Abstract

We derive self-contained, analytic expressions for the emitted Stokes and pump powers from a low-power, cw Raman laser. In addition to facilitating the physical understanding of these systems, the expressions lead to the conditions for laser threshold and impedance matching. Moreover, they provide the starting point for optimizing the device efficiency with respect to input pump power, mirror transmissions, two-photon detuning, and cavity geometry. We obtain simple, analytic expressions for the optimization conditions while retaining sufficient generality to include asymmetric mirror coatings as well as absorptions. These mathematical guidelines are balanced with practical issues to yield the most advantageous system operation parameters.

© 2002 Optical Society of America

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  1. J. K. Brasseur, K. S. Repasky, and J. L. Carlsten, “Continuous-wave Raman laser in H2,” Opt. Lett. 23, 367–369 (1998).
    [CrossRef]
  2. J. K. Brasseur, P. A. Roos, K. S. Repasky, and J. L. Carlsten, “Characterization of a continuous wave Raman laser in H2,” J. Opt. Soc. Am. B 16, 1305–1312 (1999).
    [CrossRef]
  3. P. A. Roos, J. K. Brasseur, and J. L. Carlsten, “Diode-pumped nonresonant continuous-wave Raman laser in H2 with resonant optical feedback stabilization,” Opt. Lett. 24, 1130–1132 (1999).
    [CrossRef]
  4. L. S. Meng, K. S. Repasky, P. A. Roos, and J. L. Carlsten, “Widely tunable continuous-wave Raman laser in H2 pumped by an external cavity diode laser,” Opt. Lett. 25, 472–474 (2000).
    [CrossRef]
  5. J. K. Brasseur, P. A. Roos, L. S. Meng, and J. L. Carlsten, “Frequency tuning characteristics of a continuous-wave Raman laser in H2,” J. Opt. Soc. Am. B 17, 1229–1232 (2000).
    [CrossRef]
  6. G. D. Boyd, W. D. Johnston, Jr., and I. P. Kaminow, “Optimization of the stimulated Raman scattering threshold,” IEEE J. Quantum Electron. QE-5, 203–206 (1969).
    [CrossRef]
  7. K. S. Repasky, J. K. Brasseur, L. S. Meng, and J. L. Carlsten, “Performance and design of an off-resonant continuous-wave Raman laser,” J. Opt. Soc. Am. B 15, 1667–1673 (1998).
    [CrossRef]
  8. K. S. Repasky, L. S. Meng, J. K. Brasseur, J. L. Carlsten, and R. C. Swanson, “High-efficiency, continuous-wave Raman lasers,” J. Opt. Soc. Am. B 16, 717–721 (1999).
    [CrossRef]
  9. S. Rebic, A. S. Parkins, and D. F. Walls, “Transfer of photon statistics in a Raman laser,” Opt. Commun. 156, 426–434 (1998).
    [CrossRef]
  10. P. Peterson, A. Gavrielides, and M. P. Sharma, “Modeling of high finesse, doubly resonant cw Raman lasers,” Opt. Commun. 160, 80–85 (1999).
    [CrossRef]
  11. A. E. Siegman, “Nonlinear optical effects: an optical power limiter,” Appl. Opt. 1, 739–744 (1962).
    [CrossRef]
  12. W. E. Lamb, Jr., “Theory of an optical maser,” Phys. Rev. 134, A1429–A1450 (1964).
    [CrossRef]
  13. H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562–1569 (1965).
    [CrossRef]
  14. B. N. Perry, P. Rabinowitz, and M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2001 (1983).
    [CrossRef]
  15. J. Bienfang, W. Rudolph, P. A. Roos, L. S. Meng, and J. L. Carlsten, “Steady state thermo-optic model of a continuous-wave Raman laser,” J. Opt. Soc. Am. B (to be published).
  16. W. K. Bischel and M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677–682 (1986).
    [CrossRef]
  17. P. Rabinowitz, A. Stein, R. Brickman, and A. Kaldor, “Stimulated rotational Raman scattering from para-H2 pumped by a CO2 TEA laser,” Opt. Lett. 3, 147–148 (1978).
    [CrossRef] [PubMed]
  18. M. K. Oshman and S. E. Harris, “Theory of optical parametric oscillation internal to the laser cavity,” IEEE J. Quantum Electron. QE-4, 491–502 (1968).
    [CrossRef]
  19. D. Jacob, M. Vallet, F. Bretenker, and A. Le Floch, “Supermirror phase anisotropy measurement,” Opt. Lett.. 20, 671–673 (1995).
    [CrossRef] [PubMed]
  20. P. A. Roos, J. K. Brasseur, and J. L. Carlsten, “Intensity-dependent refractive index in a nonresonant cw Raman laser that is due to thermal heating of the Raman-active gas,” J. Opt. Soc. Am. B 17, 758–763 (2000).
    [CrossRef]
  21. J. K. Brasseur, R. T. Teehan, R. J. Knize, P. A. Roos, and J. L. Carlsten, “Phase and frequency stabilization of a pump laser to a Raman active resonator,” IEEE J. Quantum Electron. 37, 1075–1083 (2001).
    [CrossRef]
  22. J. R. Murray and A. Javan, “Effects of collisions on Raman line profiles of hydrogen and deuterium gas,” J. Mol. Spectrosc. 42, 1–26 (1972).
    [CrossRef]
  23. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989) pp. 143–146.
  24. D. Zwillinger, ed., Standard Mathematical Tables and Formulae, 30th ed. (CRC, New York, 1996), p. 467.

