA experiments have been made [1214]. Hostutler et al. obtained 7.9dB amplification in a 2cm long Rb amplifier with seed laser of 50mW [12]. Zhdanov et al. obtained an amplification factor of 145 for low power Cs laser radiation [13]. The maximal DPAA output was obtained by Zhdanov et al., with 25W output power, when the seed laser was 5W under 280W diode pump power [14]. Till now, all these DPAA experiments were made in longitudinally-pumped configuration, and a corresponding model was set up by B. Pan et al. which has agreed well with experimental results [15].

Another more scalable pump scheme is the side-pumped configuration, which has been applied in DPALs [7, 10]. It can simplify the pump arrangement, decrease the demand of pump brightness, enhance the pump uniformity, lighten the power burden on optical components and be more convenient in structure design when the gaseous medium is flowed. In design of a side-pumped DPAA, a key issue has to be considered, especially for such three-dimensional volumetric medium with high gain, is the amplified spontaneous emission (ASE). The ASE will decrease the gain, and usually becomes more serious when the volume of the medium is larger and the gain is higher. So in power scaling of DPALs and DPAAs, the ASE effect must be seriously considered to see if it will be a limitation. Till now, many researchers have made studies on ASE for different kinds of high gain lasers, except for such recently developed alkali lasers. Most of the papers have discussed ASE for one-dimensional, often pencil-like geometries, such as laser rods [16, 17] or fibers [18]. For these configurations, only longitudinal ASE is considered, and for every point inside the gain medium one can define a solid angle, into which photons that are emitted have the most significant contribution to ASE. For three-dimensional amplifier with arbitrary shape, the solid angle is hard to define, and a Monte Carlo type numerical method has been applied to simulate the ASE from all photons spontaneously emitted inside the gain medium [19,20]. In this paper, the dealing of ASE is a key issue in our model. To adapt to the division scheme of the amplifier, which is needed in side-pumped configuration, we develop a new method to calculate the ASE. In our method, the longitudinal and transverse ASE effects are considered individually, and both of them are coupled into the rate equations. The results can give the range of ASE efficiency, which will be helpful for the laser design.

In section 2, the kinetic model considering both the longitudinal and transverse ASE effects for a symmetrically double-side pumped DPAA is introduced. In section 3, the numerical approaches are described. In section 4, some important influencing factors are simulated and discussed.

2. Modeling of an alkali vapor amplifier

The schematic diagram of a DPAA is shown in Fig. 1 . Because we are only interested in high power laser operation, the alkali vapor cell is pumped symmetrically by multiple diode stacks from two sides. The cell contains a homogeneous mix of alkali vapor (rubidium or cesium) and buffer gases (helium and hydrocarbons, for example methane or ethane) at operation temperature on the order of 100C. To match the beam shape of diode lasers, the cell is designed into a rectangular box (H×W×L). The pump light enters into the cell through x-z plane. In fast-axis (along x-axis), the pump light can be collimated by beam shaping optics. In slow-axis (along z-axis), the small spreading can be neglected for pumping by multiple diode stacks. The pump intensity along x-z plane can be assumed homogeneous. The seed laser enters into the cell from x-y plane and propagates along z-axis to be amplified. In the entrance plane (xOy plane), the seed laser intensity is also assumed to be homogeneous.

 

Fig. 1 Schematic diagram of a DPAA in symmetrically double-side pumped configuration. The dashed line presents the division scheme of the gain medium.

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To adapt to the pump structure, we make a two-dimension division of the alkali gain medium along x and y axes. Each divided volume element has dimensions of Δx×Δy×L that meet the condition of Δx,ΔyL. The equations that govern the distribution of population densities in a volume element are

dn1(y)dt=Γp(y)+Γl(y)+ΓASE(y)+n2(y)(A21+Q21)+n3(y)(A31+Q31),
dn2(y)dt=Γl(y)+γ32[n3(y)2n2(y)exp(ΔEkT)]ΓASE(y)n2(y)(A21+Q21),
dn3(y)dt=Γp(y)γ32[n3(y)2n2(y)exp(ΔEkT)]n3(y)(A31+Q31).
Here, ni(y)(i=1,2,3) are the longitudinally averaged population densities of the ground level (2S1/2), upper pump level (2P3/2) and upper laser level (2P1/2), which satisfies the population conservation relationship
n1(y)+n2(y)+n3(y)=ntot,
where ntot is the alkali concentration which is only decided by temperature. In our model, the temperature gradient is neglected, and ntot is assumed to be constant throughout the volume. Because the pump and laser intensities are both assumed to be homogeneous along x-axis, we assume the population densities also to be homogeneous along x-axis, despite the transverse ASE effect may cause some variations. Under this assumption, the population densities are only y dependent denoted as ni(y)(i=1,2,3). Γp and Γl are the stimulated pump absorption and laser emission rates respectively. ΓASE is the averaged ASE induced population decay rate of 2P1/2 level (‘ASE rate’ for short). γ32 is the fine structure mixing rate that relaxes the population from 2P3/2 to 2P1/2, which is usually enhanced by adding some small hydrocarbons, for example methane or ethane. A21(A31) are the spontaneous emission rates, and Q21(Q31) are the quenching rates that introduced by hydrocarbons. ΔE is the energy gap between 2P1/2 and 2P3/2 levels, kthe Boltzmann constant and Tthe absolute temperature.

The pump light is assumed to be in Gaussian spectral profile. The incident spectrally resolved pump powers at two sides are given by

Pp+(y=0,λ)=Pp(y=W,λ)=Pp4ln2πcΔνpλ2exp[4ln2cΔνp(1λ1λp)]2,
where Pp is the total pump power at one side, c the speed of light, Δνp the linewidth (FWHM) of pump light and λp the center pump wavelength. The pump lineshape will change during the absorption process, and such spectral dependence of pump light absorption has been considered in the model.

The expression of pump absorption rate Γp(y) is similar as in reference [21]

Γp(y)=1hνpL0Ip+(y,λ)×{1exp[Δn13(y)σ13(λ)Δy]}dλ+1hνpL0Ip(y,λ)×{exp[Δn13(y)σ13(λ)Δy]1}dλ,
where Δn13(y)=n1(y)n3(y)/2 is the population difference between pump transition levels, hνp the pump photon energy, Ip±(y,λ) the spectrally resolved pump intensities and σ13(λ) the spectrally resolved atomic absorption cross-section.

The laser emission rate Γl(y) is given by

Γl(y)=Iseed(y){exp[Δn21(y)σ21L]1}hν21L,
where Δn21(y)=n2(y)n1(y) is the population difference between laser transition levels, and Iseed(y) the seed laser intensity. The seed laser is assumed to be in single frequency centered at the D1 line transition (2P1/22S1/2), and σ21 is the corresponding cross-section.

Now we start to deduce the expression of ΓASE(y). In step 1, because each volume element satisfies the condition of Δx,ΔyL, we can only consider the longitudinal (one-dimension along z-axis) ASE effect in each element. In step 2, because the spontaneous emission from volume elements will affect each other, we consider such transverse ASE effect to get the final expression of ΓASE(y).

