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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 21 — Oct. 10, 2011
  • pp: 21060–21073
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Beam quality improvement by gain guiding effect in end-pumped Nd:YVO4 laser amplifiers

Zhen Xiang, Dan Wang, Sunqiang Pan, Yantao Dong, Zhigang Zhao, Tong Li, Jianhong Ge, Chong Liu, and Jun Chen  »View Author Affiliations


Optics Express, Vol. 19, Issue 21, pp. 21060-21073 (2011)
http://dx.doi.org/10.1364/OE.19.021060


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Abstract

In end-pumped Nd:YVO4 amplifiers, beam quality improvement is obtained both in theory and in experiments. A theoretical model of gain-guided laser amplifier is developed by comprehensively considering thermal effect, gain guiding and gain saturation effect. Several key parameters of the amplifier are discussed such as the input beam quality, the beam filling factor between input beam and pump beam, the ratio between input power and pump power, and the length of laser crystal. The theoretical results are confirmed by the experiments.

© 2011 OSA

1. Introduction

“Gain guiding” effect widely exists in all kinds of laser oscillators and amplifiers, such as diode-pumped solid state lasers (DPSSL) [1

1. F. Salin and J. Squier, “Gain guiding in solid-state lasers,” Opt. Lett. 17(19), 1352–1354 (1992). [CrossRef] [PubMed]

3

3. X. Yan, Q. Liu, D. Wang, and M. Gong, “Combined guiding effect in the end-pumped laser resonator,” Opt. Express 19(7), 6883–6902 (2011). [CrossRef] [PubMed]

] and amplifiers [4

4. P. R. Battle, J. G. Wessel, and J. L. Carlsten, “Excess noise in a focused-gain amplifier,” Phys. Rev. Lett. 70(11), 1607–1610 (1993). [CrossRef] [PubMed]

6

6. I. H. Deutsch, J. C. Garrison, and E. M. Wright, “Excess noise in gain-guided amplifiers,” J. Opt. Soc. Am. B 8(6), 1244–1251 (1991). [CrossRef]

], fiber optic lasers (FOL) [7

7. A. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, “Confined propagation and near single-mode laser oscillation in a gain-guided, index antiguided optical fiber,” Appl. Phys. Lett. 89(25), 251101 (2006). [CrossRef]

], free electron lasers (FEL) [8

8. J. E. LaSala, D. A. Deacon, and J. M. Madey, “Optical guiding in a free-electron-laser oscillator,” Phys. Rev. Lett. 59(18), 2047–2050 (1987). [CrossRef] [PubMed]

] and microchip lasers [9

9. A. J. Kemp, R. S. Conroy, G. J. Friel, and B. D. Sinclair, “Guiding effects in Nd:YVO4 microchip lasers operating well above threshold,” IEEE J. Quantum Electron. 35(4), 675–681 (1999). [CrossRef]

]. When a laser beam goes through an active medium with spatially non-uniform gain distribution, the transverse profile of laser intensity is reshaped. This is the gain guiding effect. For most of the end-pumped laser amplifiers, the gain coefficient is higher in the center of the active medium than in the margin. Thus the lowest order laser mode owning a better overlap with the gain profile has higher gain than all the other modes. Meanwhile, in the wings of the pump region, higher thermal-induced stress and nonlinear refractive index profile produce the larger thermal phase aberration, which increases diffraction loss of higher order modes. The high gain for the lowest order mode and the high loss for higher order mode both lead to a high beam quality laser output.

In this work, we develop a theoretical model for an end-pumped laser amplifier, in which gain guiding, gain saturation and thermal effect are all taken into account. In our model, the wave equation is solved by a practical algorithm, based on faster Fourier transform (FFT). Although this algorithm has something in common with that in the laser oscillators [3

3. X. Yan, Q. Liu, D. Wang, and M. Gong, “Combined guiding effect in the end-pumped laser resonator,” Opt. Express 19(7), 6883–6902 (2011). [CrossRef] [PubMed]

], there are still many differences between them. For a laser amplifier, the input laser beam has a great influence on the performance of the amplifier. The intensity profile of the input beam can impact the gain distribution in the active laser medium due to gain saturation effect. And the power of the input beam can change the thermal loading in the amplifier, which results in the changes of the temperature and refractive index distribution. The simulation results are discussed to show the influence of each design parameter on the performance of an amplifier. An end-pumped Nd:YVO4 laser amplifier setup is built up and investigated experimentally. The experimental results agree well with the prediction of our theoretical model.

