Abstract

A diode-side-pumped actively Q-switched intracavity frequency-doubled Nd:YAG/BaWO4/KTP Raman laser is studied experimentally and theoretically. Rate equations are used to analyze the Q-switched yellow laser by considering the transversal distributions of the intracavity photon density and the inversion population density. An 8.3 W 590 nm laser is obtained with a 125.8 W 808 nm pump power and a 15 kHz pulse repetition frequency. The corresponding optical conversion efficiency from diode laser to yellow laser is 6.57%, much higher than that of the former reported side-pumped yellow laser. The output powers with respect to the incident pump power are in agreement with the theoretical results on the whole.

©2010 Optical Society of America

1. Introduction

Stimulated Raman scattering (SRS) is an efficient method to produce new laser lines [14]. In recent years, with emergence of excellent Raman crystals, all-solid-state Raman laser has attracted much attention for the advantages of high conversion efficiency, compactness, good mechanical and thermal properties. The yellow-orange lasers in the spectral region from 550 nm to 650 nm have widely applications in metrology, remote sensing, medicine, and so on. But they are hardly obtained by use of intracavity frequency doubling Nd-doped lasers. Frequency-doubled the first Stokes Raman laser is an efficient way to obtain the yellow-orange lasers [58].

As a promising Raman medium, BaWO4 crystal has many advantages of high Raman gain for picosecond and nanosecond pulse [916], good mechanical and optical properties [17,18] and large physical size. Pavel Cerny et al. did much work to study the characteristics of BaWO4 Raman crystal with picosecond and nanosecond pump source [2,912]. In 2005, Y. F. Chen et al. investigated the characteristics of an actively Q-switched Nd:YAG/BaWO4 intracavity Raman laser, generating a 1.56 W 1181 nm Raman laser at an incident pump power of 9.2 W [13]. In 2007, S. T. Li et al. reported an diode-side-pumped intracavity frequency-doubled Nd:YAG/BaWO4 Raman laser, generating a 3.14 W 590 nm laser [14]. In 2009, a 3.36 W CW 1180 nm first order Stokes laser was obtained with a Nd:YVO4/BaWO4 Raman laser [15]. Recently, A. J. Lee et al. reported the generation of 2.9 W CW yellow laser emission from an intracavity Nd:GdVO4/BaWO4/LBO Raman laser [16].

Rate equations are an important way to describe laser operation theoretically. They are widely used to analyze intracavity frequency-doubled lasers [19,20] and Raman lasers [2123]. However, there is little report about the theoretical model of the actively Q-switched intracavity frequency-doubled Raman laser [24], and there is no comparison between the theoretical results and experimental results to our knowledge.

It is possible for end pumped lasers to achieve high conversion efficiency, but high output power is usually impeded by the heat generated in the laser medium. Compared with end pumped yellow laser, the side-pumped laser has lower conversion efficiency, but much higher output power can be obtained. In this paper, we analyze the intracavity frequency-doubled Raman laser based on the rate equations considering the transversal distributions of the intracavity photon density and the inversion population density. By numerically solving these rate equations, in which the thermal effect of the laser medium and Raman medium is taken into account, the theoretical output power is calculated. In the experiment, the characteristics of an efficient diode-side-pumped actively Q-switched intracavity KTP frequency doubled Nd:YAG/BaWO4 Raman laser were studied. A three-mirror linear coupled cavity configuration is used to collect the forward and backward propagation yellow beams. At an incident pump power of 125.8 W and a pulse repetition frequency (PRF) of 15 kHz, an average output power of 8.3 W 590 nm laser was obtained. The corresponding optical-to-optical conversion efficiency from diode laser to yellow laser was 6.57%, much higher than the former reported 3.2% conversion efficiency with side-pumped yellow laser [14]. The average output powers with respect to the incident pump power were in agreement with the experimental results on the whole.

2. Theory

In this paper, we assume the intracavity resonating lasers are in TEM00 mode. The intracavity fundamental photon densities in the laser medium φLL(r,t) and in the Raman medium φLR(r,t), the Raman photon densities in the Raman medium φRR(r,t) and in the frequency-doubling medium φRK(r,t) can be expressed as:

ϕLL(r,t)=ϕLL(0,t)exp(2r2ωLL2)
ϕLR(r,t)=ϕLR(0,t)exp(2r2ωLR2)
ϕRR(r,t)=ϕRR(0,t)exp(2r2ωRR2)
ϕRK(r,t)=ϕRK(0,t)exp(2r2ωRK2)
where r is the radial coordinate. ωLL and ωLR are the beam radii of the fundamental laser in the laser medium and Raman medium, respectively. ωRL and ωRK are the beam radii of the Raman laser in the Raman medium and frequency-doubling medium, respectively. Because of the continuity of energy flux, the following equation can be given:
ωLL2ϕLL(0,t)=ωLR2ϕLR(0,t)
ωRR2ϕRR(0,t)=ωRK2ϕRK(0,t)
The initial population inversion density is also assumed to be a Gaussian spatial distribution,
n(r,0)=n(0,0)exp(2r2ωP2)
where n(r,0) is the initial population inversion density in the laser axis, and ωP is the average radius of the pump beam in the gain medium.

When the Raman laser passes through the frequency-doubling crystal with low conversion efficiency, the output power of the frequency-doubling laser can be written as [20]:

PSH=ρπη[chνRϕRR(0,t)]2ωRR416ωRK2
where ρ is a parameter which depends on the resonator structure and the second-harmonic output method, c is the light speed in vacuum, h is Planck constant, η is a parameter to mark the ability of the frequency-doubling crystal to convert the Raman laser to the second harmonic, which can be written as:
η=ω2deff2lK2c3ε0no2ωnoωneωsin2(lKΔk/2)(lKΔk/2)2
where ω = 2πνR is the radian frequency of the Raman laser, deff is the effective nonlinear coefficient of the nonlinear crystal, ε0 is the permittivity of free space, no, noω and neω are the refractive indexes of the nonlinear crystal for the second harmonic, respectively; Δk is the phase mismatch.