2001

J. K. Brasseur, R. T. Teehan, R. J. Knize, P. A. Roos, and J. L. Carlsten, “Phase and frequency stabilization of a pump laser to a Raman active resonator,” IEEE J. Quantum Electron. 37, 1075–1083 (2001).
[CrossRef]

2000

1999

1998

1995

D. Jacob, M. Vallet, F. Bretenker, and A. Le Floch, “Supermirror phase anisotropy measurement,” Opt. Lett.. 20, 671–673 (1995).
[CrossRef] [PubMed]

1986

1983

B. N. Perry, P. Rabinowitz, and M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2001 (1983).
[CrossRef]

1978

1972

J. R. Murray and A. Javan, “Effects of collisions on Raman line profiles of hydrogen and deuterium gas,” J. Mol. Spectrosc. 42, 1–26 (1972).
[CrossRef]

1969

G. D. Boyd, W. D. Johnston, Jr., and I. P. Kaminow, “Optimization of the stimulated Raman scattering threshold,” IEEE J. Quantum Electron. QE-5, 203–206 (1969).
[CrossRef]

1968

M. K. Oshman and S. E. Harris, “Theory of optical parametric oscillation internal to the laser cavity,” IEEE J. Quantum Electron. QE-4, 491–502 (1968).
[CrossRef]

1965

1964

W. E. Lamb, Jr., “Theory of an optical maser,” Phys. Rev. 134, A1429–A1450 (1964).
[CrossRef]

1962

Bischel, W. K.

Boyd, G. D.

G. D. Boyd, W. D. Johnston, Jr., and I. P. Kaminow, “Optimization of the stimulated Raman scattering threshold,” IEEE J. Quantum Electron. QE-5, 203–206 (1969).
[CrossRef]

Brasseur, J. K.

J. K. Brasseur, R. T. Teehan, R. J. Knize, P. A. Roos, and J. L. Carlsten, “Phase and frequency stabilization of a pump laser to a Raman active resonator,” IEEE J. Quantum Electron. 37, 1075–1083 (2001).
[CrossRef]

P. A. Roos, J. K. Brasseur, and J. L. Carlsten, “Intensity-dependent refractive index in a nonresonant cw Raman laser that is due to thermal heating of the Raman-active gas,” J. Opt. Soc. Am. B 17, 758–763 (2000).
[CrossRef]

J. K. Brasseur, P. A. Roos, L. S. Meng, and J. L. Carlsten, “Frequency tuning characteristics of a continuous-wave Raman laser in H2,” J. Opt. Soc. Am. B 17, 1229–1232 (2000).
[CrossRef]

J. K. Brasseur, P. A. Roos, K. S. Repasky, and J. L. Carlsten, “Characterization of a continuous wave Raman laser in H2,” J. Opt. Soc. Am. B 16, 1305–1312 (1999).
[CrossRef]

P. A. Roos, J. K. Brasseur, and J. L. Carlsten, “Diode-pumped nonresonant continuous-wave Raman laser in H2 with resonant optical feedback stabilization,” Opt. Lett. 24, 1130–1132 (1999).
[CrossRef]

K. S. Repasky, L. S. Meng, J. K. Brasseur, J. L. Carlsten, and R. C. Swanson, “High-efficiency, continuous-wave Raman lasers,” J. Opt. Soc. Am. B 16, 717–721 (1999).
[CrossRef]

J. K. Brasseur, K. S. Repasky, and J. L. Carlsten, “Continuous-wave Raman laser in H2,” Opt. Lett. 23, 367–369 (1998).
[CrossRef]

K. S. Repasky, J. K. Brasseur, L. S. Meng, and J. L. Carlsten, “Performance and design of an off-resonant continuous-wave Raman laser,” J. Opt. Soc. Am. B 15, 1667–1673 (1998).
[CrossRef]

Bretenker, F.

