## Pulse shape symmetry and pulse width reduction in diode-pumped doubly Q-switched Nd:YVO_{4}/KTP green laser with AO and GaAs

Optics Express, Vol. 13, Issue 4, pp. 1178-1187 (2005)

http://dx.doi.org/10.1364/OPEX.13.001178

Acrobat PDF (151 KB)

### Abstract

Using both acoustic-optic (AO) Q-switcher and GaAs saturable absorber, a diode-pumped doubly Q-switched Nd:YVO_{4}/KTP green laser is realized for the first time to our knowledge. This laser can generate a symmetric and shorter pulse when compared with purely AO and passive Q-switching. A rate equation model is introduced to theoretically analyze the results obtained in the experiment, in which the spatial distributions of the intracavity photon density, the pump beam and the population-inversion density are taken into account. The numerical solutions of the rate equations are in good agreement with the experimental results.

© 2005 Optical Society of America

## 1. Introduction

1. T. T. Kajava and A. L. Gaeta, “Q switching of a diode-pumped Nd:YAG laser with GaAs,” Opt. Lett. **21**, 1244–1246 (1996). [CrossRef] [PubMed]

3. L. Chen, S. Zhao, and H. Zhao, “Passively Q-switching of a laser-diode-pumped inrtracavity-frequency-doubling Nd:NYW/KTP laser with GaAs saturable absorber,” Opt. & Laser Technol. **35**, 563–567 (2003). [CrossRef]

1. T. T. Kajava and A. L. Gaeta, “Q switching of a diode-pumped Nd:YAG laser with GaAs,” Opt. Lett. **21**, 1244–1246 (1996). [CrossRef] [PubMed]

2. T. T. Kajava and A. L. Gaeta, “Intra-cavity frequency-doubling of a Nd:YAG laser passively Q-switched with GaAs,” Opt. Commun. **137**, 93–97 (1997). [CrossRef]

4. S. Zhao, X. Zhang, J. Zheng, L. Chen, Z. Cheng, and H. Cheng, “Passively Q-switched self-frequency-doubling Nd^{3+}:GdCa_{4}O(BO_{3})_{3} laser with GaAs saturable absorber,” Opt. Eng. **41**, 559–560 (2002). [CrossRef]

5. Z. Li, Z. Xiong, N. Moore, G. C. Lim, W. L. Huang, and D. X. Huang, “Pulse width reduction in AO Q-switched diode-pumped Nd: YVO_{4} laser with GaAs coupler,” Opt. Commun. **237**, 411–416 (2004). [CrossRef]

5. Z. Li, Z. Xiong, N. Moore, G. C. Lim, W. L. Huang, and D. X. Huang, “Pulse width reduction in AO Q-switched diode-pumped Nd: YVO_{4} laser with GaAs coupler,” Opt. Commun. **237**, 411–416 (2004). [CrossRef]

_{4}/KTP green laser for the first time, to our knowledge. This laser can generate a symmetric and shorter pulse when compared with purely AO and passive Q-switching. To understand the results obtained in the experiment, we introduce a rate equation model in which the spatial distributions of the intracavity photon density, the pump beam and the population-inversion density are taken into account. The numerical solutions of the rate equations are well consistent with the experimental results.

## 2. Experimental setup and results

_{4}crystal. The output pump beam from the fiber bundle end, which is 800 µm in diameter, is focused into the laser crystal with a spot size of about 440 µm at the focal plane and far-field half-angle of 18° by a focusing optics. The mirror M

_{1}with 150-mm curvature radius is high antireflection coated at 808 nm and high reflection coated at 1064 nm. The Nd:YVO

_{4}crystal doped with 1.0 at. % Nd

^{3+}ions is 4×4×5 mm

^{3}and its absorption coefficient at 808 nm is 5.32 cm

^{-1}. Its front surface is antireflection coated at 808 nm and its rear surface is high antireflection coated at 1064 nm. It is near M

_{1}. The distance between the front surface of the AO crystal and M

_{1}is 7 cm and the distance between GaAs saturable absorber and M

_{1}is 11 cm. The mirror M

_{2}with 100-mm curvature radius is also used as the output mirror of the generated green light and the distance between M

_{1}and M

_{2}is about 22 cm. The KTP crystal cut for type-II phase matching (made by Coretech Crystal Company, Shandong University, China) is 3×3×10 mm

^{3}and both of its surfaces are antireflection coated at 1064 nm and 532 nm. The temperatures of the Nd:YVO