The loss rate of the Raman photon density in the Raman medium caused by second harmonic generation (SHG) dϕRR(r,t)/dt|SHGsatisfies the following relation:

PSH=hνRlC0dϕRR(r,t)dt|SHG2πrdr
where lC is the optical length.By using Eqs. (4) and (6), the following equation can be obtained:
0dϕRR(r,t)dt|SHG2πrdr=ρπηhνR[cϕRR(0,t)]2ωRR416ωRK2lC
So the rate equations for the laser can be written as:
0dϕLL(r,t)dt2πrdr=1tr0[2σn(r,t)ϕLL(r,t)l2ghνRclRϕLR(r,t)ϕRR(r,t)]2πrdr1tL0ϕLL(r,t)2πrdr
+ksp0ϕLR(r,t)2πrdr0dφRR(r,t)dt|SHG2πrdr
dn(r,t)dt=γσcϕLL(r,t)n(r,t)n(r,t)τ
where σ is the stimulated emission cross section of the laser crystal, g is the Raman gain coefficient, tr = 2lC/c is the round-trip transit time of light in the cavity. tL,R = tr/(LL,R-ln(R1L,RR2L,R)) are the lifetime of the fundamental and Stokes photons, respectively. LL and LR are the intrinsic loss of the fundamental laser and Raman laser respectively.Substituting (1a) and (3) into (8c), we obtain:
n(r,t)=n(0,0)exp(2r2ωP2)exp[γσcexp(2r2ωLL2)0tϕLL(0,t)dttτ]
Substituting (1-2) and (9) into (8a) and (8b), we obtain:

dϕLL(0,t)dt=4σlωLL2trϕLL(0,t)n(0,t)0{exp[2r2(1ωP2+1ωLL2)]exp[γσcexp(2r2ωLL2)0tϕLL(0,t)dttτ]}2πrdr
2ghνRclRtrωRR2ωLR2+ωRR2ϕLL(0,t)ϕRR(0,t)ϕLL(0,t)tL
dϕRR(0,t)dt=2ghνRclRϕLL(0,t)ϕRR(0,t)trωLL2ωRR2ωLR2ωLL2+ωLR2ϕRR(0,t)tR
+kspωLL2ωRR2ϕLL(0,t)ρηhνRc28lCωRR2ωRK2ϕRR2(0,t)

For intracavity frequency-doubled Raman laser, the yellow light was generated in two directions inside the frequency-doubled crystal. In order to collect the forward and backward yellow beams, a three mirror coupled cavity was employed in the experiment (This will be described in detail later in the third part). When the phase difference between the forward and backward yellow beams is θ, the magnitude parameter of the return pass caused by the coupled cavity is M (0<M<1), the parameter ρ can be expressed [25]:

ρ=1+M2+2Mcosθ
In the best possible case, the phase difference is 0 and the loss is ignored (M = 1), then ρ = 4. In the worst possible case, the phase difference is π and the loss is ignored (M = 1), then ρ = 0. For the coupled cavity, the yellow laser and the Raman laser are in different cavities, so the phase difference between the forward and backward yellow beams θ is a random value from 0 to 2π. Then the parameter ρ can be expressed:
ρ=12π02π(1+M2+2Mcosθ)dθ=1+M2
So the single pulse energy and the average power of the yellow laser can be expressed:
ESH2=(1RY)0hνRlC0dφRR(r,t)dt|SHG2πrdrdt
=(1+M2)(1RY)πη(chνR)216ωRR4ωRK20ϕRR2(0,t)dt
PSH2=fPESH2=fP(1+M2)(1RY)πη(chνR)216ωRR4ωRK20ϕRR2(0,t)dt
Numerically solving Eqs. (10a) and (10b), we can obtain φLL(0,t) and φRR(0,t). Substituting them into Eqs. (13) and (14), we can calculate the average output power and the pulse energy.

3. Experimental results and discussions

The cavity configuration is shown in Fig. 1 . M1 was a concave mirror with a curvature radius of 3000 mm. It was coated for high reflection (HR) at the range of 1000-1200 nm. M2 was a plane mirror used as the output coupler, coated for HR at 1064 nm (R>99.8%) and 1180 nm (R>99.6%) and partial transmission at 590 nm (T = 90.9%). M3 was coated for HR at 590 nm and HT at 1064 and 1180 nm (T>99.5%). The overall cavity length was 226 mm. A dichroic mirror M4 coated for HT at 590 nm (T>98.5%) and HR at 1064 and 1180 nm (R>99.0%) was used to separate the yellow laser from the residual fundamental laser at 1064 nm and the first Stokes laser at 1180 nm.

 figure: Fig. 1

Fig. 1 Experimental arrangement of the side-pumped actively Q-switched intracavity KTP frequency doubled Nd:YAG/BaWO4 Raman laser.

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A commercial diode-side-pumped Nd:YAG module (Beijing GK Laser Technology Co. Ltd., GKPM-50B) was used as the fundamental laser source. The doping concentration of Nd:YAG crystal was 1-at.%, and the length was 60 mm. The Raman active medium is an a-cut BaWO4 crystal with a length of 46.6 mm. The frequency doubling medium is a KTP crystal with dimensions of 3 × 3 × 6 mm3, cut at an angle of θ = 68.7°, ϕ = 0° for type II phase matching condition. Both sides of the Nd:YAG, BaWO4 and KTP crystals are anti-reflection (AR) coated at 1064 and 1180 nm (R<0.2%). The entrance face of the Nd:YAG is also AR coated at 808 nm. A 35-mm-long acousto-optic (AO) Q-switch (Gooch & Housego Company) is placed between the Nd:YAG crystal and the BaWO4 crystal. Both faces were HT coated at 1064 nm and 1180 nm (R<0.2%). All the crystals are wrapped with indium foil and mounted in water-cooled copper blocks. The water temperature is maintained at 20°C.

The average output power is measured by a power meter (Molectron PM10) connected to Molectron EPM2000. The pulse temporal behavior is recorded by a Tektronix digital phosphor oscilloscope (TDS 5052B, 5 G Samples/s, 500 MHz bandwidth) with a fast p-i-n photodiode.

Figure 2 shows the average output power of the 590 nm laser with respect to the incident 808 nm pump power at the PRFs of 10, 15 and 20 kHz, respectively. The solid symbols are the experimental results, the lines are theoretical results. It can be seen that the average output power strongly depended on the repetition frequency. For Q-switched laser, more population inversions are accumulated at lower repetition frequency. Then high pulse energy and peak power can be obtained. The maximum pulse energy at 10, 15 and 20 kHz is 0.67, 0.55 and 0.37 mJ respectively. The SRS belongs to the third order nonlinear effect, high peak power and pulse energy usually leads to high conversion efficiency. So with the same pump power, the 590 nm laser power at 10 kHz was higher than the powers at 15 and 20 kHz. And the laser at 10 kHz also had higher slope efficiency. In the experiment, the slope efficiency was 8.87%, 8.08% and 7.33% for the 10 kHz, 15 kHz and 20 kHz respectively. However high pulse energy and peak power may damage the coatings of the crystals. In order to avoid the damage of the crystal coatings, the pump powers at 10, 15 and 20 kHz were within 93.5, 126 and 137 W respectively. The maximum output power of 8.3 W was obtained at 125.8 W pump power and 15 kHz PRF, the corresponding optical conversion efficiency from diode laser to yellow laser is 6.57%, much higher than that of the former reported side-pumped yellow laser [14].

 figure: Fig. 2

Fig. 2 Average output power of the 590 nm laser with respect to the pump power at PRFs of 10, 15 and 20 kHz. The solid symbols are the experimental results, the lines are theoretical results.