Step 1. Longitudinal ASE effect in an individual volume element

The schematic diagram of longitudinal ASE effect in a volume element is shown in Fig. 2 . We further divide the volume element along z-axis into many sub-segment with length of Δz. Each sub-segment has a solid angle relative to the end face denoted as Ω. For example, the solid angle of the n-th sub-segment is

Ω[(n1)Δz,nΔz]=ΔxΔy[L(n1)Δz]2.
PASE(y) is the total ASE power that emitted from an end of the volume element. The contribution to PASE(y) from the n-th sub-segment is
PASE[(n1)Δz,nΔz](y)=hν21A21n2(y)ΔxΔyΔzΩ[(n1)Δz,nΔz]4π×l(λ)exp{Δn21(y)σ21(λ)[L(n1)Δz]}dλ,
where l(λ) is the normalized Lorentzian function that describes the spectral intensity distribution of spontaneous emission and σ21(λ) is the spectrally resolved atomic emission cross-section.

 

Fig. 2 Schematic diagram of longitudinal ASE effect in a volume element Δx×Δy×L.

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The total ASE power PASE(y) is then the sum of contributions from all the sub-segments

PASE(y)=limΔz0[n=1L/ΔzPASE[(n1)Δz,nΔz](y)]=hν21A21n2(y)Vl2πL4l(λ)×exp[Δn21(y)σ21(λ)L]1Δn21(y)σ21(λ)dλ.

In the deduction process, we have used the averaged solid angle Ω¯=(ΔxΔy)/(L/2)2 instead of the different solid angles for different sub-segments. Vl=ηmodeΔxΔyL is the lasing volume in a volume element, and ηmode is the mode overlap factor.

The ASE rate in a volume element is then described as

ΓASE11(y,L)=2PASE(y)hν21Vl=2A21VlπL4n2(y)Δn21(y)l(λ)×exp[Δn21(y)σ21(λ)L]1σ21(λ)dλ.

The subscript 11 means that the averaged ASE rate in the volume element is induced by the gain medium inside this volume element itself. The factor 2 is added because the ASE power emits from the two sides. We also express this ASE rate as length dependent (L), which will be used later.

Step 2. Transverse ASE effect among different volume elements

First, we consider the ASE rate in volume element 1 that induced by the ASE emitted from volume element 2 (see Fig. 3 ). O and E’ are two arbitrary points in volume elements 1 and 2. E is another point that satisfies the condition of OE = OE’. Now in order to simplify the derivation and calculation, we make another assumption: although we have considered the population densities ni(y)(i=1,2,3) as y dependent, in the calculation of transverse ASE effect, this transverse population variation is neglected. In fact, for a well designed DPAA, the transverse population variation should also be limited to a relatively low value, which will benefit the uniformity of laser intensity in the cross section as well as the heat management. Under this assumption, the influence of ASE on O that emitted from E’ is equivalent to that emitted from E. Furthermore, the influence of ASE on O that emitted from the whole volume element 2 (A’D’) is equivalent to that emitted from lines AB and CD. It should be noticed that the points A and D have already located out of the range of volume element 1.

 

Fig. 3 The influence of ASE that emitted from volume element 2 on volume element 1. Each volume element has dimensions of Δx×Δy×L. The distance between volume elements 1 and 2 is h. The lengths of lines meet the conditions of OE = OE’, OA = OA’, OD = OD’, OB = OC = h, AD = L’.

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It is seen that for an arbitrary point O in volume element 1, we can find a range of lines in this element itself (AB + CD = L’-2h), whose ASE affect on O is equivalent to that induced by the whole volume element 2. We also noticed that as the position of O changes along volume element 1, the length of AD (L’) changes and BC (2h) keeps constant. When O locates at the end, L’ reaches its maximal value of Lmax'=(L2+h2)1/2+h; and when O locates in the middle, L’ reaches its minimal value of Lmin'=2[(L/2)2+h2]1/2. For these two extreme values of L’, we can obtain the range of the ASE rate

ΓASE21min(y)<ΓASE21(y)<ΓASE21max(y),
ΓASE21min(y)=ΓASE11(y,Lmin')ΓASE11(y,2h),
ΓASE21max(y)=ΓASE11(y,Lmax')ΓASE11(y,2h).

The subscript 21 means that the ASE rate in volume element 1 is induced by volume 2. And the total ASE rate in volume element 1 is ΓASE11(y)+ΓASE21(y) (parameter L in ΓASE11(y,L) and subscripts max, min are neglected).

Now we can calculate the total ASE rate in a volume element inside the volumetric alkali gain medium (see Fig. 4 ). For an arbitrary volume element (p,q), each element will give contribution to its ASE rate, and the total ASE rate in (p,q) is

ΓASE(p,q)(y)=m=1Mn=1NΓASE(m,n)(p,q)(y),
where ΓASE(m,n)(p,q) is the ASE rate in (p,q) that induced by (m,n), the range of which can be calculated by Eq. (12)-(14). From the geometric point of view, when (p,q) locates at the corner (a in Fig. 4), ΓASE(p,q)(y) reaches its maximal value, and when (p,q) locates at the center (b in Fig. 4), ΓASE(p,q)(y) reaches its minimal value. So if we calculate ΓASE(m,n)(p,q) by Eq. (14) and assume (p,q) at the corner, we can obtain the maximal value of the total ASE in a volume element; if we calculate ΓASE(m,n)(p,q) by Eq. (13) and assume (p,q) at the center, we obtain its minimal value. The range of ASE rate is described as

 

Fig. 4 Schematic diagram of transverse ASE effect among different volume element. The alkali gain medium is divided into M segments along x-axis and N segments along y-axis. The coordinate value (p,q) represents a volume element that locates at line p and column q. Volume element a locates at the corner with position of (1,1) and element b locates in the center with position of [(N + 1)/2, (M + 1)/2]. d(1,1)(p,q) represents the distance between elements (1,1) and (p.q) et al..

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ΓASEmin(y)<ΓASE(y)<ΓASEmax(y),
ΓASEmin(y)=m=1Mn=1NΓASE(m,n)[(N+1)/2,(M+1)/2](y),ΓASE(m,n)[(N+1)/2,(M+1)/2](y)=ΓASE(m,n)[(N+1)/2,(M+1)/2](y,Lmin')ΓASE(m,n)[(N+1)/2,(M+1)/2](y,2d(m,n)[(N+1)/2,(M+1)/2]),
ΓASEmax(y)=m=1Mn=1NΓASE(m,n)(1,1)(y),ΓASE(m,n)(1,1)(y)=ΓASE(m,n)(1,1)(y,Lmax')ΓASE(m,n)(1,1)(y,2d(m,n)(1,1)).

3. Numerical approaches

In this section, we first describe the numerical approach for an individual volume element (in longitudinal dimension) and then introduce the numerical approach that connects different volume elements in this symmetrically double-side pumped configuration (in transverse dimension).

3.1 Numerical approach in longitudinal dimension

For we only consider the case of cw operation, all the derivatives in Eqs. (1)-(3) are set zero. By Eqs. (2) and (4) we can obtain the relation between n2 and n3 (parameter y is neglected here)

Iseed{exp[Δn21σ21L]1}hν21Lγ32[n32n2exp(ΔEkT)]+ΓASE(Δn21)+n2(A21+Q21)=0,

By use of searching algorithm, for a fixed value of n3, we can obtain n2 and n1 in terms of n3, which are denoted as n2(n3) and n1(n3). Take n1(n3) and n2(n3) into Eq. (3), and still use the searching algorithm, we can solve n3, and then obtain the population distribution ni(y)(i=1,2,3).

