Abstract

A modified steady-state laser theory that describes a continuous wave (cw) off-resonant Raman laser with asymmetric reflectivities for the cavity is presented. This theory takes into account different mirror reflectivities of the front and back mirrors of the Raman laser cavity for both the pump and the Stokes wavelengths. An off-resonant cw Raman laser pumped at 795 nm in diatomic hydrogen (H2) is modeled by use of the results of the steady-state theory. The predicted threshold for the cw Raman laser is 2.4 mW, and a maximum Stokes photon conversion efficiency of 83.0% is predicted for a pump power of 9.9 mW. The high Stokes photon conversion efficiency is obtained with mismatched pump-wavelength reflectivities of the front and the back mirrors of the laser cavity. By a judicious choice of mirror reflectivities, both the backreflected pump power and the transmitted pump power can be minimized, thus making a maximum amount of pump power available for nonlinear Stokes conversion.

© 1999 Optical Society of America

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References

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  1. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).
  2. N. Bloemberg, “The stimulated Raman effect,” Am. J. Phys. 35, 989 (1967).
    [CrossRef]
  3. P. Rabinowitz, A. Stein, R. Brickman, and A. Kaldor, “Efficient tunable H2 Raman lasers,” Appl. Phys. Lett. 35, 739 (1979).
    [CrossRef]
  4. L. A. Harris and J. N. Lavinos, “Generation of nanosecond infrared pulses tunable from 2.8 μm to 16 μm by efficient stimulated electronic Raman scattering,” Appl. Opt. 26, 3996 (1987).
    [CrossRef] [PubMed]
  5. J. L. Carlsten and R. G. Wenzel, “Stimulated Raman scattering in CO2-pumped para H2,” IEEE J. Quantum Electron. QE-19, 1407 (1983).
    [CrossRef]
  6. R. Max, U. Huber, I. Abdul-Halim, J. Heppner, Y. Ni, G. Willenberg, and C. O. Weiss, “Far infrared cw Raman laser gain in 14NH3,” IEEE J. Quantum Electron. QE-17, 1123 (1981).
  7. M. Poelker and P. Kumar, “Sodium Raman laser: direct measurement of narrowband Raman laser gain,” Opt. Lett. 17, 399 (1992).
    [CrossRef] [PubMed]
  8. S. N. Jabr, “Gain and noise characteristics of a continuous-wave Raman laser,” Opt. Lett. 12, 690 (1987).
    [CrossRef] [PubMed]
  9. J. K. Brasseur, K. S. Repasky, and J. L. Carlsten, “Continuous-wave Raman laser in H2,” Opt. Lett. 23, 367 (1998).
    [CrossRef]
  10. K. S. Repasky, J. K. Brasseur, L. Meng, and J. L. Carlsten, “Performance and design of an off resonant continuous-wave Raman laser,” J. Opt. Soc. Am. B 15, 1667 (1998).
    [CrossRef]
  11. A. Fried, D. K. Killinger, and H. I. Schiff, eds., Tunable Laser Spectroscopy, Lidar, and Dial Techniques for Environmental and Industrial Measurements, Proc. SPIE 2112 (1993).
  12. W. K. Bischel and M. J. Dyer, “Temperature dependence of the Raman linewidth and lineshift for the Q(0)–Q(1) transition in normal and para H2,” Phys. Rev. A 33, 3113 (1986).
    [CrossRef] [PubMed]
  13. J. J. Ottusch and D. A. Rockwell, “Measurements of Raman gain coefficients in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076 (1989).
    [CrossRef]
  14. W. K. Bischel and M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficients for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677 (1986).
    [CrossRef]
  15. Research ElectroOptics Inc, 1855 South 57th court, Boulder, Colo. 80301 can produce the mirrors with the reflectivities used in this paper.

1998 (2)

1992 (1)

1989 (1)

J. J. Ottusch and D. A. Rockwell, “Measurements of Raman gain coefficients in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076 (1989).
[CrossRef]

1987 (2)

1986 (2)

W. K. Bischel and M. J. Dyer, “Temperature dependence of the Raman linewidth and lineshift for the Q(0)–Q(1) transition in normal and para H2,” Phys. Rev. A 33, 3113 (1986).
[CrossRef] [PubMed]

W. K. Bischel and M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficients for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677 (1986).
[CrossRef]

1983 (1)

J. L. Carlsten and R. G. Wenzel, “Stimulated Raman scattering in CO2-pumped para H2,” IEEE J. Quantum Electron. QE-19, 1407 (1983).
[CrossRef]

1981 (1)

R. Max, U. Huber, I. Abdul-Halim, J. Heppner, Y. Ni, G. Willenberg, and C. O. Weiss, “Far infrared cw Raman laser gain in 14NH3,” IEEE J. Quantum Electron. QE-17, 1123 (1981).