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Table 1 shows the parameters for the calculation. Only the 1064 nm fundamental laser, 1180 nm first Stokes laser and 590 nm yellow laser were obtained in the experiment, so we ignored the high order Stokes and anti-Stokes laser generation during the theoretical calculation. The thermal effect in the laser medium and Raman medium became more and more serious with increasing pump power, it impacted the stabilization of the resonator and impeded the increasing of the 590 nm laser power. So it must be taken into account. The thermal focal length of the crystal could be calculated with the theoretical formula [26]:

1f=12dndTPheatKCA
where f is the thermal focal length, KC is the thermal conductivity of the crystal, A is the laser cross-sectional area, Pheat is the total heat dissipated by the crystal. dn/dT is the temperature dependent change in the refractive index of the crystal. With the pump power increasing from 45 W to 131 W, the thermal focal length in the Nd:YAG crystal decreased from 1337 mm to 458 mm. The heat dissipated in the Raman medium depends on the generation of the Raman laser [1]. With the pump power increasing from 45 W to 131 W, the thermal focal length in the BaWO4 crystal changed from −2205 mm to −245 mm at 15 kHz. Taking the thermal effect in the Nd:YAG and BaWO4 crystals into account, we could obtain the Raman photon densities in the Raman medium φRR(r,t) by numerically solving Eqs. (10a) and (10b). Substituting φRR(r,t) into (13-14), the output power and pulse energy could be calculated. As shown in Fig. 2, the theoretical results are in agreement with the experimental results on the whole. Some discrepancies can also be observed, the reasons may be as follows: First, nonlinear conversion strongly depends on the laser power intensity. The thermal effect can impact the beam cross section and power intensity. Maybe the thermal focal length was not accurate. Second, we approximate that the 1064 nm, 1180nm and 590 nm lasers are in TEM00 mode. In fact, there are some other high-order modes in the experiment. Third, some parameters used in the calculation may be not accurate.

Tables Icon

Table 1. Parameters for the theoretical calculation

Figure 3 shows the pulse width of the 590 nm laser with respect to the incident 808 nm pump power at the PRFs of 10, 15 and 20 kHz, respectively. Figure 4 shows the pulses temporal behavior of the 1180 nm and 590 nm lasers with a 125.8 W pump power and a 15 kHz PRF. The pulse duration of the 590 nm laser was 20 ns, the corresponding peak power was 27.6 kW.

 figure: Fig. 3

Fig. 3 The pulse width of the 590 nm laser with respect to the pump power at PRFs of 10, 15 and 20 kHz.

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 figure: Fig. 4

Fig. 4 The oscilloscope trace for the 1180 nm and 590 nm laser pulses with a 125.8 W pump power and a 15 kHz PRF.

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4. Conclusion

In summary, the rate equations have been used to analyze the Q-switched intracavity frequency doubled Raman laser. The characteristics of a diode-side-pumped actively Q-switched intracavity KTP frequency doubled Nd:YAG/BaWO4 Raman laser have been investigated. At an incident pump power of 125.8 W and a pulse repetition frequency of 15 kHz, an 8.3 W yellow laser was obtained. The corresponding optical conversion efficiency from diode laser to yellow laser was 6.57%. The average output powers with respect to the incident pump power are in agreement with the experimental results on the whole.

Acknowledgments

This research is supported by the National Natural Science Foundation of China (60778012, 50721002) and the Grant for State Key Program of China (2004CB619002).

References and links

1. H. M. Pask, “The design and operation of solid-state Raman lasers,” Prog. Quantum Electron. 27(1), 3–56 (2003). [CrossRef]  

2. P. Cerny, H. Jelinkova, P. G. Zverev, and T. T. Basiev, “Solid state lasers with Raman frequency conversion,” Prog. Quantum Electron. 28(2), 113–143 (2004). [CrossRef]  

3. Y. F. Chen, “Compact efficient all-solid-state eye-safe laser with self-frequency Raman conversion in a Nd:YVO4 crystal,” Opt. Lett. 29(18), 2172–2174 (2004). [CrossRef]   [PubMed]  

4. J. A. Piper and H. M. Pask, “Crystalline Raman lasers,” IEEE Sel. Top. Quantum Electron. 13(3), 692–704 (2007). [CrossRef]  

5. H. M. Pask, P. Dekker, R. P. Mildren, D. J. Spence, and J. A. Piper, “Wavelength-versatile visible and UV sources based on crystalline Raman lasers,” Prog. Quantum Electron. 32(3-4), 121–158 (2008). [CrossRef]  

6. A. J. Lee, H. M. Pask, P. Dekker, and J. A. Piper, “High efficiency, multi-Watt CW yellow emission from an intracavity-doubled self-Raman laser using Nd:GdVO4.,” Opt. Express 16(26), 21958–21963 (2008). [CrossRef]   [PubMed]  

7. H. Y. Zhu, Y. M. Duan, G. Zhang, C. H. Huang, Y. Wei, W. D. Chen, Y. D. Huang, and N. Ye, “Yellow-light generation of 5.7 W by intracavity doubling self-Raman laser of YVO(4)/Nd:YVO(4) composite,” Opt. Lett. 34(18), 2763–2765 (2009). [CrossRef]   [PubMed]  

8. H. Y. Zhu, Y. M. Duan, G. Zhang, C. H. Huang, Y. Wei, H. Y. Shen, Y. Q. Zheng, L. X. Huang, and Z. Q. Chen, “Efficient second harmonic generation of double-end diffusion-bonded Nd:YVO4 self-Raman laser producing 7.9 W yellow light,” Opt. Express 17(24), 21544–21550 (2009). [CrossRef]   [PubMed]  

9. P. Cerny, P. G. Zverev, H. Jelinkova, and T. T. Basiev, “Efficient Raman shifting of picosecond pulses using BaWO4 crystals,” Opt. Commun. 177(1-6), 397 (2000). [CrossRef]  

10. P. Cerny, H. Jelinkova, T. T. Basiev, and P. G. Zverev, “Highly efficient picosecond Raman generators based on the BaWO4 crystal in the near infrared, visible, and ultraviolet,” IEEE J. Quantum Electron. 38(11), 1471–1478 (2002). [CrossRef]  