The paper is organized as follows. In chapter 2, the theoretical model is presented for the laser beam going through an active medium with non-uniform gain and refractive index profile. In chapter 3, the influences of several key parameters of the amplifier on beam quality improvement are discussed, such as the input beam quality, the beam filling factor between input beam and pump beam, the ratio between input power and pump power and the length of laser crystal. In chapter 4, an experimental setup of end-pumped Nd:YVO4 laser amplifier is built up and investigated. The experimental results are compared with the theoretical simulations. The conclusions are drawn in the last chapter.

2. Theory and model

2.1 Principles of the simulation for beam propagation and power scaling

In the earlier research [11

11. B. Perry, P. Rabinowitz, and M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27(4), 1989–2002 (1983). [CrossRef]

], solving the Maxwell's equations is the primary method to get the amplified laser distribution including intensity and phase profile. Analytical methods are always used for solving the Maxwell's equations, in which the gain distribution in the active medium is assumed to be a Gaussian profile or a quadratic profile. But in practice, the gain profile in the active medium changes remarkably with the distribution of pumping beam. Meanwhile, it depends on the input signal laser intensity considering gain saturation effect. Therefore, the former hypothesis on the gain distribution is not accurate enough.Our starting point for describing a laser beam passing through an amplifier is the Maxwell's equations. In steady state condition and with the approximations of monochromatic, paraxial, and slowly varying envelope, the wave equation in the positive z direction is [12

12. J. H. Marburger, “Self-focusing theory,” Prog. Quantum Electron. 4, 35–110 (1975). [CrossRef]

]
2ψ2ikψz=(ikg+2kk0Δn)ψ,
(1)
where2=2/x2+2/y2,k=n0ω/c, k0=ω/c, Δn represents the nonlinear part of the refractive index mainly determined by the thermo-optic effect, g is the gain coefficient in the active medium and ω is the circular frequency. The electric field component E is given by
E=Re(ψ)exp[i(ωtkz)].
(2)
In general, ψ, Δn and g are the functions of spatial coordinates x, y, z. Other parameters and their values used in our simulation are listed in Table 1

Table 1. Parameters for the Theoretical Model of Gain-Guided Laser Amplifier

table-icon
View This Table
.

The formal solution of Eq. (1) can be represented as following,
ψ(x,y,z+Δz)=exp[(i2k2+g2ik0Δn)Δz]ψ(x,y,z).
(3)
The Eq. (3) can be replaced to second-order accuracy in Δz by the symmetrized spit operator [13

13. J. Fleck, J. Morris, and E. Bliss, “Small-scale self-focusing effects in a high power glass laser amplifier,” IEEE J. Quantum Electron. 14(5), 353–363 (1978). [CrossRef]

]
ψ(x,y,z+Δz)=exp(iΔz4k2)exp[(g2ik0Δn)Δz]exp(iΔz4k2)ψ(x,y,z).
(4)
The Eq. (4) is the theoretical basis of the following algorithm for solving the Eq. (1). In the right side of Eq. (4), there are three operators before the function ψ(x,y,z). Two of them are the same, i.e.exp[(iΔz/4k)2], which represent the propagating along a distance of Δz/2 in a homogeneous medium. While the other one, i.e.exp[(g/2ik0Δn)Δz], represents the amplitude and phase changes.

We show the iterative procedure in the following way (see Fig. 1
Fig. 1 The scheme for the iterative procedure of the slice algorithm operating in solving the Maxwell's equations.
). The active medium in Fig. 1 is split into many slices (S1, S2, …, Sn). Taking the slice Sk as an example, we define ψ(x,y,z) and ψ(x,y,z+Δz) are the fields at the input and output surface of slice Sk respectively. We need three steps to get ψ(x,y,z+Δz) from ψ(x,y,z), i.e., firstly propagating a distance of Δz/2, secondly adding the amplitude and phase changes and thirdly propagating a distance of Δz/2 again. The three steps exactly correspond to the three operators on the RS of Eq. (4).