1979 (1)

P. Rabinowitz, A. Stein, R. Brickman, and A. Kaldor, “Efficient tunable H2 Raman lasers,” Appl. Phys. Lett. 35, 739 (1979).
[CrossRef]

1967 (1)

N. Bloemberg, “The stimulated Raman effect,” Am. J. Phys. 35, 989 (1967).
[CrossRef]

Abdul-Halim, I.

R. Max, U. Huber, I. Abdul-Halim, J. Heppner, Y. Ni, G. Willenberg, and C. O. Weiss, “Far infrared cw Raman laser gain in 14NH3,” IEEE J. Quantum Electron. QE-17, 1123 (1981).

Bischel, W. K.

W. K. Bischel and M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficients for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677 (1986).
[CrossRef]

W. K. Bischel and M. J. Dyer, “Temperature dependence of the Raman linewidth and lineshift for the Q(0)–Q(1) transition in normal and para H2,” Phys. Rev. A 33, 3113 (1986).
[CrossRef] [PubMed]

Bloemberg, N.

N. Bloemberg, “The stimulated Raman effect,” Am. J. Phys. 35, 989 (1967).
[CrossRef]

Brasseur, J. K.

Brickman, R.

P. Rabinowitz, A. Stein, R. Brickman, and A. Kaldor, “Efficient tunable H2 Raman lasers,” Appl. Phys. Lett. 35, 739 (1979).
[CrossRef]

Carlsten, J. L.

Dyer, M. J.

W. K. Bischel and M. J. Dyer, “Temperature dependence of the Raman linewidth and lineshift for the Q(0)–Q(1) transition in normal and para H2,” Phys. Rev. A 33, 3113 (1986).
[CrossRef] [PubMed]

W. K. Bischel and M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficients for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677 (1986).
[CrossRef]

Harris, L. A.

Heppner, J.

R. Max, U. Huber, I. Abdul-Halim, J. Heppner, Y. Ni, G. Willenberg, and C. O. Weiss, “Far infrared cw Raman laser gain in 14NH3,” IEEE J. Quantum Electron. QE-17, 1123 (1981).

Huber, U.

R. Max, U. Huber, I. Abdul-Halim, J. Heppner, Y. Ni, G. Willenberg, and C. O. Weiss, “Far infrared cw Raman laser gain in 14NH3,” IEEE J. Quantum Electron. QE-17, 1123 (1981).

Jabr, S. N.

Kaldor, A.

P. Rabinowitz, A. Stein, R. Brickman, and A. Kaldor, “Efficient tunable H2 Raman lasers,” Appl. Phys. Lett. 35, 739 (1979).
[CrossRef]

Kumar, P.

Lavinos, J. N.

Max, R.

R. Max, U. Huber, I. Abdul-Halim, J. Heppner, Y. Ni, G. Willenberg, and C. O. Weiss, “Far infrared cw Raman laser gain in 14NH3,” IEEE J. Quantum Electron. QE-17, 1123 (1981).

Meng, L.

Ni, Y.

R. Max, U. Huber, I. Abdul-Halim, J. Heppner, Y. Ni, G. Willenberg, and C. O. Weiss, “Far infrared cw Raman laser gain in 14NH3,” IEEE J. Quantum Electron. QE-17, 1123 (1981).

Ottusch, J. J.

J. J. Ottusch and D. A. Rockwell, “Measurements of Raman gain coefficients in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076 (1989).
[CrossRef]

Poelker, M.

Rabinowitz, P.

P. Rabinowitz, A. Stein, R. Brickman, and A. Kaldor, “Efficient tunable H2 Raman lasers,” Appl. Phys. Lett. 35, 739 (1979).
[CrossRef]

Repasky, K. S.

Rockwell, D. A.

J. J. Ottusch and D. A. Rockwell, “Measurements of Raman gain coefficients in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076 (1989).
[CrossRef]

Stein, A.

P. Rabinowitz, A. Stein, R. Brickman, and A. Kaldor, “Efficient tunable H2 Raman lasers,” Appl. Phys. Lett. 35, 739 (1979).
[CrossRef]

Weiss, C. O.