11. P. Cerný and H. Jelínková, “Near-quantum-limit efficiency of picosecond stimulated Raman scattering in BaWO(4) crystal,” Opt. Lett. 27(5), 360-362 (2002). [CrossRef]  

12. P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun. 209(4-6), 403–409 (2002). [CrossRef]  

13. Y. F. Chen, K. W. Su, H. J. Zhang, J. Y. Wang, and M. H. Jiang, “Efficient diode-pumped actively Q-switched Nd:YAG/BaWO4 intracavity Raman laser,” Opt. Lett. 30(24), 3335–3337 (2005). [CrossRef]  

14. S. T. Li, X. Y. Zhang, Q. P. Wang, X. L. Zhang, Z. H. Cong, H. Zhang, and J. Wang, “Diode-side-pumped intracavity frequency-doubled Nd:YAG/BaWO4 Raman laser generating average output power of 3.14 W at 590 nm,” Opt. Lett. 32(20), 2951–2953 (2007). [CrossRef]   [PubMed]  

15. L. Fan, Y. X. Fan, Y. Q. Li, H. Zhang, Q. Wang, J. Wang, and H. T. Wang, “High-efficiency continuous-wave Raman conversion with a BaWO(4) Raman crystal,” Opt. Lett. 34(11), 1687–1689 (2009). [CrossRef]   [PubMed]  

16. A. J. Lee, H. M. Pask, J. A. Piper, H. J. Zhang, and J. Y. Wang, “An intracavity, frequency-doubled BaWO4 Raman laser generating multi-watt continuouswave, yellow emission,” Opt. Express 18(6), 5984–5992 (2010). [CrossRef]   [PubMed]  

17. W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005). [CrossRef]  

18. J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006). [CrossRef]  

19. R. G. Smith, “Theory of intracavity optical second harmonic generation,” IEEE J. Quantum Electron. 6(4), 215–223 (1970). [CrossRef]  

20. X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).

21. W. Chen, Y. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd:PbWO4 Raman laser,” Opt. Commun. 194(4-6), 401–407 (2001). [CrossRef]  

22. A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

23. S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006). [CrossRef]  

24. D. J. Spence, P. Dekker, and H. M. Pask, “Modeling of continuous wave intracavity Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 756–763 (2007). [CrossRef]  

25. J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18(3), 70 (1971). [CrossRef]  

26. W. Koechner, Solid-state laser engineering, Springer Series in Optical Sciences, Springer, Berlin, 1999, fifth revised and updated edition.

References

  • View by:

  1. H. M. Pask, “The design and operation of solid-state Raman lasers,” Prog. Quantum Electron. 27(1), 3–56 (2003).
    [Crossref]
  2. P. Cerny, H. Jelinkova, P. G. Zverev, and T. T. Basiev, “Solid state lasers with Raman frequency conversion,” Prog. Quantum Electron. 28(2), 113–143 (2004).
    [Crossref]
  3. Y. F. Chen, “Compact efficient all-solid-state eye-safe laser with self-frequency Raman conversion in a Nd:YVO4 crystal,” Opt. Lett. 29(18), 2172–2174 (2004).
    [Crossref] [PubMed]
  4. J. A. Piper and H. M. Pask, “Crystalline Raman lasers,” IEEE Sel. Top. Quantum Electron. 13(3), 692–704 (2007).
    [Crossref]
  5. H. M. Pask, P. Dekker, R. P. Mildren, D. J. Spence, and J. A. Piper, “Wavelength-versatile visible and UV sources based on crystalline Raman lasers,” Prog. Quantum Electron. 32(3-4), 121–158 (2008).
    [Crossref]
  6. A. J. Lee, H. M. Pask, P. Dekker, and J. A. Piper, “High efficiency, multi-Watt CW yellow emission from an intracavity-doubled self-Raman laser using Nd:GdVO4.,” Opt. Express 16(26), 21958–21963 (2008).
    [Crossref] [PubMed]
  7. H. Y. Zhu, Y. M. Duan, G. Zhang, C. H. Huang, Y. Wei, W. D. Chen, Y. D. Huang, and N. Ye, “Yellow-light generation of 5.7 W by intracavity doubling self-Raman laser of YVO(4)/Nd:YVO(4) composite,” Opt. Lett. 34(18), 2763–2765 (2009).
    [Crossref] [PubMed]
  8. H. Y. Zhu, Y. M. Duan, G. Zhang, C. H. Huang, Y. Wei, H. Y. Shen, Y. Q. Zheng, L. X. Huang, and Z. Q. Chen, “Efficient second harmonic generation of double-end diffusion-bonded Nd:YVO4 self-Raman laser producing 7.9 W yellow light,” Opt. Express 17(24), 21544–21550 (2009).
    [Crossref] [PubMed]
  9. P. Cerny, P. G. Zverev, H. Jelinkova, and T. T. Basiev, “Efficient Raman shifting of picosecond pulses using BaWO4 crystals,” Opt. Commun. 177(1-6), 397 (2000).
    [Crossref]
  10. P. Cerny, H. Jelinkova, T. T. Basiev, and P. G. Zverev, “Highly efficient picosecond Raman generators based on the BaWO4 crystal in the near infrared, visible, and ultraviolet,” IEEE J. Quantum Electron. 38(11), 1471–1478 (2002).
    [Crossref]
  11. P. Cerný and H. Jelínková, “Near-quantum-limit efficiency of picosecond stimulated Raman scattering in BaWO(4) crystal,” Opt. Lett. 27(5), 360-362 (2002).
    [Crossref]
  12. P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun. 209(4-6), 403–409 (2002).
    [Crossref]
  13. Y. F. Chen, K. W. Su, H. J. Zhang, J. Y. Wang, and M. H. Jiang, “Efficient diode-pumped actively Q-switched Nd:YAG/BaWO4 intracavity Raman laser,” Opt. Lett. 30(24), 3335–3337 (2005).
    [Crossref]
  14. S. T. Li, X. Y. Zhang, Q. P. Wang, X. L. Zhang, Z. H. Cong, H. Zhang, and J. Wang, “Diode-side-pumped intracavity frequency-doubled Nd:YAG/BaWO4 Raman laser generating average output power of 3.14 W at 590 nm,” Opt. Lett. 32(20), 2951–2953 (2007).
    [Crossref] [PubMed]
  15. L. Fan, Y. X. Fan, Y. Q. Li, H. Zhang, Q. Wang, J. Wang, and H. T. Wang, “High-efficiency continuous-wave Raman conversion with a BaWO(4) Raman crystal,” Opt. Lett. 34(11), 1687–1689 (2009).
    [Crossref] [PubMed]
  16. A. J. Lee, H. M. Pask, J. A. Piper, H. J. Zhang, and J. Y. Wang, “An intracavity, frequency-doubled BaWO4 Raman laser generating multi-watt continuouswave, yellow emission,” Opt. Express 18(6), 5984–5992 (2010).
    [Crossref] [PubMed]
  17. W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
    [Crossref]
  18. J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
    [Crossref]
  19. R. G. Smith, “Theory of intracavity optical second harmonic generation,” IEEE J. Quantum Electron. 6(4), 215–223 (1970).
    [Crossref]
  20. X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).
  21. W. Chen, Y. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd:PbWO4 Raman laser,” Opt. Commun. 194(4-6), 401–407 (2001).
    [Crossref]
  22. A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).
  23. S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
    [Crossref]
  24. D. J. Spence, P. Dekker, and H. M. Pask, “Modeling of continuous wave intracavity Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 756–763 (2007).
    [Crossref]
  25. J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18(3), 70 (1971).
    [Crossref]
  26. W. Koechner, Solid-state laser engineering, Springer Series in Optical Sciences, Springer, Berlin, 1999, fifth revised and updated edition.

