Abstract

A steady-state theory that describes the performance of a cw off-resonant Raman laser is presented. The cw Raman laser is constructed in a nonconfocal high-finesse cavity that allows for high Raman gain with low pump powers. Threshold values of the pump laser used to pump the cw Raman laser are predicted to be as low as 1 mW. The maximum photon-conversion efficiency for the cw Raman laser is predicted to be 50%. The theory is compared with experimental results from a cw Raman laser that operates with a pump wavelength of 532 nm and a Stokes-shifted wavelength of 683 nm. A threshold pump power of 2 mW and a maximum photon-conversion efficiency of 34%±6% was measured. With the mirrors used in the experiment, these values correspond to the predictions from the steady-state cw Raman laser theory. The theoretical model is then used to design cw Raman lasers operate near the maximum conversion efficiency in the 1–4-μm wavelength region.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
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  5. N. Bloemberg, “The stimulated Raman effect,” Am. J. Phys. 35, 989 (1967).
    [CrossRef]
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    [CrossRef]
  7. M. G. Raymer and J. Mostowski, “Stimulated Raman scat-tering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
    [CrossRef]
  8. P. Rabinowitz, A. Stein, R. Brickman, and A. Kaldor, “Efficient tunable H2 Raman lasers,” Appl. Phys. Lett. 35, 739 (1979).
    [CrossRef]
  9. L. A. Harris and J. N. Lavinos, “Generation of nanosecond infrared pulses tunable from 2.8 to 16 μm by efficient stimulated electronic Raman scattering,” Appl. Opt. 26, 3996 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  24. The mirrors used for the cw Raman laser were purchased from Research ElectroOptics Inc., 1855 South 57th Court, Boulder, Colo., 80301.
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1998 (1)

1996 (1)

1995 (1)

1993 (1)

X. W. Xia, W. J. Sandle, R. J. Ballagh, and D. W. Warrington, “Observation of cw stimulated Raman emission in the neon 2p-1s manifold,” Opt. Commun. 96, 99 (1993).
[CrossRef]

1992 (1)

1989 (2)

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Stimulated Raman scattering in the visible in a multipass cell,” IEEE J. Quantum Electron. 24, 1741 (1989).
[CrossRef]

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

1988 (1)

1987 (2)

1986 (2)

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 (1986).
[CrossRef]

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

1983 (2)

M. Ohtsu, H. Kotani, and H. Tagawa, “Spectral measurements of NH3 and H2O for pollutant gas monitoring by 1.5 μm InGaAsP/InP diode lasers,” Jpn. J. Appl. Phys., 22, 1553 (1983).
[CrossRef]

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 (2)

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).

M. G. Raymer and J. Mostowski, “Stimulated Raman scat-tering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
[CrossRef]

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]

1965 (1)

Y. R. Shen and N. Bloemberg, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137, 1787 (1965).
[CrossRef]

Am. J. Phys. (1)

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

Appl. Opt. (4)

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. (4)

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).

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Stimulated Raman scattering in the visible in a multipass cell,” IEEE J. Quantum Electron. 24, 1741 (1989).
[CrossRef]

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

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

M. Ohtsu, H. Kotani, and H. Tagawa, “Spectral measurements of NH3 and H2O for pollutant gas monitoring by 1.5 μm InGaAsP/InP diode lasers,” Jpn. J. Appl. Phys., 22, 1553 (1983).
[CrossRef]

Opt. Commun. (1)

X. W. Xia, W. J. Sandle, R. J. Ballagh, and D. W. Warrington, “Observation of cw stimulated Raman emission in the neon 2p-1s manifold,” Opt. Commun. 96, 99 (1993).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (1)

Y. R. Shen and N. Bloemberg, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137, 1787 (1965).
[CrossRef]

Phys. Rev. A (2)

M. G. Raymer and J. Mostowski, “Stimulated Raman scat-tering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
[CrossRef]

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

Other (6)

The mirrors used for the cw Raman laser were purchased from Research ElectroOptics Inc., 1855 South 57th Court, Boulder, Colo., 80301.

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, New York, 1989); see also R. G. Harrison and Weiping Lu, “Origin of periodic, chaotic, and bistable emission from a Raman laser,” Phys. Rev. Lett. 63, 1372 (1989) for a related theoretical treatment without pump depletion.
[CrossRef] [PubMed]

E. Hecht, Optics, 3rd ed. (Addison-Wesley, New York, 1998).

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

H. I. Schiff, ed., Measurement of Atmospheric Gases, Proc. SPIE 1433 (1991).

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 (12)

Fig. 1
Fig. 1

Wavelengths for the available room-temperature laser diodes and the wavelengths these diodes can be shifted to by use of Raman scattering in different Raman media. By use of the available room-temperature diode lasers as pump sources, cw Raman lasers can be built to cover the 1–4-μm spectral region.