Define
ψ1(x,y,z+Δz/2)=exp(iΔz4k2)ψ(x,y,z),
(5)
which represents the input beam ψ propagating a distance of Δz/2 in a homogeneous medium with refractive index n0. With the help of scalar angle-spectrum theory of diffraction based on FFT, we have the solution of Eq. (5) as
ψ1(x,y,z+Δz/2)=F1{F[ψ(x,y,z)]exp(ik(Δz/2)1λl2fx2λl2fy2)},
(6)
whereF, F1are the Fourier transform operator and inverse Fourier transform operator respectively, and fx, y are the spatial angular frequencies in the Fourier domain.

Define
ψ2(x,y,z+Δz/2)=exp[Δz(g2ik0Δn)]ψ1(x,y,z+Δz/2),
(7)
which represents the amplitude and phase changes of the input beam after going through a slice with length of Δz. Owing to the fact that Δz in our calculation is very small, it is reasonable to take g and Δn as constant in the range of Δz. The g is determined by input and pump beam intensity profile at the position of zz/2. The Δn is determined by the temperature distribution at zz/2 caused by pump beam.

Define
ψ(x,y,z+Δz)=exp(iΔz4k2)ψ2(x,y,z+Δz/2).
(8)
Employing the similar method (scalar angle-spectrum theory of diffraction), we have the field at the output surface of the slice Sk,
ψ(x,y,z+Δz)=F1{F[ψ2(x,y,z+Δz/2)]exp(ik(Δz/2).1λl2fx2λl2fy2)}.
(9)
So far, we obtain the approximate solution of beam distribution passing through the slice Sk. By means of iteration (see Fig. 1), the laser beam distribution after going through the entire active medium could be obtained with numerical method.

2.2 Gain saturation effect

The gain coefficient g in the active medium is a key parameter for gain guiding effect. With the increase of g, the gain guiding effect is reinforced. For an end-pumped four-level laser system, the small signal gain coefficient g0 is proportional to the pump power deposition density, which is a function of the incident pump intensity distribution Ppump and the absorption coefficient α at the pump wavelength λp. Assuming the normalized pump intensity profile does not change with the length of the gain medium, we can simply express g0 as [14

14. W. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423 (1988). [CrossRef]

]
g0=ασ21τfPpumphvpexp(αz).
(10)
For small input power, the gain coefficient g nearly equals to the small signal gain coefficient g0. However, in the situation of high input power, the gain coefficient g could be changed distinctly by the input laser distribution Il (x,y,z). Therefore, the gain saturation effect must be taken into account. The basic equation governing the growth rate of the input beam along a lossless amplifier is given as
g(x,y,z)=1Il(x,y,z)dIl(x,y,z)dz=g0(x,y,z)1+Il(x,y,z)/Isat,
(11)
where Isat is the saturation intensity, whose physical meaning is that the input beam intensity required to reduce the gain to one half of the small signal value, and
Isat=hvl/σ21τf.
(12)
According Eq. (11), since the gain coefficient g and input laser distribution Il (x,y,z) are interrelated, it is difficult to obtain an analytical expression of the gain coefficient. However, we can use the iteration algorithm mentioned above to solve this problem approximately.