When the population densities are obtained, we can calculate the amplified laser power and other pump power inverted channels by

Plaser(y)=Pseed(y)×{exp[Δn21(y)σ21L]1},
Pfluorescence(y)=Vl[n2(y)A21E21+n3(y)A31E31],
Pquenching(y)=Vl[n2(y)Q21E21+n3(y)Q31E31],
Pheat(y)=Vlγ32[n3(y)2n2(y)exp(ΔEkT)],
PASE(y)=VlE21ΓASE(y).
where Plaser(y) is the output amplified laser power, Pfluorescence(y), Pquenching(y),Pheat(y) and PASE(y) are fluorescence, quenching, waste heat and ASE powers in a volume element respectively.

3.2 Numerical approach in transverse dimension

In transverse dimension, we have developed an iterative algorithm, which is described below:

  • (a) First, we calculate the transverse population distribution for the single-side pumped configuration, that is, with no consideration of Pp(y,λ). The propagation equation of Pp+(y,λ) is given by
    Pp+(y+Δy,λ)=Pp+(y,λ)exp[Δn13(y)σ13(λ)Δy],

    Take the already known Pp+(0,λ) together with numerical approach 3.1 and Eq. (25), we can solve an initial transverse population distribution ni(0)(y)(y[0,W],i=1,2,3).

  • (b) For symmetrically double-side pumped configuration, the population densities in steady state should also be symmetrically distributed. Here, the symmetrically distributed population density is assumed to be
    ni(0)*(y)={ni(0)(y)y[0,W/2]ni(0)(Wy)y[W/2,W](i=1,2,3),
  • (c) Let the pump light Pp+(y,λ) pass the gain medium through the population distribution ni(0)*(y) by Eq. (25), we can obtain the unabsorbed pump power Pp+(0)(W,λ) at the other side of the gain medium.
  • (d) In steady state, the unabsorbed pump power for both forward and backward propagating pump lights should be equal, that is Pp+(W,λ)=Pp(0,λ). Here we assume the amplifier to be in steady state, and the total pump power at one side should be
    Pptot(1)(0,λ)=Pp+(0,λ)+Pp(0)(0,λ)=Pp+(0,λ)+Pp+(0)(W,λ)

    Now the laser can be seen as single-side pumped with Pptot(1)(0,λ) as a new pump light. As similar as in step (a), we can use approach 3.1 to calculate a new population distribution ni(1)(y)(y[0,W],i=1,2,3). In the calculation, the propagation equation for Pp+(0,λ) is Eq. (25), and for Pp(0)(0,λ) is

    Pp(y+Δy,λ)=Pp(y,λ)exp[Δn13(y)σ13(λ)Δy].

  • (e) By step (b), we can obtain a symmetrically distributed population ni(1)*(y). Compare ni(1)*(y) with ni(0)*(y), if ni(1)*(y)=ni(0)*(y)(y[0,W],i=1,2,3), then ni(1)*(y) is the final solution, and other laser information has been obtained in the calculation process. If ni(1)*(y)ni(0)*(y)(y[0,W],i=1,2,3), then substitute ni(0)*(y) by ni(1)*(y), and repeat steps (c)-(e) to continue the iterative process for a final solution.

4. Simulation results and discussion

In this section, we have simulated the influence of some important factors, and the results could give us a further comprehension of the characteristics of DPAAs.

4.1 Influence of the temperature

The operation temperature decides the number density of the alkali atoms, which will dramatically affect the DPAA’s characteristics. In the calculation, the parameters are chosen as follows: the dimensions of the alkali gain medium are set as L×W×H=20cm×5cm×5cm. The buffer gases include 400torr methane and 1120torr helium (measured at 20C), which result in an atomic absorption linewidth (FWHM) of 0.09nm at a typical temperature of 120C. The pump intensity is set as a moderate value of Ip=5kW/cm2 with linewidth (FWHM) of 0.2nm, which could be realized by volume Bragg gratings (VBGs). The line shapes of the atomic absorption and pump light are assumed to be in Lorentzian and Gaussian profiles with overlapped center wavelengths. The seed laser intensity is set as a relatively weak value of Is=100W/cm2.

The simulation results are shown in Fig. 5 . We can see that for a DPAA, an optimal operation temperature exists for a maximal amplification factor [Fig. 5(a)]. As the temperature increases, the alkali atom concentration increases which enhances the pump absorption fraction, but the laser extraction efficiency ηoptabs decreases [Fig. 5(b)]. For the absorbed pump power, it has five main inverted channels: laser, fluorescence, ASE, heat and non-radiative transition loss (quenching). From Fig. 5(c), we can see that the fluorescence and ASE efficiency (the maximal value calculated here) will increase as temperature increases, which induce the decrease of the laser extraction efficiency. The heat efficiency is always below 1.8%, which is in correspondence with the Rb quantum defect (1.9%).

 

Fig. 5 Temperature influence on characteristics of a DPAA. In (a), the amplification factor is defined as G(dB)=10log10(Plaser/Pseed). In (b), ηoptopt=(PlaserPseed)/Ppump is the laser extraction efficiency relative to total pump power (denoted as ‘opt-opt’ in the figure), ηabsorb is the pump power absorption efficiency, ηoptabs=(PlaserPseed)/(Ppumpηabsorb) is the laser extraction efficiency relative to absorbed pump power. (c) shows other inverted channels of the absorbed pump power, which are calculated by Eqs. (21)-(24).

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4.2 Influence of seed laser and pump intensities

As a three-level laser system, the DPAA needs to be pumped at relatively high intensities, usually in a range of 1~10kW/cm2. Figure 6 shows the influence of pump intensity at different seed laser intensities. For the temperature characteristic of the DPAA, the simulation results are given at temperatures which are optimized for maximal laser extraction efficiencies (ηoptopt). Other parameters are the same as in 4.1. We notice that as the intensity changes, the total seed or pump powers will change correspondingly, and we only care about the efficiencies rather than the power values. It is seen that for a constant seed laser intensity, as the pump intensity increases, both the amplification factor and the laser extraction efficiency increase [Fig. 6(a) and (b)]. And for a higher pump intensity, a higher optimal temperature is needed because more alkali concentration is required for sufficient pump power absorption [Fig. 6(c)]. A comparison shows that when the seed laser is weak, the amplification factor is high but the laser extraction efficiency is low, that is, a large fraction of pump power is wasted. As a contrast, when the seed laser is strong, the amplification factor is relatively low but the laser extraction efficiency dramatically increases, and becomes more sensitive to the change of pump intensity.

 

Fig. 6 Intensity influence on characteristics of a DPAA. The simulation results are given at optimal temperatures for maximal laser extraction efficiencies (ηoptopt) under different seed laser and pump intensities.