Fig. 2
Fig. 2

Schematic diagram of fields reflected from, and transmitted through and between, the mirrors of the HFC.

Fig. 3
Fig. 3

Plot of the output Stokes power as a function of the input pump power. Solid, dashed, dotted–dashed, and dotted curves denote pump lasers at 532, 795, 1330, and 1550 nm, respectively, and Stokes-shifted wavelengths of 683, 1187, 2973, and 4350 nm, respectively. The mirror reflectivities at both the pump and the Stokes wavelengths are 99.98%, and the mirror absorptions at both the pump and the Stokes wavelengths are 15 ppm.

Fig. 4
Fig. 4

Plot of the Stokes output power (solid curve), the total output pump power (dashed curve), the reflected pump power (dotted–dashed curve) and the transmitted pump power (dotted curve) for a pump wavelength of 532 nm and a Stokes-shifted wavelength of 683 nm. The mirror reflectivities at both the pump and the Stokes wavelengths are R=99.95%, and the mirror absorptions at both the pump and the Stokes wavelengths are A=50 ppm.

Fig. 5
Fig. 5

Plot of the Stokes photon-conversion efficiency as a function of input pump power. The pump (Stokes) wavelength is 532 nm (683 nm). The mirror absorptions at both the pump and the Stokes wavelengths are A=0 ppm. The solid, dashed, dotted–dashed, and dotted curves were calculated, respectively, for mirror reflectivities of R=99.98%, 99.95%, 99.92%, and 99.89%. The maximum photon-conversion efficiency for each mirror reflectivity is 50%.

Fig. 6
Fig. 6

Plot of the Stokes photon-conversion efficiency as a function of the input pump power. The pump (Stokes) wavelength is 532 nm (683 nm). The mirror reflectivities at both the pump and the Stokes wavelengths are R=99.95%. The solid dashed, dotted–dashed, and dotted curves were calculated, respectively, for mirror absorptions of A=0, 15, 50, and 100 ppm.

Fig. 7
Fig. 7

Plot of the output Stokes power at 683 nm as a function of the input pump power at 532 nm. Solid curve, the theoretical predictions; filled circles, experimental measurements. The experiment and the theory are in good agreement.

Fig. 8
Fig. 8

Plot of the Stokes photon-conversion efficiency at 683 nm as a function of the input pump power at 532 nm. Solid curve, the theoretical predictions; filled circles, experimental measurements. A maximum Stokes photon-conversion efficiency of 34%±5.4% is shown.

Fig. 9
Fig. 9

Solid line curve, plot of the reflectivity that yields the maximum Stokes power-conversion efficiency as a function of the input pump power. The pump (Stokes) wavelength is 532 nm (683 nm). Also the maximum Stokes power-conversion efficiency as a function of the input pump power is shown for absorptions of A=15 ppm (dashed curve), A=50 ppm (dotted–dashed curve), and A=100 ppm (dotted curve).

Fig. 10
Fig. 10

Same as Fig. 8, except that the pump (Stokes) wavelength is 795 nm (1187 nm).

Fig. 11
Fig. 11

Same as Fig. 8, except that the pump (Stokes) wavelength is 1330 nm (2973 nm).

Fig. 12
Fig. 12

Same as Fig. 8, except that the pump (Stokes) wavelength is 1550 nm (4350 nm).

Equations (23)

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ES(z, t)=½ ES(t)exp(-iωSt)u(z)+c.c.,
u(z)=sin(kz),
kc=Nπcl=Ω,
S(z, t)=½S(t)exp(-iωSt)u(z)+c.c.,
ES(t)t=-i(Ω-ωS)ES(t)+12 i ωS S(t),
S(t)=2 exp(iωSt) 1M 0lu*(z)Tr(ρp)dz,
Tr(ρp)=e(x21ρ12+x21*ρ21+x23*ρ23+x23ρ32).
ES(t)t=GS|Ep(t)|2ES(t),
ΠSt=2GSΠpΠS-LSΠS,
GS=c2l 4αg tan-1(l/b)λS+λp,
ΠS=ΠS(0)exp(-LSt).
LS=-(c/l)ln(R).
Πp=LSl(λS+λp)4cαg tan-1(l/b).
Πp=P0 d2T(1-R)2,
d2=LS2GS (1-R)2T 1P0.
Pp=P0RdT1-R-12+dT1-R2,
Δ=AP01+d2TR(1-R)2+d2T(1-R)2.
PS=(λp/λS)(P0-Pp-Δ),
P0(th)=LS2GS (1-R)2T,
CS=λpλS T+d 2TR1-R-d2(1+R)T2+AT(1-R)2.
Cph=λSλp CS.
dmax=TR(1-R2) (1-R)2(T2+AT).
P0(max)=LS2GS (1-R)2T 1dmax.

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