_{4}crystal and the KTP crystal are controlled at 20 °C and 22 °C by means of a temperature controller, respectively. M

_{3}is a plane mirror and its surface is high reflection coated at 1064 nm and 532 nm. The KTP crystal is near M

_{3}and the distance between M

_{2}and M

_{3}is about 8 cm. The filter is used for separating 532-nm green laser from the remainder 1064-nm fundamental wave leaking out from the resonator. A TED620B digital oscilloscope (Tektronix Inc., USA) is used to measure the generated-green-laser pulse width and a LPE-1B power meter (Institute of Physics, Chinese Academy of Science) is used to measure the generated-green-laser power.

*f*

_{p}=40 kHz as shown in Fig. 2(b). It is noticed that the pulse profile is rather symmetric with about 15 ns in both the rise and fall edges. Under the same conditions, the pulse width of the AO Q-switched laser is 71.6 ns as shown in Fig. 2(a), and the pulse profile is asymmetric with a fast rise time of about 28 ns and a slow falling edge of about 44 ns as well as a long decaying tail. The pulse width of the passively Q-switched laser is 56.8 ns as shown in Fig. 2(c), and the pulse profile is also asymmetric with a slow rise time of about 32 ns and a fast falling edge of about 25 ns. From Fig. 2, we can see that the doubly Q-switched laser has a symmetric pulse temporal profile and shorter pulse width compared to the other two Q-switched lasers.

*f*

_{p}=10 kHz is shown by the scattered marks in Fig. 3, from which we can see that the double Q-switching considerably shortened the laser pulses when compared with the other two methods of Q-switching.

_{4}/KTP green laser with AO and GaAs, the pulse profile is rather symmetric and the pulse width is obviously compressed when compared with the other two methods of Q-switching.

*f*

_{p}=10 kHz. It indicates that although the average output power from the double Q-switching is smaller than that from the AO Q-switching, it is much higher than that from the passive Q-switching.

## 3. Theoretical analysis

### 3.1 The spatial distribution of the photon density

_{4}/KTP green laser depicted in Fig. 1, in which Nd:YVO

_{4}works as gain medium, AO modulator works as active Q-switcher, and GaAs works as passive Q-switcher, KTP works as frequency-doubling crystal. If the intracavity photon density is assumed to be a Gaussian spatial distribution during the entire formatting process of the diode-pumped doubly Q-switched laser pulse, the intracavity photon density

*ϕ*(

*r*,

*t*) for the TEM

_{00}mode can be expressed as

*r*is the radial coordinate;

*w*

_{l}is the average radius of the TEM

_{00}mode, which is mainly determined by the geometry of the resonator;

*ϕ*(0,

*t*) is the photon density in the laser axis.

*ϕ*

_{g}(

*r*,

*t*),

*ϕ*

_{a}(r, t),

*ϕ*

_{s}(

*r*,

*t*), and

*ϕ*

_{k}(

*r*,

*t*) at the positions of Nd:YVO

_{4}gain medium, AO crystal, GaAs saturable absorber, and KTP crystal can be expressed as [6

6. G. Li, S. Zhao, H. Zhao, K. Yang, and S. Ding, “Rate equations and solutions of a laser-diode end-pumped passively Q-switched intracavity doubling laser by taking into account intracavity laser spatial distribution,” Opt. Commun. **234**, 321–328 (2004). [CrossRef]

*w*

_{g},

*w*

_{a},

*w*

_{s}, and

*w*

_{k}are the radii of the TEM

_{00}mode at the above-mentioned four positions, respectively.

*w*

_{p}is the average radius of the pump light in the gain medium;

*η*=1-exp(-

*αl*) is the absorptivity of the gain medium, in which

*α*is the absorption coefficient and

*l*is the length of the gain medium;

*P*

_{in}is the incident pump power;

*n*

_{1}is the refractive index of the gain medium;

*K*

_{c}is the thermal conductivity; d

*n*/d

*T*is the thermal dispersion coefficient;

*α*

_{T}is the thermal expansion coefficient; ξ is the fractional thermal load; and for our a-cut Nd:YVO

_{4}crystal:

*K*

_{c}=5.23×10

^{-3}Wmm

^{-1}K

^{-1}, d

*n*/d

*T*=3×10

^{-6}K

^{-1},

*α*

_{T}=4.43×10

^{-6}K

^{-1}, ξ=0.24 [7–9

9. J. Harrison and R. J. Martinsen, “Thermal modeling for mode-size estimation in microlasers with application to linear arrays in Nd:YAG and Tm, Ho:YLF,” IEEE J. Quantum Electron. **30**, 2628–2633 (1994). [CrossRef]

*w*

_{p}(

*z*) may be given as

*z*is the longitudinal coordinate and the pumped end of the laser crystal is taken as

*z*=0;

*w*

_{p}

_{0}is the radius at the pump beam waist and can be obtained by using the method given in Ref. [10

10. F. Song, C. Zhang, X. Ding, J. Xu, G. Zhang, M. Leigh, and N. Peyghambarian, “Determination of thermal focal length and pumping radius in gain medium in laser-diode-pumped Nd:YVO_{4} lasers,” Appl. Phys. Lett. **81**, 2145–2147 (2002). [CrossRef]

*θ*

_{p}and

*z*

_{0}are the far-field half-angle and the distance between the focal plane of the pump beam in the gain medium and the pumped end of the laser crystal. If the absorption factor of the gain medium in the laser axis exp(-

*αz*) is considered, we can obtain the dependence of the average pump beam radius in the gain medium

*w*

_{p}on

*z*

_{0}, and the minimum

*w*

_{p}=216.6 µm is at

*z*

_{0}=1.0 mm, where the maximum generated-green-laser power can be obtained at a certain pump power.

_{00}mode at the mirror M

_{1}and M

_{3}, that is,

*w*

_{g}and

*w*

_{k}as functions of incident pump power with

*w*

_{p}=216.6 µm, and the results are shown in Fig. 6.

*w*

_{a},

*w*

_{s}and the average radius of the TEM

_{00}mode

*w*

_{l}as functions of incident pump power are also shown in Fig. 6.

## 3.2 Nonlinear loss due to harmonic conversion

*ω*is the angle frequency of the fundamental wave.

11. J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect on KTP type-II phase-matching second-harmonic generation,” Opt. Commun. **199**, 207–214 (2001). [CrossRef]

*d*

_{eff}is the effective nonlinear coefficient;

*c*is the light velocity in vacuum;

*n*

_{e}2

^{ω}is the refractive index of SHW.

*z*direction, yields

*l*

_{k}is the length of KTP.

*ε*

_{0}is the dielectric permeability of vacuum;

*P*(

*ω*,0)=(1/2)

*A*

_{k}

*ħωcϕ*

_{k}(0,

*t*) is the incident fundamental power in the axis of KTP, in which

*A*

_{k}is the area of fundamental wave at the position of KTP,

*ħω*is the single photon energy of the fundamental wave,

*ϕ*

_{k}(0,

*t*) is the photon density in the laser axis at the position of KTP.

## 3.3 Rate equations and solutions

12. J. Dong, J. Lu, A. Shirakawa, and K. Ueda, “Optimization of the laser performance in Nd^{3+}:YAG ceramic microship lasers,” Appl. Phys. B **80**, 39–43 (2005). [CrossRef]

_{4}/KTP green laser with AO and GaAs [6

6. G. Li, S. Zhao, H. Zhao, K. Yang, and S. Ding, “Rate equations and solutions of a laser-diode end-pumped passively Q-switched intracavity doubling laser by taking into account intracavity laser spatial distribution,” Opt. Commun. **234**, 321–328 (2004). [CrossRef]

*n*(

*r*,

*z*,

*t*) is the spatial distribution of the population-inversion density;

*n*

_{0}is the total population density of the EL2 defect level (including EL2

^{0}and EL2

^{+}) of GaAs saturable absorber;

*n*

^{+}(

*r*,

*t*) is the population density of positively charged EL2

^{+};σ and

*l*are the stimulated-emission cross section and length of Nd:YVO

_{4}gain medium, respectively; σ

^{0}and σ

^{+}are the absorption cross sections of EL2

^{0}and EL2

^{+}, respectively;

*l*

_{s}is the length of the saturable absorber;

*t*

_{r}is the round-trip time of light in the resonator {

*t*

_{r}=[2

*n*

_{1}

*l*+2

*n*

_{2}

*l*

_{a}+2

*n*

_{3}

*l*

_{s}+2

*n*

_{4}

*l*

_{k}+2(

*L*

_{e}-

*l*-

*l*

_{a}-

*l*

_{s}-

*l*

_{k})]/

*c*}, in which

*n*

_{1},

*n*

_{2},

*n*

_{3}, and

*n*

_{4}are the refractive indices of Nd:YVO

_{4}gain medium, AO crystal, GaAs saturable absorber, and KTP crystal, respectively,