R. Max, U. Huber, I. Abdul-Halim, J. Heppner, Y. Ni, G. Willenberg, and C. O. Weiss, “Far infrared cw Raman laser gain in 14NH3,” IEEE J. Quantum Electron. QE-17, 1123 (1981).

Wenzel, R. G.

J. L. Carlsten and R. G. Wenzel, “Stimulated Raman scattering in CO2-pumped para H2,” IEEE J. Quantum Electron. QE-19, 1407 (1983).
[CrossRef]

Willenberg, G.

R. Max, U. Huber, I. Abdul-Halim, J. Heppner, Y. Ni, G. Willenberg, and C. O. Weiss, “Far infrared cw Raman laser gain in 14NH3,” IEEE J. Quantum Electron. QE-17, 1123 (1981).

Am. J. Phys. (1)

N. Bloemberg, “The stimulated Raman effect,” Am. J. Phys. 35, 989 (1967).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. Rabinowitz, A. Stein, R. Brickman, and A. Kaldor, “Efficient tunable H2 Raman lasers,” Appl. Phys. Lett. 35, 739 (1979).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. L. Carlsten and R. G. Wenzel, “Stimulated Raman scattering in CO2-pumped para H2,” IEEE J. Quantum Electron. QE-19, 1407 (1983).
[CrossRef]

R. Max, U. Huber, I. Abdul-Halim, J. Heppner, Y. Ni, G. Willenberg, and C. O. Weiss, “Far infrared cw Raman laser gain in 14NH3,” IEEE J. Quantum Electron. QE-17, 1123 (1981).

J. J. Ottusch and D. A. Rockwell, “Measurements of Raman gain coefficients in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076 (1989).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (3)

Phys. Rev. A (1)

W. K. Bischel and M. J. Dyer, “Temperature dependence of the Raman linewidth and lineshift for the Q(0)–Q(1) transition in normal and para H2,” Phys. Rev. A 33, 3113 (1986).
[CrossRef] [PubMed]

Other (3)

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

Research ElectroOptics Inc, 1855 South 57th court, Boulder, Colo. 80301 can produce the mirrors with the reflectivities used in this paper.

A. Fried, D. K. Killinger, and H. I. Schiff, eds., Tunable Laser Spectroscopy, Lidar, and Dial Techniques for Environmental and Industrial Measurements, Proc. SPIE 2112 (1993).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the pump fields reflected from and between and transmitted through the mirrors of the Raman laser cavity.

Fig. 2
Fig. 2

Plot of the Stokes photon conversion efficiency as a function of the input pump power. The dashed curve represents the matched-mirror case, and the solid curve represents the mismatched-mirror case. A maximum Stokes photon conversion efficiency of 83.0% and a threshold of 2.4 mW for the mismatched-mirror case is predicted.

Fig. 3
Fig. 3

Plot of the reflected pump power as a function of the input pump power. The dashed curve represents the matched-mirror case, and the solid curve represents the matched-mirror case. The reflected pump power is not available for Stokes conversion, so for maximum conversion efficiency the reflected pump power needs to be a minimum.

Fig. 4
Fig. 4

Plot of the transmitted pump power as a function of the input pump power. The dashed curve represents the matched-mirror case, and the solid curve represents the mismatched-mirror case. The reduction of the transmitted pump power for the mismatched-mirror translates to higher Stokes photon conversion efficiencies.

Tables (1)

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Table 1 Effects of Front Mirror Reflectivity at the Pump Wavelength

Equations (8)

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Πp=Pod2T1p[1+(R2p)1/2]2[1-(R1p R2p)1/2]2,
Πp=(λs+λp)ln(1/R1s R2s)8αg tan-1(l/b),
d2=ln(1/R1s R2s)(λs+λp)[1-(R1p R2p)1/2]28αg tan-1(l/b)T1p[1+(R2p)1/2]21Po.
Pp=PodT1p(R2p)1/21[1-(R1pR2p)1/2]-(R1p)1/22+PoT1pT2pd21[1-(R1pR2p)1/2]2.
Δ=PoA1p+A1pT1pR2pd21[1-(R1p R2p)1/2]2+A2pT1pd21[1-(R1pR2p)1/2]2.
Ps=1-A1s+A2s2-R1s-R2sλpλs(Po-Pp-Δ),
Cph=λsλpPsPo.
Ps(back)=T2sT1s+T2sPs.

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