D. Jacob, M. Vallet, F. Bretenker, and A. Le Floch, “Supermirror phase anisotropy measurement,” Opt. Lett.. 20, 671–673 (1995).
[CrossRef] [PubMed]

Brickman, R.

Carlsten, J. L.

J. K. Brasseur, R. T. Teehan, R. J. Knize, P. A. Roos, and J. L. Carlsten, “Phase and frequency stabilization of a pump laser to a Raman active resonator,” IEEE J. Quantum Electron. 37, 1075–1083 (2001).
[CrossRef]

L. S. Meng, K. S. Repasky, P. A. Roos, and J. L. Carlsten, “Widely tunable continuous-wave Raman laser in H2 pumped by an external cavity diode laser,” Opt. Lett. 25, 472–474 (2000).
[CrossRef]

P. A. Roos, J. K. Brasseur, and J. L. Carlsten, “Intensity-dependent refractive index in a nonresonant cw Raman laser that is due to thermal heating of the Raman-active gas,” J. Opt. Soc. Am. B 17, 758–763 (2000).
[CrossRef]

J. K. Brasseur, P. A. Roos, L. S. Meng, and J. L. Carlsten, “Frequency tuning characteristics of a continuous-wave Raman laser in H2,” J. Opt. Soc. Am. B 17, 1229–1232 (2000).
[CrossRef]

J. K. Brasseur, P. A. Roos, K. S. Repasky, and J. L. Carlsten, “Characterization of a continuous wave Raman laser in H2,” J. Opt. Soc. Am. B 16, 1305–1312 (1999).
[CrossRef]

P. A. Roos, J. K. Brasseur, and J. L. Carlsten, “Diode-pumped nonresonant continuous-wave Raman laser in H2 with resonant optical feedback stabilization,” Opt. Lett. 24, 1130–1132 (1999).
[CrossRef]

K. S. Repasky, L. S. Meng, J. K. Brasseur, J. L. Carlsten, and R. C. Swanson, “High-efficiency, continuous-wave Raman lasers,” J. Opt. Soc. Am. B 16, 717–721 (1999).
[CrossRef]

J. K. Brasseur, K. S. Repasky, and J. L. Carlsten, “Continuous-wave Raman laser in H2,” Opt. Lett. 23, 367–369 (1998).
[CrossRef]

K. S. Repasky, J. K. Brasseur, L. S. Meng, and J. L. Carlsten, “Performance and design of an off-resonant continuous-wave Raman laser,” J. Opt. Soc. Am. B 15, 1667–1673 (1998).
[CrossRef]

Dyer, M. J.

Gavrielides, A.

P. Peterson, A. Gavrielides, and M. P. Sharma, “Modeling of high finesse, doubly resonant cw Raman lasers,” Opt. Commun. 160, 80–85 (1999).
[CrossRef]

Harris, S. E.

M. K. Oshman and S. E. Harris, “Theory of optical parametric oscillation internal to the laser cavity,” IEEE J. Quantum Electron. QE-4, 491–502 (1968).
[CrossRef]

Jacob, D.

D. Jacob, M. Vallet, F. Bretenker, and A. Le Floch, “Supermirror phase anisotropy measurement,” Opt. Lett.. 20, 671–673 (1995).
[CrossRef] [PubMed]

Javan, A.

J. R. Murray and A. Javan, “Effects of collisions on Raman line profiles of hydrogen and deuterium gas,” J. Mol. Spectrosc. 42, 1–26 (1972).
[CrossRef]

Johnston Jr., W. D.

G. D. Boyd, W. D. Johnston, Jr., and I. P. Kaminow, “Optimization of the stimulated Raman scattering threshold,” IEEE J. Quantum Electron. QE-5, 203–206 (1969).
[CrossRef]

Kaldor, A.

Kaminow, I. P.

G. D. Boyd, W. D. Johnston, Jr., and I. P. Kaminow, “Optimization of the stimulated Raman scattering threshold,” IEEE J. Quantum Electron. QE-5, 203–206 (1969).
[CrossRef]

Knize, R. J.

