Abstract

The spectrum of the stimulated electronic Raman gain at 650 nm in Ne I, pumped by a 633-nm He–Ne cw laser in the same cavity, is derived. The question of the proper Raman-gain linewidth is addressed. It is shown that the gain has a nearly Doppler-free component whose width is measured as 30 ± 10 MHz (FWHM) at 6 Torr. This value agrees reasonably well with the residual Doppler broadening but not with collisional broadening rates. A simple calculation is included that shows the quantum-limited frequency uncertainty of the 650-nm laser to be higher by a factor of 1.5 than the frequency uncertainty of the 633-nm laser at equal power.

© 1987 Optical Society of America

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References

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  1. L. S. Vasilenko, V. P. Chebotaev, A. V. Shishaev, Pis'ma Zh. Eksp. Teor. Fiz. 12, 6 (1970)[JETP Lett. 12, 113 (1970)].
  2. D. E. Roberts, E. N. Forston, Phys. Rev. Lett. 31, 1539 (1973).
    [Crossref]
  3. M. D. Levenson, N. Bloembergen, Phys. Lett. 32, 645 (1974).
    [Crossref]
  4. J. Assendrup, B. Grover, L. Hall, S. Jabr, Appl. Phys. Lett. 48, 86 (1986).
    [Crossref]
  5. C. Moore, Atomic Energy Levels, Circ. 467 (U.S. National Bureau of Standards, Washington, D.C., 1949), Vol. 1.
  6. D. C. Hanna, M. A. Yuratich, D. Cotter, in Nonlinear Optics of Free Atoms and Molecules, D. A. MacAdam, ed., Vol. 17 of Springer Series in Optical Sciences(Springer-Verlag, Berlin, 1979).
  7. T. A. Dorschner, H. A. Haus, M. Holz, I. Smith, H. Statz, IEEE J. Quantum Electron. QE-14, 1376 (1980).
    [Crossref]
  8. R. W. Hellwarth, Phys. Rev. 130, 1850 (1963).
    [Crossref]
  9. Note that in their derivation Dorschner et al.7 have assumed that Nj ≪ Ni, as in a four-level laser. Later in their paper they considered effects of pump rates on Nj variation and even suggested the possible use of squeeze states to reduce phase noise.

1986 (1)

J. Assendrup, B. Grover, L. Hall, S. Jabr, Appl. Phys. Lett. 48, 86 (1986).
[Crossref]

1980 (1)

T. A. Dorschner, H. A. Haus, M. Holz, I. Smith, H. Statz, IEEE J. Quantum Electron. QE-14, 1376 (1980).
[Crossref]

1974 (1)

M. D. Levenson, N. Bloembergen, Phys. Lett. 32, 645 (1974).
[Crossref]

1973 (1)

D. E. Roberts, E. N. Forston, Phys. Rev. Lett. 31, 1539 (1973).
[Crossref]

1970 (1)

L. S. Vasilenko, V. P. Chebotaev, A. V. Shishaev, Pis'ma Zh. Eksp. Teor. Fiz. 12, 6 (1970)[JETP Lett. 12, 113 (1970)].

1963 (1)

R. W. Hellwarth, Phys. Rev. 130, 1850 (1963).
[Crossref]

Assendrup, J.

J. Assendrup, B. Grover, L. Hall, S. Jabr, Appl. Phys. Lett. 48, 86 (1986).
[Crossref]

Bloembergen, N.

M. D. Levenson, N. Bloembergen, Phys. Lett. 32, 645 (1974).
[Crossref]

Chebotaev, V. P.

L. S. Vasilenko, V. P. Chebotaev, A. V. Shishaev, Pis'ma Zh. Eksp. Teor. Fiz. 12, 6 (1970)[JETP Lett. 12, 113 (1970)].

Cotter, D.

D. C. Hanna, M. A. Yuratich, D. Cotter, in Nonlinear Optics of Free Atoms and Molecules, D. A. MacAdam, ed., Vol. 17 of Springer Series in Optical Sciences(Springer-Verlag, Berlin, 1979).

Dorschner, T. A.