2.3 Thermo-optic effect

The general steady-state heat conduction equation for an anisotropic cubic solid in Cartesian coordinates is given by [15

15. M. Sabaeian, H. Nadgaran, and L. Mousave, “Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser,” Appl. Opt. 47(13), 2317–2325 (2008). [CrossRef] [PubMed]

]
Kx2T(x,y,z)x2+Ky2T(x,y,z)y2+Kz2T(x,y,z)z2=Q(x,y,z),
(13)
where T and Q are the temperature and thermal loading intensity in the active medium respectively. In this context, the crystal is pumped by a super-Gaussian laser beam. We suppose the distribution of thermal loading is the super-Gaussian profile in the radial direction and an exponential decay along the axis of the crystal rod. The thermal loading intensity distribution in the active medium is given by
Q(x,y,z)=Q0exp[2(x2+y2)2/wp4]exp(αz),
(14)
where Q0 is the thermal loading intensity in the center of the input surface of the crystal.
Q0=η(IpIextract)crystalexp[2(x2+y2)2/wp4]exp(αz)dxdydz,
(15)
in which Iextract is the extracted power by the input laser beam, i.e., Iextract = IoutIin. η is the fraction of residual pump power converted into heat. We set η=0.43 by considering the fact that “dark neodymium ions” which absorb pump photons but do not contribute to the population inversion, and the absorbed pump power partly changing into fluorescence. This value is the same as the value of non laser emitting process according to Walter Koechner [16

16. W. Koechner, Solid-State Laser Engineering, 6th ed. (Springer-Verlag Publication, 2006), Chap. 7.

].

The temperature gradient induces the refractive index changes Δn in the active medium. For a paraxial beam propagating in the z direction, neglecting the axial strain and strain-induced birefringence, we could get

Δn=dndT(TT0).
(16)

2.4 Methods to evaluate the beam quality

3. Simulation results and analyses

The configuration of a typical end-pumped laser amplifier is shown in Fig. 2
Fig. 2 The configuration of a typical end-pumped laser amplifier.
. The composite YVO4/Nd:YVO4 crystal is end-pumped by fiber-coupled diodes. The pump beam has a super-Gaussian profile. We suppose that it does not diverge over the length of gain medium, i.e., the pump beam radius wp is constant.

To show the relationship between output beam quality and input beam quality, three different input beams with spherical aberration are composed, which are the Gaussian beam with spherical aberration (GA), the hollow beam with spherical aberration (HA), and the quasi-Gaussian beam with spherical aberration (QGA). Their distributions and beam quality factors are shown in Fig. 3
Fig. 3 The power distributions and fitting curves of three composed input beams. (a) the Gaussian beam with spherical aberration (GA), (b) the hollow beam with spherical aberration (HA), (c) the quasi-Gaussian beam with spherical aberration (QGA).
. These input beams are formed by means of amplitude distribution multiplying the phase with spherical aberration, i.e.,
ψ(x,y,0)=A(x,y,0)exp[iφ(x,y,0)],
(19)
where A and φ represent the amplitude and phase distribution respectively. For most of the high power oscillators and amplifiers, the deterioration of beam quality is caused by the spherical aberration in phase. The phase distribution φ has the expression as
φ(x,y,0)=c0(x2+y2)2+φ0,
(20)
where φ0 is a constant and c0 is the spherical aberration coefficient. In this way, we have the input signal beams for our simulations, which are similar to those in actual master-oscillator power-amplifier (MOPA) systems. If we consider only the amplitude distribution of the three input beams (i.e. φ=φ0 with c0 is zero), the GA, HA and QGA beams have little difference on the beam quality factors, which are 1.0, 1.15 and 1.1 respectively. By changing the value of c0, we could obtain different beam quality factors. In this way, Fig. 3 shows three different beams with the same beam quality factor of 2.2 but different intensity profiles.

Figure 4
Fig. 4 The relationship between M2 factor of input beam and M2 factor of output beam.
shows the M2 factor of output beam as a function of the M2 factor of input beam for wp = 400μm. The three sets of dots represent the situations for three different input beams respectively. The beam quality improvements are obvious in Fig. 4 for all these beams, though their input beam distributions are quite different. The best output beam quality is obtained (M2 = 1.08) with the input beam M2 factor of 1.5. We also observe that if the input beam has a very good beam quality, for example M2 = 1.1, the quality of output beam is deteriorated instead of getting better after going through the amplifier, which was also illustrated by Minassian etc. in experiments [19

19. A. Minassian, B. Thompson, G. Smith, and M. Damzen, “High-power scaling (>100 W) of a diode-pumped TEM00 Nd:GdVO4 laser system,” IEEE J. Sel. Top. Quantum Electron. 11(3), 621–625 (2005). [CrossRef]