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To get a further understanding of the intensity influence, we also calculated the pump absorption efficiency and some main pump inverted channels (fluorescence and ASE) in Fig. 7 . We can see that, when the seed laser is weak, the pump absorption fraction is low [Fig. 7(a)]. This is because a low seed laser intensity is not sufficient to pull down the population from 2P1/2 to 2S1/2 energy levels through stimulated emission process. Thus the recycling of an alkali atom (2S1/22P3/22P1/22S1/2) is bottlenecked in the stimulated emission process, which will in turn affect the pump power absorption. As the same with solid or fiber laser amplifiers, when the seed laser is weak, the ASE effect becomes strong [Fig. 7(b)]. For Is=1W/cm2, the ASE efficiency reaches 80% at Ip=10kW/cm2, while for Is=1000W/cm2, the ASE efficiency is always kept below 2%. This indicates that in the case of saturated amplification, the ASE can be well suppressed and not become a limitation in power scaling of a DPAA. We also notice that the ASE efficiency increases as the pump intensity increases. Although a higher pump intensity will induce a stronger ASE effect, it can suppress the fluorescence efficiency dramatically [Fig. 7(c)]. For the case of saturated amplification, the degree of fluorescence suppression by a high pump intensity is stronger than the lightly increased ASE effect. In addition, a high pump intensity will enhance the pump absorption, so we should focus the diode pump light into high intensity for a high efficient DPAA.

 

Fig. 7 Intensity influence on pump power absorption, ASE and fluorescence efficiencies of a DPAA at optimal temperature.

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We also studied the range of ASE efficiency that calculated by Eq. (16)-(18) at different seed laser intensities. The results show that when the ASE is well suppressed, the range is also small. For example, the ASE range is about 18% for Is=1W/cm2 and only 0.7% for Is=1000W/cm2. Because in optimal design, the ASE should be suppressed to a relatively low value, so the range estimation of the ASE could be rather accurate. For simplification, all the ASE efficiencies are showed as the maximal values in this paper.

4.3 Influence of the gain medium’s dimensions

The width influence was shown in Fig. (8) . The pump intensity is set as Ip=5kW/cm2, the seed laser intensity Is=100W/cm2, and other parameters the same. The results show that as the width increases, both the amplification factor and the laser extraction efficiency decreases [Fig. 8(a) and (b)]. The main reason is the obvious increase of ASE, while the efficiencies of other pump inverted channels nearly keep constant [Fig. 8(c)]. The optimal temperature experiences a decrease as the width increases, because lower alkali atom concentration is required when the pump absorption distance becomes longer. In real design, when the ASE effect can be strongly suppressed with saturated amplification, the width could be relatively longer with lower optimal temperature, which will benefit the chemical stability and lifetime for the laser systems.

 

Fig. 8 Width influence on characteristics of a DPAA at optimal temperature.

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The length influence is shown in Fig. (9) . The width is set as 5cm with other parameters the same. It should be noticed that for a constant pump intensity, the total pump power increases as length increases. The results show that a longer length can effectively enhance the pump absorption [Fig. 9(b)] and suppress the ASE effect [Fig. 9(c)], thus results in a higher laser extraction efficiency. The reason is that, as compared with a short gain medium, the amplified seed laser will be much stronger in the longer part, which will enhance the pump absorption [Fig. 7(a)] and ASE suppression [Fig. 7(b)] in this longer part as well as for the whole amplifier. Other pump inverted channels (fluorescence, heat and quenching) and the optimal temperature are not sensitive to the change of the length. From these results, we can come to a conclusion that a longer gain medium will benefit both the amplification and laser extraction efficiency with enhanced ability to suppress the ASE effect.

 

Fig. 9 Length influence on characteristics of a DPAA at optimal temperature.

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The height of the gain medium is not specially discussed here. Because we assume the pump and laser intensity uniform along the height dimension (x-axis), and it only affects the calculation of the ASE effect here. In real design of a DPAA, the height adjustment is equivalent with the adjustment of the pump intensity when the pump power is fixed, except for a different transverse ASE effect. And another design consideration of the height is to adapt to the beam shape of the seed laser.

5. Conclusion

In this article, a model is set up for a DPAA in symmetrically double-side pumped configuration. For the three-dimensional volumetric alkali medium with high gain, the ASE may become a key issue in power scaling. And we have developed a new method to calculate the range of ASE efficiency, which has considered both the longitudinal and transverse ASE effects. To solve the model, an iterative numerical approach is proposed. To study the characteristics of the DPAA, some important influencing factors are simulated and discussed, including the operation temperature, pump and seed laser intensities and the gain medium’s dimensions. From the simulation results, we have obtained some useful conclusions: as the same with DPALs, an optimal temperature exists for DPAAs for maximal laser extraction efficiency; at constant pump and seed laser intensities, the shape of a narrower but longer gain medium will benefit the suppression of ASE; a high pump intensity is required to effectively suppress the fluorescence; when the seed laser is weak, ASE will dominate the stored pump power, and a strong seed intensity is needed to effectively suppress the ASE; in power scaling of DPAAs, the ASE effect will not become a limitation but can be effectively suppressed by use of the saturated amplification scheme. Till now, no experiment of a side-pumped DPAA has been reported, and further experimental studies are necessary to verify the validity of our model.

References and links

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2. C. V. Sulham, G. P. Perram, M. P. Wilkinson, and D. A. Hostutler, “A pulsed, optically-pumped rubidium laser at high pump intensity,” Opt. Commun. 283(21), 4328–4332 (2010). [CrossRef]  

3. W. S. Miller, C. V. Sulham, J. C. Holtgrave, and G. P. Perram, “Limitations of an optically pumped rubidium laser imposed by atom recycle rate,” Appl. Phys. B 103(4), 819–824 (2011). [CrossRef]  

4. B. Zhdanov and R. J. Knize, “Diode-pumped 10 W continuous wave cesium laser,” Opt. Lett. 32(15), 2167–2169 (2007). [CrossRef]   [PubMed]  

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, J. Sell, and R. J. Knize, “Multiple laser diode array pumped Cs laser with 48W output power,” Electron. Lett. 44(9), 582–583 (2008). [CrossRef]  

7. B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Cs laser with unstable cavity transversely pumped by multiple diode lasers,” Opt. Express 17(17), 14767–14770 (2009). [CrossRef]   [PubMed]  

8. J. Zweiback, G. Hager, and W. F. Krupke, “High efficiency hydrocarbon-free resonance transition potassium laser,” Opt. Commun. 282(9), 1871–1873 (2009). [CrossRef]  

9. J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G, 75810G-5 (2010). [CrossRef]  

10. J. Zweiback and A. Komashko, “High-energy transversely pumped alkali vapor lasers,” Proc. SPIE 7915, 791509, 791509-7 (2011). [CrossRef]  

11. Y. Zheng, M. Niigaki, H. Miyajima, T. Hiruma, and H. Kan, “High-efficiency 894-nm laser emission of laser-diode-bar-pumped cesium-vapor laser,” Appl. Phys. Express 2, 032501 (2009). [CrossRef]  

12. D. A. Hostutler and W. L. Klennert, “Power enhancement of a Rubidium vapor laser with a master oscillator power amplifier,” Opt. Express 16(11), 8050–8053 (2008). [CrossRef]   [PubMed]  

13. B. V. Zhdanov and R. J. Knize, “Efficienct diode pumped cesium vapor amplifier,” Opt. Commun. 281(15-16), 4068–4070 (2008). [CrossRef]  