2010 (1)

2009 (3)

2008 (2)

H. M. Pask, P. Dekker, R. P. Mildren, D. J. Spence, and J. A. Piper, “Wavelength-versatile visible and UV sources based on crystalline Raman lasers,” Prog. Quantum Electron. 32(3-4), 121–158 (2008).
[Crossref]

A. J. Lee, H. M. Pask, P. Dekker, and J. A. Piper, “High efficiency, multi-Watt CW yellow emission from an intracavity-doubled self-Raman laser using Nd:GdVO4.,” Opt. Express 16(26), 21958–21963 (2008).
[Crossref] [PubMed]

2007 (3)

J. A. Piper and H. M. Pask, “Crystalline Raman lasers,” IEEE Sel. Top. Quantum Electron. 13(3), 692–704 (2007).
[Crossref]

S. T. Li, X. Y. Zhang, Q. P. Wang, X. L. Zhang, Z. H. Cong, H. Zhang, and J. Wang, “Diode-side-pumped intracavity frequency-doubled Nd:YAG/BaWO4 Raman laser generating average output power of 3.14 W at 590 nm,” Opt. Lett. 32(20), 2951–2953 (2007).
[Crossref] [PubMed]

D. J. Spence, P. Dekker, and H. M. Pask, “Modeling of continuous wave intracavity Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 756–763 (2007).
[Crossref]

2006 (2)

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
[Crossref]

2005 (2)

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Y. F. Chen, K. W. Su, H. J. Zhang, J. Y. Wang, and M. H. Jiang, “Efficient diode-pumped actively Q-switched Nd:YAG/BaWO4 intracavity Raman laser,” Opt. Lett. 30(24), 3335–3337 (2005).
[Crossref]

2004 (2)

P. Cerny, H. Jelinkova, P. G. Zverev, and T. T. Basiev, “Solid state lasers with Raman frequency conversion,” Prog. Quantum Electron. 28(2), 113–143 (2004).
[Crossref]

Y. F. Chen, “Compact efficient all-solid-state eye-safe laser with self-frequency Raman conversion in a Nd:YVO4 crystal,” Opt. Lett. 29(18), 2172–2174 (2004).
[Crossref] [PubMed]

2003 (2)

H. M. Pask, “The design and operation of solid-state Raman lasers,” Prog. Quantum Electron. 27(1), 3–56 (2003).
[Crossref]

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

2002 (4)

X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).

P. Cerny, H. Jelinkova, T. T. Basiev, and P. G. Zverev, “Highly efficient picosecond Raman generators based on the BaWO4 crystal in the near infrared, visible, and ultraviolet,” IEEE J. Quantum Electron. 38(11), 1471–1478 (2002).
[Crossref]

P. Cerný and H. Jelínková, “Near-quantum-limit efficiency of picosecond stimulated Raman scattering in BaWO(4) crystal,” Opt. Lett. 27(5), 360-362 (2002).
[Crossref]

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun. 209(4-6), 403–409 (2002).
[Crossref]

2001 (1)

W. Chen, Y. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd:PbWO4 Raman laser,” Opt. Commun. 194(4-6), 401–407 (2001).
[Crossref]

2000 (1)

P. Cerny, P. G. Zverev, H. Jelinkova, and T. T. Basiev, “Efficient Raman shifting of picosecond pulses using BaWO4 crystals,” Opt. Commun. 177(1-6), 397 (2000).
[Crossref]

1971 (1)

J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18(3), 70 (1971).
[Crossref]

1970 (1)

R. G. Smith, “Theory of intracavity optical second harmonic generation,” IEEE J. Quantum Electron. 6(4), 215–223 (1970).
[Crossref]

Apanasevich, P. A.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Basiev, T. T.

P. Cerny, H. Jelinkova, P. G. Zverev, and T. T. Basiev, “Solid state lasers with Raman frequency conversion,” Prog. Quantum Electron. 28(2), 113–143 (2004).
[Crossref]

P. Cerny, H. Jelinkova, T. T. Basiev, and P. G. Zverev, “Highly efficient picosecond Raman generators based on the BaWO4 crystal in the near infrared, visible, and ultraviolet,” IEEE J. Quantum Electron. 38(11), 1471–1478 (2002).
[Crossref]

P. Cerny, P. G. Zverev, H. Jelinkova, and T. T. Basiev, “Efficient Raman shifting of picosecond pulses using BaWO4 crystals,” Opt. Commun. 177(1-6), 397 (2000).
[Crossref]

Batay, L. E.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Boughton, R. I.

J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
[Crossref]

Cerny, P.

P. Cerny, H. Jelinkova, P. G. Zverev, and T. T. Basiev, “Solid state lasers with Raman frequency conversion,” Prog. Quantum Electron. 28(2), 113–143 (2004).
[Crossref]

P. Cerny, H. Jelinkova, T. T. Basiev, and P. G. Zverev, “Highly efficient picosecond Raman generators based on the BaWO4 crystal in the near infrared, visible, and ultraviolet,” IEEE J. Quantum Electron. 38(11), 1471–1478 (2002).
[Crossref]

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun. 209(4-6), 403–409 (2002).
[Crossref]

P. Cerny, P. G. Zverev, H. Jelinkova, and T. T. Basiev, “Efficient Raman shifting of picosecond pulses using BaWO4 crystals,” Opt. Commun. 177(1-6), 397 (2000).
[Crossref]

Cerný, P.

Chang, J.

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

Chen, W.