]. This is mainly caused by two aspects. Firstly, the thermal distortion induced by spherical aberration in the amplifier is larger than that of the input beam in this situation, which could remarkably modify the phase distribution of the input beam, and lead to the degradation of beam quality. Secondly, the physical mechanism of gain guiding effect is that it magnifies the fundamental mode but suppresses higher order modes, which results in better beam quality laser output. The input beam with high beam quality means that it has only a small percentage of higher order modes. This results in the limited function of gain guiding effect for beam quality improvement. Therefore, in this situation, the gain guiding effect could not enhance the beam quality, whereas the thermal distortion deteriorates it.

Figure 5
Fig. 5 The dependency of the M2 factor of output beam and output power on the pump radii in the situation of wl = 300, 400, 500μm respectively.
shows the M2 factor of output beam and the output power with different pump radii in the situation of wl = 300, 400, 500μm respectively. For each curve in the Fig. 5(a), there is an optimum pump radius wp, which corresponds to the best output beam quality. The optimum wp always has a value of ~0.9 times of wl. This means an effective transverse gain aperture for mode selection. If wp is too small, such as wp = 100μm, output beam quality is deteriorated rapidly due to severe thermal effect induced by the concentrating pump. If wp is too large, such as wp = 900μm, M2 factor of the output beam is approximately equal to that of the input beam. This is because the large pump area decreases the gain intensity, which weakens the gain guiding effect according to Eq. (11). For the output power from the amplifier, things are little different. Larger pump radius always leads to lower output power. One can see in Fig. 5(b) that an increase of the pump radius leads to an almost linear decrease of the output power for all these three situations.

Figure 7
Fig. 7 The M2 factor of output beam and output power versus the length of crystal.
depicts the M2 factor of output beam and output power versus the length of crystal from 2mm to 18mm. The M2 factor of output beam decreases with the increase of crystal length till L = 14mm and then keeps nearly unchanged (M2 = 1.2). Furthermore, the output power increases with the increase of crystal length till L = 16mm.

4. Experimental results

The experimental setup is the same as that shown in Fig. 2. A composite a-cut Nd:YVO4 crystal is used as the gain medium, which is an efficient four-level laser crystal to provide high gain when being pumped at 808nm and lasing at 1064nm. The composite crystal consisted of a 2mm thermal bonding end-cap on both ends and 16mm 0.3 at.% doped region. The undoped end cap was used to weaken the thermal effects [5

5. X. Yan, Q. Liu, X. Fu, D. Wang, and M. Gong, “Gain guiding effect in end-pumped Nd:YVO4 MOPA lasers,” J. Opt. Soc. Am. B 27(6), 1286–1290 (2010). [CrossRef]

]. Both end surfaces of the crystal are anti-reflection (AR) coated at 808nm and 1064nm. A fiber coupled laser diode (LD) delivering maximum output power of 50W is used to pump the laser crystal. Using a simple telescope imaging system as the coupling lens system, we could obtain the different pump spot sizes. The fiber had a 0.22 numerical aperture and a 400μm diameter. The laser crystal is pumped through a dichroic 45° mirror which is AR-coated for the pump wavelength and high-reflection coated for the laser wavelength. The temperature of the LD is controlled by a thermoelectric cooling module (TECM), and the center wavelength of the LD could be temperature-tuned by adjusting the temperature of the LD with TECM. The effective cooling of laser crystal is realized by mounting the crystal with indium foil in a water cooled copper holder.

The signal beam is from a Nd:YVO4 oscillator. We can control the signal beam quality by changing the resonator length and the pump power. To show the beam quality improvement due to the gain guiding effect in the amplifier, we use a signal beam with M2 factor of 2.2. It is coupled by a positive lens into the amplifier. The signal beam has a nearly Gaussian profile in the far field after the coupling lens. But it has different intensity patterns at different positions in the focal region. This is typical for a Gaussian beam with strong spherical aberrations. In this way, we can have signal beams with the same M2 factor but different intensity patterns. The beam intensity profiles of signal beam and output beam from the amplifier are shown in Fig. 8
Fig. 8 The beam profiles and beam quality factors before and after the amplification. (a), (c) are from the same signal beam but at different positions near the focal region; (b), (d) are from the corresponding output beam respectively.
. The intensity profiles in Fig. 8(a) and Fig. 8(c) are from the same signal beam but at different positions near the focal region. The profiles in Fig. 8(b) and Fig. 8(d) are from the corresponding output beam respectively. The beam quality is improved to be M2 = 1.4 for both of the two situations.