14. B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Scaling of diode pumped Cs laser: transverse pump, unstable cavity, MOPA,” Proc. SPIE 7581, 75810F, 75810F-6 (2010). [CrossRef]  

15. B. Pan, Y. Wang, Q. Zhu, and J. Yang, “Modeling of an alkali vapor laser MOPA system,” Opt. Commun. 284(7), 1963–1966 (2011). [CrossRef]  

16. L. Allen and G. I. Peters, “Amplified spontaneous emission and external signal amplification in an inverted medium,” Phys. Rev. A 8(4), 2031–2047 (1973). [CrossRef]  

17. P. A. Schulz, K. F. Wall, and R. L. Aggarwal, “Simple model for amplified spontaneous emission in a Ti:A12O3 amplifier,” Opt. Lett. 13(12), 1081–1083 (1988). [CrossRef]   [PubMed]  

18. C. R. Giles and E. Desurvire, “Modeling Erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991). [CrossRef]  

19. D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008). [CrossRef]  

20. C. Goren, Y. Tzuk, G. Marcus, and S. Pearl, “Amplified spontaneous emission in slab amplifiers,” IEEE J. Quantum Electron. 42(12), 1239–1247 (2006). [CrossRef]  

21. 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]  

References

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  1. R. H. Page, R. J. Beach, V. K. Kanz, and W. F. Krupke, “Multimode-diode-pumped gas (alkali-vapor) laser,” Opt. Lett. 31(3), 353–355 (2006).
    [Crossref] [PubMed]
  2. C. V. Sulham, G. P. Perram, M. P. Wilkinson, and D. A. Hostutler, “A pulsed, optically-pumped rubidium laser at high pump intensity,” Opt. Commun. 283(21), 4328–4332 (2010).
    [Crossref]
  3. W. S. Miller, C. V. Sulham, J. C. Holtgrave, and G. P. Perram, “Limitations of an optically pumped rubidium laser imposed by atom recycle rate,” Appl. Phys. B 103(4), 819–824 (2011).
    [Crossref]
  4. B. Zhdanov and R. J. Knize, “Diode-pumped 10 W continuous wave cesium laser,” Opt. Lett. 32(15), 2167–2169 (2007).
    [Crossref] [PubMed]
  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, J. Sell, and R. J. Knize, “Multiple laser diode array pumped Cs laser with 48W output power,” Electron. Lett. 44(9), 582–583 (2008).
    [Crossref]
  7. B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Cs laser with unstable cavity transversely pumped by multiple diode lasers,” Opt. Express 17(17), 14767–14770 (2009).
    [Crossref] [PubMed]
  8. J. Zweiback, G. Hager, and W. F. Krupke, “High efficiency hydrocarbon-free resonance transition potassium laser,” Opt. Commun. 282(9), 1871–1873 (2009).
    [Crossref]
  9. J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G, 75810G-5 (2010).
    [Crossref]
  10. J. Zweiback and A. Komashko, “High-energy transversely pumped alkali vapor lasers,” Proc. SPIE 7915, 791509, 791509-7 (2011).
    [Crossref]
  11. Y. Zheng, M. Niigaki, H. Miyajima, T. Hiruma, and H. Kan, “High-efficiency 894-nm laser emission of laser-diode-bar-pumped cesium-vapor laser,” Appl. Phys. Express 2, 032501 (2009).
    [Crossref]
  12. D. A. Hostutler and W. L. Klennert, “Power enhancement of a Rubidium vapor laser with a master oscillator power amplifier,” Opt. Express 16(11), 8050–8053 (2008).
    [Crossref] [PubMed]
  13. B. V. Zhdanov and R. J. Knize, “Efficienct diode pumped cesium vapor amplifier,” Opt. Commun. 281(15-16), 4068–4070 (2008).
    [Crossref]
  14. B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Scaling of diode pumped Cs laser: transverse pump, unstable cavity, MOPA,” Proc. SPIE 7581, 75810F, 75810F-6 (2010).
    [Crossref]
  15. B. Pan, Y. Wang, Q. Zhu, and J. Yang, “Modeling of an alkali vapor laser MOPA system,” Opt. Commun. 284(7), 1963–1966 (2011).
    [Crossref]
  16. L. Allen and G. I. Peters, “Amplified spontaneous emission and external signal amplification in an inverted medium,” Phys. Rev. A 8(4), 2031–2047 (1973).
    [Crossref]
  17. P. A. Schulz, K. F. Wall, and R. L. Aggarwal, “Simple model for amplified spontaneous emission in a Ti:A12O3 amplifier,” Opt. Lett. 13(12), 1081–1083 (1988).
    [Crossref] [PubMed]
  18. C. R. Giles and E. Desurvire, “Modeling Erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
    [Crossref]
  19. D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
    [Crossref]
  20. C. Goren, Y. Tzuk, G. Marcus, and S. Pearl, “Amplified spontaneous emission in slab amplifiers,” IEEE J. Quantum Electron. 42(12), 1239–1247 (2006).
    [Crossref]
  21. 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]

2011 (4)

W. S. Miller, C. V. Sulham, J. C. Holtgrave, and G. P. Perram, “Limitations of an optically pumped rubidium laser imposed by atom recycle rate,” Appl. Phys. B 103(4), 819–824 (2011).
[Crossref]

J. Zweiback and A. Komashko, “High-energy transversely pumped alkali vapor lasers,” Proc. SPIE 7915, 791509, 791509-7 (2011).
[Crossref]

B. Pan, Y. Wang, Q. Zhu, and J. Yang, “Modeling of an alkali vapor laser MOPA system,” Opt. Commun. 284(7), 1963–1966 (2011).
[Crossref]

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]

2010 (3)

J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G, 75810G-5 (2010).
[Crossref]

B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Scaling of diode pumped Cs laser: transverse pump, unstable cavity, MOPA,” Proc. SPIE 7581, 75810F, 75810F-6 (2010).
[Crossref]

C. V. Sulham, G. P. Perram, M. P. Wilkinson, and D. A. Hostutler, “A pulsed, optically-pumped rubidium laser at high pump intensity,” Opt. Commun. 283(21), 4328–4332 (2010).
[Crossref]

2009 (3)

B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Cs laser with unstable cavity transversely pumped by multiple diode lasers,” Opt. Express 17(17), 14767–14770 (2009).
[Crossref] [PubMed]

J. Zweiback, G. Hager, and W. F. Krupke, “High efficiency hydrocarbon-free resonance transition potassium laser,” Opt. Commun. 282(9), 1871–1873 (2009).
[Crossref]

Y. Zheng, M. Niigaki, H. Miyajima, T. Hiruma, and H. Kan, “High-efficiency 894-nm laser emission of laser-diode-bar-pumped cesium-vapor laser,” Appl. Phys. Express 2, 032501 (2009).
[Crossref]

2008 (5)

D. A. Hostutler and W. L. Klennert, “Power enhancement of a Rubidium vapor laser with a master oscillator power amplifier,” Opt. Express 16(11), 8050–8053 (2008).
[Crossref] [PubMed]

B. V. Zhdanov and R. J. Knize, “Efficienct diode pumped cesium vapor amplifier,” Opt. Commun. 281(15-16), 4068–4070 (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, J. Sell, and R. J. Knize, “Multiple laser diode array pumped Cs laser with 48W output power,” Electron. Lett. 44(9), 582–583 (2008).
[Crossref]

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

2007 (1)

2006 (2)

R. H. Page, R. J. Beach, V. K. Kanz, and W. F. Krupke, “Multimode-diode-pumped gas (alkali-vapor) laser,” Opt. Lett. 31(3), 353–355 (2006).
[Crossref] [PubMed]

C. Goren, Y. Tzuk, G. Marcus, and S. Pearl, “Amplified spontaneous emission in slab amplifiers,” IEEE J. Quantum Electron. 42(12), 1239–1247 (2006).
[Crossref]

1991 (1)

C. R. Giles and E. Desurvire, “Modeling Erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

1988 (1)

1973 (1)

L. Allen and G. I. Peters, “Amplified spontaneous emission and external signal amplification in an inverted medium,” Phys. Rev. A 8(4), 2031–2047 (1973).
[Crossref]

Aggarwal, R. L.