W. Chen, Y. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd:PbWO4 Raman laser,” Opt. Commun. 194(4-6), 401–407 (2001).
[Crossref]

Chen, W. D.

Chen, Y. F.

Chen, Z. Q.

Cheng, X.

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Cong, Z. H.

Danailov, M. B.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Dekker, P.

H. M. Pask, P. Dekker, R. P. Mildren, D. J. Spence, and J. A. Piper, “Wavelength-versatile visible and UV sources based on crystalline Raman lasers,” Prog. Quantum Electron. 32(3-4), 121–158 (2008).
[Crossref]

A. J. Lee, H. M. Pask, P. Dekker, and J. A. Piper, “High efficiency, multi-Watt CW yellow emission from an intracavity-doubled self-Raman laser using Nd:GdVO4.,” Opt. Express 16(26), 21958–21963 (2008).
[Crossref] [PubMed]

D. J. Spence, P. Dekker, and H. M. Pask, “Modeling of continuous wave intracavity Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 756–763 (2007).
[Crossref]

Demidovich, A. A.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Ding, S. H.

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

Duan, Y. M.

Falk, J.

J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18(3), 70 (1971).
[Crossref]

Fan, J. D.

J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
[Crossref]

Fan, L.

Fan, S. Z.

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

Fan, Y. X.

Ge, W. W.

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Grabtchikov, A. S.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Hait, V. L.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Hitz, C. B.

J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18(3), 70 (1971).
[Crossref]

Hu, X.

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Huang, C. H.

Huang, L. X.

Huang, Y. D.

Inagawa, Y.

W. Chen, Y. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd:PbWO4 Raman laser,” Opt. Commun. 194(4-6), 401–407 (2001).
[Crossref]

Jabczynski, J.

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun. 209(4-6), 403–409 (2002).
[Crossref]

Jelinkova, H.

P. Cerny, H. Jelinkova, P. G. Zverev, and T. T. Basiev, “Solid state lasers with Raman frequency conversion,” Prog. Quantum Electron. 28(2), 113–143 (2004).
[Crossref]

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun. 209(4-6), 403–409 (2002).
[Crossref]

P. Cerny, H. Jelinkova, T. T. Basiev, and P. G. Zverev, “Highly efficient picosecond Raman generators based on the BaWO4 crystal in the near infrared, visible, and ultraviolet,” IEEE J. Quantum Electron. 38(11), 1471–1478 (2002).
[Crossref]

P. Cerny, P. G. Zverev, H. Jelinkova, and T. T. Basiev, “Efficient Raman shifting of picosecond pulses using BaWO4 crystals,” Opt. Commun. 177(1-6), 397 (2000).
[Crossref]

Jelínková, H.

Jia, P.

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

Jiang, M.

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Jiang, M. H.

J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
[Crossref]

Y. F. Chen, K. W. Su, H. J. Zhang, J. Y. Wang, and M. H. Jiang, “Efficient diode-pumped actively Q-switched Nd:YAG/BaWO4 intracavity Raman laser,” Opt. Lett. 30(24), 3335–3337 (2005).
[Crossref]

Kiefer, W.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Kopczynski, K.

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun. 209(4-6), 403–409 (2002).
[Crossref]

Kuzmin, A. N.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Kuzmin, O. V.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Lee, A. J.

Li, H.

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Li, J. F.

X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).

Li, P.

X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).

Li, S. T.

S. T. Li, X. Y. Zhang, Q. P. Wang, X. L. Zhang, Z. H. Cong, H. Zhang, and J. Wang, “Diode-side-pumped intracavity frequency-doubled Nd:YAG/BaWO4 Raman laser generating average output power of 3.14 W at 590 nm,” Opt. Lett. 32(20), 2951–2953 (2007).
[Crossref] [PubMed]

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

Li, Y. Q.

Lisinetskii, V. A.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Liu, J. H.

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Liu, Z. J.

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

Mildren, R. P.

H. M. Pask, P. Dekker, R. P. Mildren, D. J. Spence, and J. A. Piper, “Wavelength-versatile visible and UV sources based on crystalline Raman lasers,” Prog. Quantum Electron. 32(3-4), 121–158 (2008).
[Crossref]

Omatsu, T.

W. Chen, Y. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd:PbWO4 Raman laser,” Opt. Commun. 194(4-6), 401–407 (2001).
[Crossref]

Orlovich, V. A.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Pask, H. M.

A. J. Lee, H. M. Pask, J. A. Piper, H. J. Zhang, and J. Y. Wang, “An intracavity, frequency-doubled BaWO4 Raman laser generating multi-watt continuouswave, yellow emission,” Opt. Express 18(6), 5984–5992 (2010).
[Crossref] [PubMed]

A. J. Lee, H. M. Pask, P. Dekker, and J. A. Piper, “High efficiency, multi-Watt CW yellow emission from an intracavity-doubled self-Raman laser using Nd:GdVO4.,” Opt. Express 16(26), 21958–21963 (2008).
[Crossref] [PubMed]

H. M. Pask, P. Dekker, R. P. Mildren, D. J. Spence, and J. A. Piper, “Wavelength-versatile visible and UV sources based on crystalline Raman lasers,” Prog. Quantum Electron. 32(3-4), 121–158 (2008).
[Crossref]

J. A. Piper and H. M. Pask, “Crystalline Raman lasers,” IEEE Sel. Top. Quantum Electron. 13(3), 692–704 (2007).
[Crossref]

D. J. Spence, P. Dekker, and H. M. Pask, “Modeling of continuous wave intracavity Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 756–763 (2007).
[Crossref]

H. M. Pask, “The design and operation of solid-state Raman lasers,” Prog. Quantum Electron. 27(1), 3–56 (2003).
[Crossref]

Piper, J. A.

A. J. Lee, H. M. Pask, J. A. Piper, H. J. Zhang, and J. Y. Wang, “An intracavity, frequency-doubled BaWO4 Raman laser generating multi-watt continuouswave, yellow emission,” Opt. Express 18(6), 5984–5992 (2010).
[Crossref] [PubMed]

H. M. Pask, P. Dekker, R. P. Mildren, D. J. Spence, and J. A. Piper, “Wavelength-versatile visible and UV sources based on crystalline Raman lasers,” Prog. Quantum Electron. 32(3-4), 121–158 (2008).
[Crossref]

A. J. Lee, H. M. Pask, P. Dekker, and J. A. Piper, “High efficiency, multi-Watt CW yellow emission from an intracavity-doubled self-Raman laser using Nd:GdVO4.,” Opt. Express 16(26), 21958–21963 (2008).
[Crossref] [PubMed]

J. A. Piper and H. M. Pask, “Crystalline Raman lasers,” IEEE Sel. Top. Quantum Electron. 13(3), 692–704 (2007).
[Crossref]

Ran, D. G.