Figure 9
Fig. 9 The M2 factor of output beam with different input beam radius in experiments and in theory.
shows the M2 factor of output beam with different input beam radii in theory and in experiment respectively. It can be seen from the curve that wl slightly larger than wp makes the best results for beam quality enhancement in a gain-guided laser amplifier. This has been predicted in chapter 3. And it is shown again the beam filling factor is very important for an end-pumped laser amplifier.

In general, the LD operating temperature influences the pump wavelength, which leads to variation of active medium absorption coefficient. This is an effective instrument for us to adjust the performance of the amplifier, such as the gain and thermal distribution. We measured the optical spectrum of the pump diodes in our experiments. With the diodes output power of 25W, the central wavelength is 807nm at 30°C. It can be temperature-tuned with a coefficient of 0.3nm/°C. Figure 11
Fig. 11 The M2 factor of output beam with LD operating temperature in experiment.
shows the output beam quality from the amplifier with different LD temperature. The absorption coefficient is not only determined by the pump diodes wavelength but also by Nd3+ ion doping concentration in the active medium. In our experiment, with 0.3 at.% doping concentration, the output beam quality goes better with higher LD operating temperature.

5. Conclusions

Acknowledgments

Project supported by the National Natural Science Foundation of China (Grant No. 60908013).

References and links

1.

F. Salin and J. Squier, “Gain guiding in solid-state lasers,” Opt. Lett. 17(19), 1352–1354 (1992). [CrossRef] [PubMed]

2.

A. Ritsataki, G. New, R. Melish, S. C. W. Hyde, P. M. W. French, and J. Taylor, “Theoretical modeling of gain-guiding effects in experimental all-solid-state KLM lasers,” IEEE J. Sel. Top. Quantum Electron. 4(2), 185–192 (1998). [CrossRef]

3.

X. Yan, Q. Liu, D. Wang, and M. Gong, “Combined guiding effect in the end-pumped laser resonator,” Opt. Express 19(7), 6883–6902 (2011). [CrossRef] [PubMed]

4.

P. R. Battle, J. G. Wessel, and J. L. Carlsten, “Excess noise in a focused-gain amplifier,” Phys. Rev. Lett. 70(11), 1607–1610 (1993). [CrossRef] [PubMed]

5.

X. Yan, Q. Liu, X. Fu, D. Wang, and M. Gong, “Gain guiding effect in end-pumped Nd:YVO4 MOPA lasers,” J. Opt. Soc. Am. B 27(6), 1286–1290 (2010). [CrossRef]

6.

I. H. Deutsch, J. C. Garrison, and E. M. Wright, “Excess noise in gain-guided amplifiers,” J. Opt. Soc. Am. B 8(6), 1244–1251 (1991). [CrossRef]

7.

A. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, “Confined propagation and near single-mode laser oscillation in a gain-guided, index antiguided optical fiber,” Appl. Phys. Lett. 89(25), 251101 (2006). [CrossRef]

8.

J. E. LaSala, D. A. Deacon, and J. M. Madey, “Optical guiding in a free-electron-laser oscillator,” Phys. Rev. Lett. 59(18), 2047–2050 (1987). [CrossRef] [PubMed]

9.

A. J. Kemp, R. S. Conroy, G. J. Friel, and B. D. Sinclair, “Guiding effects in Nd:YVO4 microchip lasers operating well above threshold,” IEEE J. Quantum Electron. 35(4), 675–681 (1999). [CrossRef]

10.

A. E. Siegman, “Excess spontaneous emission in non-Hermitian optical systems. I. Laser amplifiers,” Phys. Rev. A 39(3), 1253–1263 (1989). [CrossRef] [PubMed]

11.