Albach, D.

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

Allen, L.

L. Allen and G. I. Peters, “Amplified spontaneous emission and external signal amplification in an inverted medium,” Phys. Rev. A 8(4), 2031–2047 (1973).
[Crossref]

Assémat, F.

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

Bahbah, S.

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

Beach, R. J.

Bourdet, G.

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

Boyadjian, G.

Chanteloup, J.-C.

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

Chen, J.

Desurvire, E.

C. R. Giles and E. Desurvire, “Modeling Erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

Giles, C. R.

C. R. Giles and E. Desurvire, “Modeling Erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

Goren, C.

C. Goren, Y. Tzuk, G. Marcus, and S. Pearl, “Amplified spontaneous emission in slab amplifiers,” IEEE J. Quantum Electron. 42(12), 1239–1247 (2006).
[Crossref]

Hager, G.

J. Zweiback, G. Hager, and W. F. Krupke, “High efficiency hydrocarbon-free resonance transition potassium laser,” Opt. Commun. 282(9), 1871–1873 (2009).
[Crossref]

Hiruma, T.

Y. Zheng, M. Niigaki, H. Miyajima, T. Hiruma, and H. Kan, “High-efficiency 894-nm laser emission of laser-diode-bar-pumped cesium-vapor laser,” Appl. Phys. Express 2, 032501 (2009).
[Crossref]

Holtgrave, J. C.

W. S. Miller, C. V. Sulham, J. C. Holtgrave, and G. P. Perram, “Limitations of an optically pumped rubidium laser imposed by atom recycle rate,” Appl. Phys. B 103(4), 819–824 (2011).
[Crossref]

Hostutler, D. A.

C. V. Sulham, G. P. Perram, M. P. Wilkinson, and D. A. Hostutler, “A pulsed, optically-pumped rubidium laser at high pump intensity,” Opt. Commun. 283(21), 4328–4332 (2010).
[Crossref]

D. A. Hostutler and W. L. Klennert, “Power enhancement of a Rubidium vapor laser with a master oscillator power amplifier,” Opt. Express 16(11), 8050–8053 (2008).
[Crossref] [PubMed]

Hua, W.

Kan, H.

Y. Zheng, M. Niigaki, H. Miyajima, T. Hiruma, and H. Kan, “High-efficiency 894-nm laser emission of laser-diode-bar-pumped cesium-vapor laser,” Appl. Phys. Express 2, 032501 (2009).
[Crossref]

Kanz, V. K.

Klennert, W. L.

Knize, R. J.

B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Scaling of diode pumped Cs laser: transverse pump, unstable cavity, MOPA,” Proc. SPIE 7581, 75810F, 75810F-6 (2010).
[Crossref]

B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Cs laser with unstable cavity transversely pumped by multiple diode lasers,” Opt. Express 17(17), 14767–14770 (2009).
[Crossref] [PubMed]

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, J. Sell, and R. J. Knize, “Multiple laser diode array pumped Cs laser with 48W output power,” Electron. Lett. 44(9), 582–583 (2008).
[Crossref]

B. V. Zhdanov and R. J. Knize, “Efficienct diode pumped cesium vapor amplifier,” Opt. Commun. 281(15-16), 4068–4070 (2008).
[Crossref]

B. Zhdanov and R. J. Knize, “Diode-pumped 10 W continuous wave cesium laser,” Opt. Lett. 32(15), 2167–2169 (2007).
[Crossref] [PubMed]

Komashko, A.

J. Zweiback and A. Komashko, “High-energy transversely pumped alkali vapor lasers,” Proc. SPIE 7915, 791509, 791509-7 (2011).
[Crossref]

J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G, 75810G-5 (2010).
[Crossref]

Krupke, W. F.

J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G, 75810G-5 (2010).
[Crossref]

J. Zweiback, G. Hager, and W. F. Krupke, “High efficiency hydrocarbon-free resonance transition potassium laser,” Opt. Commun. 282(9), 1871–1873 (2009).
[Crossref]

R. H. Page, R. J. Beach, V. K. Kanz, and W. F. Krupke, “Multimode-diode-pumped gas (alkali-vapor) laser,” Opt. Lett. 31(3), 353–355 (2006).
[Crossref] [PubMed]

Le Touzé, G.

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

Li, Y.

Lu, Q.

Marcus, G.

C. Goren, Y. Tzuk, G. Marcus, and S. Pearl, “Amplified spontaneous emission in slab amplifiers,” IEEE J. Quantum Electron. 42(12), 1239–1247 (2006).
[Crossref]

Miller, W. S.

W. S. Miller, C. V. Sulham, J. C. Holtgrave, and G. P. Perram, “Limitations of an optically pumped rubidium laser imposed by atom recycle rate,” Appl. Phys. B 103(4), 819–824 (2011).
[Crossref]

Miyajima, H.

Y. Zheng, M. Niigaki, H. Miyajima, T. Hiruma, and H. Kan, “High-efficiency 894-nm laser emission of laser-diode-bar-pumped cesium-vapor laser,” Appl. Phys. Express 2, 032501 (2009).
[Crossref]

Niigaki, M.

Y. Zheng, M. Niigaki, H. Miyajima, T. Hiruma, and H. Kan, “High-efficiency 894-nm laser emission of laser-diode-bar-pumped cesium-vapor laser,” Appl. Phys. Express 2, 032501 (2009).
[Crossref]

Page, R. H.

Pan, B.

B. Pan, Y. Wang, Q. Zhu, and J. Yang, “Modeling of an alkali vapor laser MOPA system,” Opt. Commun. 284(7), 1963–1966 (2011).
[Crossref]

Pearl, S.

C. Goren, Y. Tzuk, G. Marcus, and S. Pearl, “Amplified spontaneous emission in slab amplifiers,” IEEE J. Quantum Electron. 42(12), 1239–1247 (2006).
[Crossref]

Perram, G. P.

W. S. Miller, C. V. Sulham, J. C. Holtgrave, and G. P. Perram, “Limitations of an optically pumped rubidium laser imposed by atom recycle rate,” Appl. Phys. B 103(4), 819–824 (2011).
[Crossref]

C. V. Sulham, G. P. Perram, M. P. Wilkinson, and D. A. Hostutler, “A pulsed, optically-pumped rubidium laser at high pump intensity,” Opt. Commun. 283(21), 4328–4332 (2010).
[Crossref]

Peters, G. I.