*L*

_{e}is the cavity length,

*l*

_{a}is the length of the AO crystal,

*c*is the velocity of light in vacuum;

*B*=6

*βh*

*γc*(

*w*

_{g}/

*w*

_{s})

^{2}is the coupling coefficient of TPA in GaAs [3

3. L. Chen, S. Zhao, and H. Zhao, “Passively Q-switching of a laser-diode-pumped inrtracavity-frequency-doubling Nd:NYW/KTP laser with GaAs saturable absorber,” Opt. & Laser Technol. **35**, 563–567 (2003). [CrossRef]

*β*is the absorption coefficient of two photons,

*hγ*is the single photon energy of the fundamental wave;

*L*is the intrinsic loss; τ is the stimulated-radiation lifetime of the gain medium;

*W*

_{p}=

*P*

_{in}

*η*/

*hγ*

_{p}is the pump rate, where

*hγ*

_{p}is the single-photon energy of the pump light;

*δ*

_{a}(

*t*) is the loss function of the AO Q-switcher, which is defined as [14]

*δ*

_{a}is the intrinsic diffraction loss of the AO Q-switcher;

*t*

_{s}is the turnoff time of the AO Q-switcher.

*n*(0, 0, 0) is the initial population-inversion density in the laser axis;

*n*

^{+}is the initial population density of positively charged EL2

^{+}of GaAs saturable absorber. From Eq. (19), we can deduce

*n*(0, 0, 0) accumulated during a modulation period of the AO modulator

*f*

_{p}is the modulation frequency of the AO modulator;

*w*

_{p}(0) is the pump beam radius at

*z*=0.

_{4}/KTP green laser

_{4}/KTP green laser with GaAs saturable absorber.

*f*

_{p}=10 kHz is shown in Fig. 3 by the solid lines.

## 4. Conclusions

_{4}/KTP green laser using both AO Q-switcher and GaAs saturable absorber for the first time, to our knowledge. This laser can generate a symmetric and shorter pulse when compared with purely AO and passive Q-switching. A rate equation model is introduced to theoretically analyze the results obtained in the experiment, in which the spatial distributions of the intracavity photon density, the pump beam and the population-inversion density are taken into account. The numerical solutions of the rate equations agree with the experimental results well.

## Acknowledgments

## References and links

1. | T. T. Kajava and A. L. Gaeta, “Q switching of a diode-pumped Nd:YAG laser with GaAs,” Opt. Lett. |

2. | T. T. Kajava and A. L. Gaeta, “Intra-cavity frequency-doubling of a Nd:YAG laser passively Q-switched with GaAs,” Opt. Commun. |

3. | L. Chen, S. Zhao, and H. Zhao, “Passively Q-switching of a laser-diode-pumped inrtracavity-frequency-doubling Nd:NYW/KTP laser with GaAs saturable absorber,” Opt. & Laser Technol. |

4. | S. Zhao, X. Zhang, J. Zheng, L. Chen, Z. Cheng, and H. Cheng, “Passively Q-switched self-frequency-doubling Nd |

5. | Z. Li, Z. Xiong, N. Moore, G. C. Lim, W. L. Huang, and D. X. Huang, “Pulse width reduction in AO Q-switched diode-pumped Nd: YVO |

6. | G. Li, S. Zhao, H. Zhao, K. Yang, and S. Ding, “Rate equations and solutions of a laser-diode end-pumped passively Q-switched intracavity doubling laser by taking into account intracavity laser spatial distribution,” Opt. Commun. |

7. | J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect in gain-media on optimum design of LD-end pumped solid state laser,” Acta Photonica Sinica |

8. | C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. |

9. | J. Harrison and R. J. Martinsen, “Thermal modeling for mode-size estimation in microlasers with application to linear arrays in Nd:YAG and Tm, Ho:YLF,” IEEE J. Quantum Electron. |

10. | F. Song, C. Zhang, X. Ding, J. Xu, G. Zhang, M. Leigh, and N. Peyghambarian, “Determination of thermal focal length and pumping radius in gain medium in laser-diode-pumped Nd:YVO |

11. | J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect on KTP type-II phase-matching second-harmonic generation,” Opt. Commun. |