B. Perry, P. Rabinowitz, and M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27(4), 1989–2002 (1983). [CrossRef]

12.

J. H. Marburger, “Self-focusing theory,” Prog. Quantum Electron. 4, 35–110 (1975). [CrossRef]

13.

J. Fleck, J. Morris, and E. Bliss, “Small-scale self-focusing effects in a high power glass laser amplifier,” IEEE J. Quantum Electron. 14(5), 353–363 (1978). [CrossRef]

14.

W. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423 (1988). [CrossRef]

15.

M. Sabaeian, H. Nadgaran, and L. Mousave, “Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser,” Appl. Opt. 47(13), 2317–2325 (2008). [CrossRef] [PubMed]

16.

W. Koechner, Solid-State Laser Engineering, 6th ed. (Springer-Verlag Publication, 2006), Chap. 7.

17.

C. Serrat, M. Van Exter, N. Van Druten, and J. Woerdman, “Transverse mode formation in microlasers by combined gain-and index-guiding,” IEEE J. Quantum Electron. 35(9), 1314–1321 (1999). [CrossRef]

18.

N. Hodgson and H. Weber, Laser Resonators and Beam Propagation, Fundamentals, Advanced Concepts and Applications, 2nd ed. (Springer-Verlag Publication, 2005), Chap. 24.

19.

A. Minassian, B. Thompson, G. Smith, and M. Damzen, “High-power scaling (>100 W) of a diode-pumped TEM00 Nd:GdVO4 laser system,” IEEE J. Sel. Top. Quantum Electron. 11(3), 621–625 (2005). [CrossRef]

20.

B. Schulz, M. Frede, R. Wilhelm, and D. Kracht, “High power end-pumped Nd:YVO4 amplifier,” in Conference on Advanced Solid-State Photonics, Technical Digest (CD) (Optical Society of America, 2006), paper WB15.

OCIS Codes
(140.3280) Lasers and laser optics : Laser amplifiers
(140.3430) Lasers and laser optics : Laser theory
(140.3480) Lasers and laser optics : Lasers, diode-pumped

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 29, 2011
Revised Manuscript: September 12, 2011
Manuscript Accepted: September 27, 2011
Published: October 7, 2011

Citation
Zhen Xiang, Dan Wang, Sunqiang Pan, Yantao Dong, Zhigang Zhao, Tong Li, Jianhong Ge, Chong Liu, and Jun Chen, "Beam quality improvement by gain guiding effect in end-pumped Nd:YVO4 laser amplifiers," Opt. Express 19, 21060-21073 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-21060


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References

  1. F. Salin and J. Squier, “Gain guiding in solid-state lasers,” Opt. Lett.17(19), 1352–1354 (1992). [CrossRef] [PubMed]
  2. A. Ritsataki, G. New, R. Melish, S. C. W. Hyde, P. M. W. French, and J. Taylor, “Theoretical modeling of gain-guiding effects in experimental all-solid-state KLM lasers,” IEEE J. Sel. Top. Quantum Electron.4(2), 185–192 (1998). [CrossRef]
  3. X. Yan, Q. Liu, D. Wang, and M. Gong, “Combined guiding effect in the end-pumped laser resonator,” Opt. Express19(7), 6883–6902 (2011). [CrossRef] [PubMed]
  4. P. R. Battle, J. G. Wessel, and J. L. Carlsten, “Excess noise in a focused-gain amplifier,” Phys. Rev. Lett.70(11), 1607–1610 (1993). [CrossRef] [PubMed]
  5. X. Yan, Q. Liu, X. Fu, D. Wang, and M. Gong, “Gain guiding effect in end-pumped Nd:YVO4 MOPA lasers,” J. Opt. Soc. Am. B27(6), 1286–1290 (2010). [CrossRef]
  6. I. H. Deutsch, J. C. Garrison, and E. M. Wright, “Excess noise in gain-guided amplifiers,” J. Opt. Soc. Am. B8(6), 1244–1251 (1991). [CrossRef]
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