L. Allen and G. I. Peters, “Amplified spontaneous emission and external signal amplification in an inverted medium,” Phys. Rev. A 8(4), 2031–2047 (1973).
[Crossref]

Piatti, P.

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

Pluvinage, M.

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

Schulz, P. A.

Sell, J.

B. V. Zhdanov, J. Sell, and R. J. Knize, “Multiple laser diode array pumped Cs laser with 48W output power,” Electron. Lett. 44(9), 582–583 (2008).
[Crossref]

Shaffer, M. K.

B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Scaling of diode pumped Cs laser: transverse pump, unstable cavity, MOPA,” Proc. SPIE 7581, 75810F, 75810F-6 (2010).
[Crossref]

B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Cs laser with unstable cavity transversely pumped by multiple diode lasers,” Opt. Express 17(17), 14767–14770 (2009).
[Crossref] [PubMed]

Stooke, A.

Sulham, C. V.

W. S. Miller, C. V. Sulham, J. C. Holtgrave, and G. P. Perram, “Limitations of an optically pumped rubidium laser imposed by atom recycle rate,” Appl. Phys. B 103(4), 819–824 (2011).
[Crossref]

C. V. Sulham, G. P. Perram, M. P. Wilkinson, and D. A. Hostutler, “A pulsed, optically-pumped rubidium laser at high pump intensity,” Opt. Commun. 283(21), 4328–4332 (2010).
[Crossref]

Tzuk, Y.

C. Goren, Y. Tzuk, G. Marcus, and S. Pearl, “Amplified spontaneous emission in slab amplifiers,” IEEE J. Quantum Electron. 42(12), 1239–1247 (2006).
[Crossref]

Vincent, B.

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

Voci, A.

Wall, K. F.

Wang, H.

Wang, Y.

B. Pan, Y. Wang, Q. Zhu, and J. Yang, “Modeling of an alkali vapor laser MOPA system,” Opt. Commun. 284(7), 1963–1966 (2011).
[Crossref]

Wilkinson, M. P.

C. V. Sulham, G. P. Perram, M. P. Wilkinson, and D. A. Hostutler, “A pulsed, optically-pumped rubidium laser at high pump intensity,” Opt. Commun. 283(21), 4328–4332 (2010).
[Crossref]

Xu, X.

Yang, J.

B. Pan, Y. Wang, Q. Zhu, and J. Yang, “Modeling of an alkali vapor laser MOPA system,” Opt. Commun. 284(7), 1963–1966 (2011).
[Crossref]

Yang, Z.

Zhdanov, B.

Zhdanov, B. V.

B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Scaling of diode pumped Cs laser: transverse pump, unstable cavity, MOPA,” Proc. SPIE 7581, 75810F, 75810F-6 (2010).
[Crossref]

B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Cs laser with unstable cavity transversely pumped by multiple diode lasers,” Opt. Express 17(17), 14767–14770 (2009).
[Crossref] [PubMed]

B. V. Zhdanov, J. Sell, and R. J. Knize, “Multiple laser diode array pumped Cs laser with 48W output power,” Electron. Lett. 44(9), 582–583 (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 and R. J. Knize, “Efficienct diode pumped cesium vapor amplifier,” Opt. Commun. 281(15-16), 4068–4070 (2008).
[Crossref]

Zheng, Y.

Y. Zheng, M. Niigaki, H. Miyajima, T. Hiruma, and H. Kan, “High-efficiency 894-nm laser emission of laser-diode-bar-pumped cesium-vapor laser,” Appl. Phys. Express 2, 032501 (2009).
[Crossref]

Zhu, Q.

B. Pan, Y. Wang, Q. Zhu, and J. Yang, “Modeling of an alkali vapor laser MOPA system,” Opt. Commun. 284(7), 1963–1966 (2011).
[Crossref]

Zweiback, J.

J. Zweiback and A. Komashko, “High-energy transversely pumped alkali vapor lasers,” Proc. SPIE 7915, 791509, 791509-7 (2011).
[Crossref]

J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G, 75810G-5 (2010).
[Crossref]

J. Zweiback, G. Hager, and W. F. Krupke, “High efficiency hydrocarbon-free resonance transition potassium laser,” Opt. Commun. 282(9), 1871–1873 (2009).
[Crossref]

Appl. Phys. B (1)

W. S. Miller, C. V. Sulham, J. C. Holtgrave, and G. P. Perram, “Limitations of an optically pumped rubidium laser imposed by atom recycle rate,” Appl. Phys. B 103(4), 819–824 (2011).
[Crossref]

Appl. Phys. Express (1)

Y. Zheng, M. Niigaki, H. Miyajima, T. Hiruma, and H. Kan, “High-efficiency 894-nm laser emission of laser-diode-bar-pumped cesium-vapor laser,” Appl. Phys. Express 2, 032501 (2009).
[Crossref]

Electron. Lett. (1)

B. V. Zhdanov, J. Sell, and R. J. Knize, “Multiple laser diode array pumped Cs laser with 48W output power,” Electron. Lett. 44(9), 582–583 (2008).
[Crossref]

IEEE J. Quantum Electron. (1)

C. Goren, Y. Tzuk, G. Marcus, and S. Pearl, “Amplified spontaneous emission in slab amplifiers,” IEEE J. Quantum Electron. 42(12), 1239–1247 (2006).
[Crossref]

J. Lightwave Technol. (1)

C. R. Giles and E. Desurvire, “Modeling Erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys.: Conf. Series (1)

D. Albach, F. Assémat, S. Bahbah, G. Bourdet, J.-C. Chanteloup, P. Piatti, M. Pluvinage, B. Vincent, and G. Le Touzé, “A key issue for next generation Diode Pumped Solid State Laser Drivers for IFE: Amplified Spontaneous Emission in large size, high gain Yb:YAG slabs,” J. Phys.: Conf. Series 112(3), 032057 (2008).
[Crossref]

Opt. Commun. (4)

B. Pan, Y. Wang, Q. Zhu, and J. Yang, “Modeling of an alkali vapor laser MOPA system,” Opt. Commun. 284(7), 1963–1966 (2011).
[Crossref]

B. V. Zhdanov and R. J. Knize, “Efficienct diode pumped cesium vapor amplifier,” Opt. Commun. 281(15-16), 4068–4070 (2008).
[Crossref]

J. Zweiback, G. Hager, and W. F. Krupke, “High efficiency hydrocarbon-free resonance transition potassium laser,” Opt. Commun. 282(9), 1871–1873 (2009).
[Crossref]

C. V. Sulham, G. P. Perram, M. P. Wilkinson, and D. A. Hostutler, “A pulsed, optically-pumped rubidium laser at high pump intensity,” Opt. Commun. 283(21), 4328–4332 (2010).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (1)

L. Allen and G. I. Peters, “Amplified spontaneous emission and external signal amplification in an inverted medium,” Phys. Rev. A 8(4), 2031–2047 (1973).
[Crossref]

Proc. SPIE (3)

B. V. Zhdanov, M. K. Shaffer, and R. J. Knize, “Scaling of diode pumped Cs laser: transverse pump, unstable cavity, MOPA,” Proc. SPIE 7581, 75810F, 75810F-6 (2010).
[Crossref]