J. K. Brasseur, R. T. Teehan, R. J. Knize, P. A. Roos, and J. L. Carlsten, “Phase and frequency stabilization of a pump laser to a Raman active resonator,” IEEE J. Quantum Electron. 37, 1075–1083 (2001).
[CrossRef]

Kogelnik, H.

Lamb Jr., W. E.

W. E. Lamb, Jr., “Theory of an optical maser,” Phys. Rev. 134, A1429–A1450 (1964).
[CrossRef]

Le Floch, A.

D. Jacob, M. Vallet, F. Bretenker, and A. Le Floch, “Supermirror phase anisotropy measurement,” Opt. Lett.. 20, 671–673 (1995).
[CrossRef] [PubMed]

Meng, L. S.

Murray, J. R.

J. R. Murray and A. Javan, “Effects of collisions on Raman line profiles of hydrogen and deuterium gas,” J. Mol. Spectrosc. 42, 1–26 (1972).
[CrossRef]

Newstein, M.

B. N. Perry, P. Rabinowitz, and M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2001 (1983).
[CrossRef]

Oshman, M. K.

M. K. Oshman and S. E. Harris, “Theory of optical parametric oscillation internal to the laser cavity,” IEEE J. Quantum Electron. QE-4, 491–502 (1968).
[CrossRef]

Parkins, A. S.

S. Rebic, A. S. Parkins, and D. F. Walls, “Transfer of photon statistics in a Raman laser,” Opt. Commun. 156, 426–434 (1998).
[CrossRef]

Perry, B. N.

B. N. Perry, P. Rabinowitz, and M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2001 (1983).
[CrossRef]

Peterson, P.

P. Peterson, A. Gavrielides, and M. P. Sharma, “Modeling of high finesse, doubly resonant cw Raman lasers,” Opt. Commun. 160, 80–85 (1999).
[CrossRef]

Rabinowitz, P.

Rebic, S.

S. Rebic, A. S. Parkins, and D. F. Walls, “Transfer of photon statistics in a Raman laser,” Opt. Commun. 156, 426–434 (1998).
[CrossRef]

Repasky, K. S.

Roos, P. A.

Sharma, M. P.

P. Peterson, A. Gavrielides, and M. P. Sharma, “Modeling of high finesse, doubly resonant cw Raman lasers,” Opt. Commun. 160, 80–85 (1999).
[CrossRef]

Siegman, A. E.

Stein, A.

Swanson, R. C.

Teehan, R. T.

J. K. Brasseur, R. T. Teehan, R. J. Knize, P. A. Roos, and J. L. Carlsten, “Phase and frequency stabilization of a pump laser to a Raman active resonator,” IEEE J. Quantum Electron. 37, 1075–1083 (2001).
[CrossRef]

Vallet, M.

D. Jacob, M. Vallet, F. Bretenker, and A. Le Floch, “Supermirror phase anisotropy measurement,” Opt. Lett.. 20, 671–673 (1995).
[CrossRef] [PubMed]

Walls, D. F.

S. Rebic, A. S. Parkins, and D. F. Walls, “Transfer of photon statistics in a Raman laser,” Opt. Commun. 156, 426–434 (1998).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

M. K. Oshman and S. E. Harris, “Theory of optical parametric oscillation internal to the laser cavity,” IEEE J. Quantum Electron. QE-4, 491–502 (1968).
[CrossRef]

G. D. Boyd, W. D. Johnston, Jr., and I. P. Kaminow, “Optimization of the stimulated Raman scattering threshold,” IEEE J. Quantum Electron. QE-5, 203–206 (1969).
[CrossRef]

J. K. Brasseur, R. T. Teehan, R. J. Knize, P. A. Roos, and J. L. Carlsten, “Phase and frequency stabilization of a pump laser to a Raman active resonator,” IEEE J. Quantum Electron. 37, 1075–1083 (2001).
[CrossRef]

J. Mol. Spectrosc.

J. R. Murray and A. Javan, “Effects of collisions on Raman line profiles of hydrogen and deuterium gas,” J. Mol. Spectrosc. 42, 1–26 (1972).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

S. Rebic, A. S. Parkins, and D. F. Walls, “Transfer of photon statistics in a Raman laser,” Opt. Commun. 156, 426–434 (1998).
[CrossRef]

P. Peterson, A. Gavrielides, and M. P. Sharma, “Modeling of high finesse, doubly resonant cw Raman lasers,” Opt. Commun. 160, 80–85 (1999).
[CrossRef]

Opt. Lett.

Opt. Lett..