J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
[Crossref]

Ren, C.

X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).

Shen, H. Y.

Smith, R. G.

R. G. Smith, “Theory of intracavity optical second harmonic generation,” IEEE J. Quantum Electron. 6(4), 215–223 (1970).
[Crossref]

Spence, D. J.

H. M. Pask, P. Dekker, R. P. Mildren, D. J. Spence, and J. A. Piper, “Wavelength-versatile visible and UV sources based on crystalline Raman lasers,” Prog. Quantum Electron. 32(3-4), 121–158 (2008).
[Crossref]

D. J. Spence, P. Dekker, and H. M. Pask, “Modeling of continuous wave intracavity Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 756–763 (2007).
[Crossref]

Su, F. F.

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

Su, K. W.

Sulc, J.

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun. 209(4-6), 403–409 (2002).
[Crossref]

Sun, S. Q.

J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
[Crossref]

Takeuchi, N.

W. Chen, Y. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd:PbWO4 Raman laser,” Opt. Commun. 194(4-6), 401–407 (2001).
[Crossref]

Tateda, M.

W. Chen, Y. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd:PbWO4 Raman laser,” Opt. Commun. 194(4-6), 401–407 (2001).
[Crossref]

Usuki, Y.

W. Chen, Y. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd:PbWO4 Raman laser,” Opt. Commun. 194(4-6), 401–407 (2001).
[Crossref]

Wang, H. T.

Wang, J.

Wang, J. Y.

Wang, Q.

Wang, Q. P.

S. T. Li, X. Y. Zhang, Q. P. Wang, X. L. Zhang, Z. H. Cong, H. Zhang, and J. Wang, “Diode-side-pumped intracavity frequency-doubled Nd:YAG/BaWO4 Raman laser generating average output power of 3.14 W at 590 nm,” Opt. Lett. 32(20), 2951–2953 (2007).
[Crossref] [PubMed]

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).

Wang, Y. J.

J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
[Crossref]

Wei, Y.

Xia, H. R.

J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
[Crossref]

Xu, H.

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Xu, X.

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Yarborough, J. M.

J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18(3), 70 (1971).
[Crossref]

Ye, N.

Zendzian, W.

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun. 209(4-6), 403–409 (2002).
[Crossref]

Zhang, G.

Zhang, H.

Zhang, H. J.

A. J. Lee, H. M. Pask, J. A. Piper, H. J. Zhang, and J. Y. Wang, “An intracavity, frequency-doubled BaWO4 Raman laser generating multi-watt continuouswave, yellow emission,” Opt. Express 18(6), 5984–5992 (2010).
[Crossref] [PubMed]

J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
[Crossref]

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Y. F. Chen, K. W. Su, H. J. Zhang, J. Y. Wang, and M. H. Jiang, “Efficient diode-pumped actively Q-switched Nd:YAG/BaWO4 intracavity Raman laser,” Opt. Lett. 30(24), 3335–3337 (2005).
[Crossref]

Zhang, S. S.

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

Zhang, X. L.

Zhang, X. Y.

S. T. Li, X. Y. Zhang, Q. P. Wang, X. L. Zhang, Z. H. Cong, H. Zhang, and J. Wang, “Diode-side-pumped intracavity frequency-doubled Nd:YAG/BaWO4 Raman laser generating average output power of 3.14 W at 590 nm,” Opt. Lett. 32(20), 2951–2953 (2007).
[Crossref] [PubMed]

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).

Zhao, S. Z.

X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).

Zheng, J. A.

X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).

Zheng, Y. Q.

Zhu, H. Y.

Zverev, P. G.

P. Cerny, H. Jelinkova, P. G. Zverev, and T. T. Basiev, “Solid state lasers with Raman frequency conversion,” Prog. Quantum Electron. 28(2), 113–143 (2004).
[Crossref]

P. Cerny, H. Jelinkova, T. T. Basiev, and P. G. Zverev, “Highly efficient picosecond Raman generators based on the BaWO4 crystal in the near infrared, visible, and ultraviolet,” IEEE J. Quantum Electron. 38(11), 1471–1478 (2002).
[Crossref]

P. Cerny, P. G. Zverev, H. Jelinkova, and T. T. Basiev, “Efficient Raman shifting of picosecond pulses using BaWO4 crystals,” Opt. Commun. 177(1-6), 397 (2000).
[Crossref]

Appl. Phys. B (1)

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B 76, 509 (2003).

Appl. Phys. Lett. (1)

J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18(3), 70 (1971).
[Crossref]

IEEE J. Quantum Electron. (3)

S. H. Ding, X. Y. Zhang, Q. P. Wang, F. F. Su, P. Jia, S. T. Li, S. Z. Fan, J. Chang, S. S. Zhang, and Z. J. Liu, “Theoretical and experimental study on the self-Raman laser with Nd:YVO4 crystal,” IEEE J. Quantum Electron. 42, 927- 933 (2006).
[Crossref]

R. G. Smith, “Theory of intracavity optical second harmonic generation,” IEEE J. Quantum Electron. 6(4), 215–223 (1970).
[Crossref]

P. Cerny, H. Jelinkova, T. T. Basiev, and P. G. Zverev, “Highly efficient picosecond Raman generators based on the BaWO4 crystal in the near infrared, visible, and ultraviolet,” IEEE J. Quantum Electron. 38(11), 1471–1478 (2002).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

D. J. Spence, P. Dekker, and H. M. Pask, “Modeling of continuous wave intracavity Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 756–763 (2007).
[Crossref]

IEEE Sel. Top. Quantum Electron. (1)

J. A. Piper and H. M. Pask, “Crystalline Raman lasers,” IEEE Sel. Top. Quantum Electron. 13(3), 692–704 (2007).
[Crossref]

J. Appl. Phys. (1)

J. D. Fan, H. J. Zhang, Y. J. Wang, M. H. Jiang, R. I. Boughton, D. G. Ran, S. Q. Sun, and H. R. Xia, “Growth and thermal properties of SrWO4 single crystal,” J. Appl. Phys. 100(6), 063513 (2006).
[Crossref]

J. Cryst. Growth (1)

W. W. Ge, H. J. Zhang, J. Y. Wang, J. H. Liu, H. Li, X. Cheng, H. Xu, X. Xu, X. Hu, and M. Jiang, “The thermal and optical properties of BaWO4 single crystal,” J. Cryst. Growth 276(1-2), 208–214 (2005).
[Crossref]

Opt. Commun. (3)