J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G, 75810G-5 (2010).
[Crossref]

J. Zweiback and A. Komashko, “High-energy transversely pumped alkali vapor lasers,” Proc. SPIE 7915, 791509, 791509-7 (2011).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Schematic diagram of a DPAA in symmetrically double-side pumped configuration. The dashed line presents the division scheme of the gain medium.
Fig. 2
Fig. 2 Schematic diagram of longitudinal ASE effect in a volume element Δx×Δy×L .
Fig. 3
Fig. 3 The influence of ASE that emitted from volume element 2 on volume element 1. Each volume element has dimensions of Δx×Δy×L . The distance between volume elements 1 and 2 is h. The lengths of lines meet the conditions of OE = OE’, OA = OA’, OD = OD’, OB = OC = h, AD = L’.
Fig. 4
Fig. 4 Schematic diagram of transverse ASE effect among different volume element. The alkali gain medium is divided into M segments along x-axis and N segments along y-axis. The coordinate value (p,q) represents a volume element that locates at line p and column q. Volume element a locates at the corner with position of (1,1) and element b locates in the center with position of [(N + 1)/2, (M + 1)/2]. d (1,1)(p,q) represents the distance between elements (1,1) and (p.q) et al..
Fig. 5
Fig. 5 Temperature influence on characteristics of a DPAA. In (a), the amplification factor is defined as G(dB)=10 log 10 ( P laser / P seed ) . In (b), η optopt =( P laser P seed )/ P pump is the laser extraction efficiency relative to total pump power (denoted as ‘opt-opt’ in the figure), η absorb is the pump power absorption efficiency, η optabs =( P laser P seed )/( P pump η absorb ) is the laser extraction efficiency relative to absorbed pump power. (c) shows other inverted channels of the absorbed pump power, which are calculated by Eqs. (21)-(24).
Fig. 6
Fig. 6 Intensity influence on characteristics of a DPAA. The simulation results are given at optimal temperatures for maximal laser extraction efficiencies ( η optopt ) under different seed laser and pump intensities.
Fig. 7
Fig. 7 Intensity influence on pump power absorption, ASE and fluorescence efficiencies of a DPAA at optimal temperature.
Fig. 8
Fig. 8 Width influence on characteristics of a DPAA at optimal temperature.
Fig. 9
Fig. 9 Length influence on characteristics of a DPAA at optimal temperature.

Equations (28)

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d n 1 (y) dt = Γ p (y)+ Γ l (y)+ Γ ASE (y)+ n 2 (y)( A 21 + Q 21 )+ n 3 (y)( A 31 + Q 31 ),
d n 2 (y) dt = Γ l (y)+ γ 32 [ n 3 (y)2 n 2 (y)exp( ΔE kT )] Γ ASE (y) n 2 (y)( A 21 + Q 21 ),
d n 3 (y) dt = Γ p (y) γ 32 [ n 3 (y)2 n 2 (y)exp( ΔE kT )] n 3 (y)( A 31 + Q 31 ).
n 1 (y)+ n 2 (y)+ n 3 (y)= n tot ,
P p + (y=0,λ)= P p (y=W,λ)= P p 4ln2 π c Δ ν p λ 2 exp [ 4 ln2 c Δ ν p ( 1 λ 1 λ p )] 2 ,
Γ p (y) = 1 h ν p L 0 I p + (y,λ)×{ 1exp[Δ n 13 (y) σ 13 (λ)Δy] }dλ + 1 h ν p L 0 I p (y,λ)×{ exp[Δ n 13 (y) σ 13 (λ)Δy]1 }dλ,
Γ l (y)= I seed (y){exp[Δ n 21 (y) σ 21 L]1} h ν 21 L ,
Ω [(n1)Δz,nΔz] = ΔxΔy [L(n1)Δz] 2 .
P ASE [(n1)Δz,nΔz] (y)=h ν 21 A 21 n 2 (y)ΔxΔyΔz Ω [(n1)Δz,nΔz] 4π × l(λ) exp{ Δ n 21 (y) σ 21 (λ)[L(n1)Δz] }dλ,
P ASE (y)= lim Δz0 [ n=1 L/Δz P ASE[(n1)Δz,nΔz] (y) ] =h ν 21 A 21 n 2 (y) V l 2 π L 4 l(λ)× exp[Δ n 21 (y) σ 21 (λ)L]1 Δ n 21 (y) σ 21 (λ) dλ.
Γ ASE11 (y,L)= 2 P ASE (y) h ν 21 V l = 2 A 21 V l π L 4 n 2 (y) Δ n 21 (y) l(λ)× exp[Δ n 21 (y) σ 21 (λ)L]1 σ 21 (λ) dλ.
Γ ASE21min (y)< Γ ASE21 (y)< Γ ASE21max (y),
Γ ASE21min (y)= Γ ASE11 (y, L min ' ) Γ ASE11 (y,2h),
Γ ASE21max (y)= Γ ASE11 (y, L max ' ) Γ ASE11 (y,2h).
Γ ASE(p,q) (y)= m=1 M n=1 N Γ ASE(m,n)(p,q) (y) ,
Γ ASEmin (y)< Γ ASE (y)< Γ ASEmax (y),
Γ ASEmin (y)= m=1 M n=1 N Γ ASE(m,n)[(N+1)/2,(M+1)/2] (y) , Γ ASE(m,n)[(N+1)/2,(M+1)/2] (y)= Γ ASE(m,n)[(N+1)/2,(M+1)/2] (y, L min ' ) Γ ASE(m,n)[(N+1)/2,(M+1)/2] (y,2 d (m,n)[(N+1)/2,(M+1)/2] ),
Γ ASEmax (y)= m=1 M n=1 N Γ ASE(m,n)(1,1) (y) , Γ ASE(m,n)(1,1) (y)= Γ ASE(m,n)(1,1) (y, L max ' ) Γ ASE(m,n)(1,1) (y,2 d (m,n)(1,1) ).
I seed {exp[Δ n 21 σ 21 L]1} h ν 21 L γ 32 [ n 3 2 n 2 exp( ΔE kT )]+ Γ ASE (Δ n 21 )+ n 2 ( A 21 + Q 21 )=0,
P laser (y)= P seed (y)×{exp[Δ n 21 (y) σ 21 L]1},
P fluorescence (y)= V l [ n 2 (y) A 21 E 21 + n 3 (y) A 31 E 31 ],
P quenching (y)= V l [ n 2 (y) Q 21 E 21 + n 3 (y) Q 31 E 31 ],
P heat (y)= V l γ 32 [ n 3 (y)2 n 2 (y)exp( ΔE kT )],
P ASE (y)= V l E 21 Γ ASE (y).
P p + (y+Δy,λ)= P p + (y,λ)exp[Δ n 13 (y) σ 13 (λ)Δy],
n i (0) * (y)= { n i (0) (y) y[0,W/2] n i (0) (Wy) y[W/2,W] (i=1,2,3),
P p tot(1) (0,λ)= P p + (0,λ)+ P p (0) (0,λ)= P p + (0,λ)+ P p +(0) (W,λ)
P p (y+Δy,λ)= P p (y,λ)exp[Δ n 13 (y) σ 13 (λ)Δy].

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