12. | J. Dong, J. Lu, A. Shirakawa, and K. Ueda, “Optimization of the laser performance in Nd |

13. | G. Li, S. Zhao, K. Yang, and H. Zhao, “Diode-pumped passively Q-switched Nd:YVO |

14. | X. Zhang, J. Yang, R. Han, and J. Yao, “Acousto-optic-dye double Q-switched laser: theory and experiments,” Chin. J. Lasers |

**OCIS Codes**

(140.3480) Lasers and laser optics : Lasers, diode-pumped

(140.3530) Lasers and laser optics : Lasers, neodymium

(140.3540) Lasers and laser optics : Lasers, Q-switched

(140.3580) Lasers and laser optics : Lasers, solid-state

**ToC Category:**

Research Papers

**History**

Original Manuscript: January 26, 2005

Revised Manuscript: January 24, 2005

Published: February 21, 2005

**Citation**

Guiqiu Li, Zhengzhi Zhao, Kejian Yan, Dechun Li, and Jing Zou, "Pulse shape symmetry and pulse width reduction in diode-pumped doubly Q-switched Nd:YVO4/KTP green laser with AO and GaAs," Opt. Express **13**, 1178-1187 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-4-1178

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### References

- T. T. Kajava and A. L. Gaeta, “Q switching of a diode-pumped Nd:YAG laser with GaAs,” Opt. Lett. 21, 1244-1246 (1996). [CrossRef] [PubMed]
- T. T. Kajava and A. L. Gaeta, “ Intra-cavity frequency-doubling of a Nd:YAG laser passively Q-switched with GaAs,” Opt. Commun. 137, 93-97 (1997). [CrossRef]
- L. Chen, S. Zhao, and H. Zhao, “Passively Q-switching of a laser-diode-pumped inrtracavity-frequencydoubling Nd:NYW/KTP laser with GaAs saturable absorber,” Opt. & Laser Technol. 35, 35-567 (2003). [CrossRef]
- S. Zhao, X. Zhang, J. Zheng, L. Chen, Z. Cheng, and H. Cheng, “Passively Q-switched self-frequencydoubling Nd3+:GdCa4O(BO3)3 laser with GaAs saturable absorber,” Opt. Eng. 41, 559-560 (2002). [CrossRef]
- Z. Li, Z. Xiong, N. Moore, G. C. Lim, W. L. Huang, and D. X. Huang, “Pulse width reduction in AO Qswitched diode-pumped Nd: YVO4 laser with GaAs coupler,” Opt. Commun. 237, 411-416 (2004). [CrossRef]
- G. Li, S. Zhao, H. Zhao, K. Yang, and S. Ding, “Rate equations and solutions of a laser-diode end-pumped passively Q-switched intracavity doubling laser by taking into account intracavity laser spatial distribution,” Opt. Commun. 234, 321-328 (2004). [CrossRef]
- J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect in gain-media on optimum design of LD-end pumped solid state laser,” Acta Photonica Sinica 30, 724-729 (2001) (in Chinese).
- C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605-1615 (1994). [CrossRef]
- J. Harrison and R. J. Martinsen, “Thermal modeling for mode-size estimation in microlasers with application to linear arrays in Nd:YAG and Tm,Ho:YLF,” IEEE J. Quantum Electron. 30, 2628-2633 (1994). [CrossRef]
- F. Song, C. Zhang, X. Ding, J. Xu, G. Zhang, M. Leigh, and N. Peyghambarian, “Determination of thermal focal length and pumping radius in gain medium in laser-diode-pumped Nd:YVO4 lasers,” Appl. Phys. Lett. 81, 2145-2147 (2002). [CrossRef]
- J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect on KTP type-II phasematching second-harmonic generation,” Opt. Commun. 199, 207-214 (2001). [CrossRef]
- J. Dong, J. Lu, A. Shirakawa, and K. Ueda, “Optimization of the laser performance in Nd3+:YAG ceramic microship lasers,” Appl. Phys. B 80, 39-43 (2005). [CrossRef]
- G. Li, S. Zhao, K. Yang, and H. Zhao, “Diode-pumped passively Q-switched Nd:YVO4 laser with GaAs saturable absorber,” Chin. Opt. Lett. 2, 462-465 (2004).
- X. Zhang, J. Yang, R. Han, and J. Yao, “Acousto-optic-dye double Q-switched laser: theory and experiments,” Chin. J. Lasers 19, 241-246 (1992) (in Chinese).

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