W. Chen, Y. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd:PbWO4 Raman laser,” Opt. Commun. 194(4-6), 401–407 (2001).
[Crossref]

P. Cerny, P. G. Zverev, H. Jelinkova, and T. T. Basiev, “Efficient Raman shifting of picosecond pulses using BaWO4 crystals,” Opt. Commun. 177(1-6), 397 (2000).
[Crossref]

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun. 209(4-6), 403–409 (2002).
[Crossref]

Opt. Express (3)

Opt. Lett. (6)

Prog. Quantum Electron. (3)

H. M. Pask, P. Dekker, R. P. Mildren, D. J. Spence, and J. A. Piper, “Wavelength-versatile visible and UV sources based on crystalline Raman lasers,” Prog. Quantum Electron. 32(3-4), 121–158 (2008).
[Crossref]

H. M. Pask, “The design and operation of solid-state Raman lasers,” Prog. Quantum Electron. 27(1), 3–56 (2003).
[Crossref]

P. Cerny, H. Jelinkova, P. G. Zverev, and T. T. Basiev, “Solid state lasers with Raman frequency conversion,” Prog. Quantum Electron. 28(2), 113–143 (2004).
[Crossref]

Sci. China Ser. F (1)

X. Y. Zhang, Q. P. Wang, S. Z. Zhao, J. F. Li, P. Li, C. Ren, and J. A. Zheng, “Theory of intracavity-frequency-doubled solid state four level lasers,” Sci. China Ser. F 45, 130 (2002).

Other (1)

W. Koechner, Solid-state laser engineering, Springer Series in Optical Sciences, Springer, Berlin, 1999, fifth revised and updated edition.

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Figures (4)

Fig. 1
Fig. 1 Experimental arrangement of the side-pumped actively Q-switched intracavity KTP frequency doubled Nd:YAG/BaWO4 Raman laser.
Fig. 2
Fig. 2 Average output power of the 590 nm laser with respect to the pump power at PRFs of 10, 15 and 20 kHz. The solid symbols are the experimental results, the lines are theoretical results.
Fig. 3
Fig. 3 The pulse width of the 590 nm laser with respect to the pump power at PRFs of 10, 15 and 20 kHz.
Fig. 4
Fig. 4 The oscilloscope trace for the 1180 nm and 590 nm laser pulses with a 125.8 W pump power and a 15 kHz PRF.

Tables (1)

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Table 1 Parameters for the theoretical calculation

Equations (26)

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ϕ L L ( r , t ) = ϕ L L ( 0 , t ) exp ( 2 r 2 ω L L 2 )
ϕ L R ( r , t ) = ϕ L R ( 0 , t ) exp ( 2 r 2 ω L R 2 )
ϕ R R ( r , t ) = ϕ R R ( 0 , t ) exp ( 2 r 2 ω R R 2 )
ϕ R K ( r , t ) = ϕ R K ( 0 , t ) exp ( 2 r 2 ω R K 2 )
ω L L 2 ϕ L L ( 0 , t ) = ω L R 2 ϕ L R ( 0 , t )
ω R R 2 ϕ R R ( 0 , t ) = ω R K 2 ϕ R K ( 0 , t )
n ( r , 0 ) = n ( 0 , 0 ) exp ( 2 r 2 ω P 2 )
P S H = ρ π η [ c h ν R ϕ R R ( 0 , t ) ] 2 ω R R 4 16 ω R K 2
η = ω 2 d e f f 2 l K 2 c 3 ε 0 n o 2 ω n o ω n e ω sin 2 ( l K Δ k / 2 ) ( l K Δ k / 2 ) 2
P S H = h ν R l C 0 d ϕ R R ( r , t ) d t | S H G 2 π r d r
0 d ϕ R R ( r , t ) d t | S H G 2 π r d r = ρ π η h ν R [ c ϕ R R ( 0 , t ) ] 2 ω R R 4 16 ω R K 2 l C
0 d ϕ L L ( r , t ) d t 2 π r d r = 1 t r 0 [ 2 σ n ( r , t ) ϕ L L ( r , t ) l 2 g h ν R c l R ϕ L R ( r , t ) ϕ R R ( r , t ) ] 2 π r d r
1 t L 0 ϕ L L ( r , t ) 2 π r d r
+ k s p 0 ϕ L R ( r , t ) 2 π r d r 0 d φ R R ( r , t ) d t | S H G 2 π r d r
d n ( r , t ) d t = γ σ c ϕ L L ( r , t ) n ( r , t ) n ( r , t ) τ
n ( r , t ) = n ( 0 , 0 ) exp ( 2 r 2 ω P 2 ) exp [ γ σ c exp ( 2 r 2 ω L L 2 ) 0 t ϕ L L ( 0 , t ) d t t τ ]
d ϕ L L ( 0 , t ) d t = 4 σ l ω L L 2 t r ϕ L L ( 0 , t ) n ( 0 , t ) 0 { exp [ 2 r 2 ( 1 ω P 2 + 1 ω L L 2 ) ] exp [ γ σ c exp ( 2 r 2 ω L L 2 ) 0 t ϕ L L ( 0 , t ) d t t τ ] } 2 π r d r
2 g h ν R c l R t r ω R R 2 ω L R 2 + ω R R 2 ϕ L L ( 0 , t ) ϕ R R ( 0 , t ) ϕ L L ( 0 , t ) t L
d ϕ R R ( 0 , t ) d t = 2 g h ν R c l R ϕ L L ( 0 , t ) ϕ R R ( 0 , t ) t r ω L L 2 ω R R 2 ω L R 2 ω L L 2 + ω L R 2 ϕ R R ( 0 , t ) t R
+ k s p ω L L 2 ω R R 2 ϕ L L ( 0 , t ) ρ η h ν R c 2 8 l C ω R R 2 ω R K 2 ϕ R R 2 ( 0 , t )
ρ = 1 + M 2 + 2 M cos θ
ρ = 1 2 π 0 2 π ( 1 + M 2 + 2 M cos θ ) d θ = 1 + M 2
E S H 2 = ( 1 R Y ) 0 h ν R l C 0 d φ R R ( r , t ) d t | S H G 2 π r d r d t
= ( 1 + M 2 ) ( 1 R Y ) π η ( c h ν R ) 2 16 ω R R 4 ω R K 2 0 ϕ R R 2 ( 0 , t ) d t
P S H 2 = f P E S H 2 = f P ( 1 + M 2 ) ( 1 R Y ) π η ( c h ν R ) 2 16 ω R R 4 ω R K 2 0 ϕ R R 2 ( 0 , t ) d t
1 f = 1 2 d n d T P h e a t K C A

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