D. Jacob, M. Vallet, F. Bretenker, and A. Le Floch, “Supermirror phase anisotropy measurement,” Opt. Lett.. 20, 671–673 (1995).
[CrossRef] [PubMed]

Phys. Rev.

W. E. Lamb, Jr., “Theory of an optical maser,” Phys. Rev. 134, A1429–A1450 (1964).
[CrossRef]

Phys. Rev. A

B. N. Perry, P. Rabinowitz, and M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2001 (1983).
[CrossRef]

Other

J. Bienfang, W. Rudolph, P. A. Roos, L. S. Meng, and J. L. Carlsten, “Steady state thermo-optic model of a continuous-wave Raman laser,” J. Opt. Soc. Am. B (to be published).

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989) pp. 143–146.

D. Zwillinger, ed., Standard Mathematical Tables and Formulae, 30th ed. (CRC, New York, 1996), p. 467.

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Figures (5)

Fig. 1
Fig. 1

Output Stokes power (arbitrary units) from Eq. (1) as a function of the mirror transmission coefficients [in parts in 106 (ppm)] at the pump and Stokes wavelengths for equal absorption coefficients of 35 ppm. Note that the optimal Stokes transmission coefficient is lower than that for the pump. The other parameters used for Figs. 13 are P1=0.44 MW, λp=795 nm, and λS=1187 nm.

Fig. 2
Fig. 2

Output Stokes power (arbitrary units) from Eq. (1) as a function of the mirror transmission coefficients (ppm) at the pump and the Stokes wavelengths when the absorption coefficient for the pump wavelength is smaller (5 ppm) than that for the Stokes wavelength (35 ppm). Here the optimal Stokes transmission is larger, whereas that for the pump decreases.

Fig. 3
Fig. 3

Output Stokes power (arbitrary units) from Eq. (1) as a function of the mirror transmission coefficients (ppm) at the pump and the Stokes wavelengths when the absorption coefficient for the pump wavelength (35 ppm) is larger than that for the Stokes wavelength (5 ppm). For this case the optimal Stokes transmission decreases and that for the pump increases.

Fig. 4
Fig. 4

Photon conversion efficiency as a function of input pump power relative to the threshold power of curve a. We assume that the accessible pump powers are limited to the region at the left of the vertical dotted line. Curve a shows the efficiency when the mirror transmissions are chosen such that the maximum available pump power is four times the threshold pump power. Curve b shows the efficiency when the transmissions increase to match Eqs. (13) and (14) of Section 4. Curve c shows the efficiency for even larger transmissions.

Fig. 5
Fig. 5

Inverse cosecant function of Eq. (4) as a function of the ratio of the mirror curvature radius to the resonator length. The two filled circles mark ratios that represent familiar cavity geometries. The open squares represent ratios that we have used experimentally. The ostensibly optimal ratio is 1/2, indicating a concentric cavity geometry. However, practical considerations favor larger ratios.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

PPf=14P1TPf(1-RSfRSb)1/2-PIn2,
PPb=1/4P1TPb(1-RSfRSb),
PSf(b)=12λPλSTSf(b)TPf1-RSfRSbP1PIn1/2-12P1(1-RPfRPb).
P1λP+λS2α0 csc-12r/l.
PThresh=14P1(1-RSfRSb)(1-RPfRPb)2TPfπ24P1FPFS,
PMatched=1/4P1(1-RSfRSb)TPf
=11+APTP2PThresh(RPf=RPb)
=41+ΛPTPf2PThresh(RPfRPb),
PSbPInλSλP=14TSbTPf(1-RSfRSb)(1-RPfRPb).
PSPInλSλP=1211+ASTS1+APTP,
PSbPInλSλP=11+ΛSTSb1+ΛPTPf,
TSTP=PIn/P1.
TP=APASPInP11/2,
TS=ASAPPInP11/2-AS.
PSPInλSλP=121-P1PInAPAS1/22.
TPf=ΛPΛS8PInP11/2,
TSb=ΛSΛP8PInP11/2-ΛS,
PSbPInλSλP=1-P18PInΛPΛS1/22.
PThresh=PIn41+P1PInAPAS1/22.
L=(Γ/2)2Δ2+(Γ/2)2.
Δ=±Γ2PIn4PThresh-11/2,
EPssf=-RPfEPin+1/2TPjEPss,
E=2PAμ0ε01/2,
PPf=(½TPfΠP-RPfPIn)2,
ΠP=λP+λS2α0 tan-1lb(1-RSfRSb),
csc-1(x)=tan-11x2-1,

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