T. A. Dorschner, H. A. Haus, M. Holz, I. Smith, H. Statz, IEEE J. Quantum Electron. QE-14, 1376 (1980).
[Crossref]

Forston, E. N.

D. E. Roberts, E. N. Forston, Phys. Rev. Lett. 31, 1539 (1973).
[Crossref]

Grover, B.

J. Assendrup, B. Grover, L. Hall, S. Jabr, Appl. Phys. Lett. 48, 86 (1986).
[Crossref]

Hall, L.

J. Assendrup, B. Grover, L. Hall, S. Jabr, Appl. Phys. Lett. 48, 86 (1986).
[Crossref]

Hanna, D. C.

D. C. Hanna, M. A. Yuratich, D. Cotter, in Nonlinear Optics of Free Atoms and Molecules, D. A. MacAdam, ed., Vol. 17 of Springer Series in Optical Sciences(Springer-Verlag, Berlin, 1979).

Haus, H. A.

T. A. Dorschner, H. A. Haus, M. Holz, I. Smith, H. Statz, IEEE J. Quantum Electron. QE-14, 1376 (1980).
[Crossref]

Hellwarth, R. W.

R. W. Hellwarth, Phys. Rev. 130, 1850 (1963).
[Crossref]

Holz, M.

T. A. Dorschner, H. A. Haus, M. Holz, I. Smith, H. Statz, IEEE J. Quantum Electron. QE-14, 1376 (1980).
[Crossref]

Jabr, S.

J. Assendrup, B. Grover, L. Hall, S. Jabr, Appl. Phys. Lett. 48, 86 (1986).
[Crossref]

Levenson, M. D.

M. D. Levenson, N. Bloembergen, Phys. Lett. 32, 645 (1974).
[Crossref]

Moore, C.

C. Moore, Atomic Energy Levels, Circ. 467 (U.S. National Bureau of Standards, Washington, D.C., 1949), Vol. 1.

Roberts, D. E.

D. E. Roberts, E. N. Forston, Phys. Rev. Lett. 31, 1539 (1973).
[Crossref]

Shishaev, A. V.

L. S. Vasilenko, V. P. Chebotaev, A. V. Shishaev, Pis'ma Zh. Eksp. Teor. Fiz. 12, 6 (1970)[JETP Lett. 12, 113 (1970)].

Smith, I.

T. A. Dorschner, H. A. Haus, M. Holz, I. Smith, H. Statz, IEEE J. Quantum Electron. QE-14, 1376 (1980).
[Crossref]

Statz, H.

T. A. Dorschner, H. A. Haus, M. Holz, I. Smith, H. Statz, IEEE J. Quantum Electron. QE-14, 1376 (1980).
[Crossref]

Vasilenko, L. S.

L. S. Vasilenko, V. P. Chebotaev, A. V. Shishaev, Pis'ma Zh. Eksp. Teor. Fiz. 12, 6 (1970)[JETP Lett. 12, 113 (1970)].

Yuratich, M. A.

D. C. Hanna, M. A. Yuratich, D. Cotter, in Nonlinear Optics of Free Atoms and Molecules, D. A. MacAdam, ed., Vol. 17 of Springer Series in Optical Sciences(Springer-Verlag, Berlin, 1979).

Appl. Phys. Lett. (1)

J. Assendrup, B. Grover, L. Hall, S. Jabr, Appl. Phys. Lett. 48, 86 (1986).
[Crossref]

IEEE J. Quantum Electron. (1)

T. A. Dorschner, H. A. Haus, M. Holz, I. Smith, H. Statz, IEEE J. Quantum Electron. QE-14, 1376 (1980).
[Crossref]

Phys. Lett. (1)

M. D. Levenson, N. Bloembergen, Phys. Lett. 32, 645 (1974).
[Crossref]

Phys. Rev. (1)

R. W. Hellwarth, Phys. Rev. 130, 1850 (1963).
[Crossref]

Phys. Rev. Lett. (1)

D. E. Roberts, E. N. Forston, Phys. Rev. Lett. 31, 1539 (1973).
[Crossref]

Pis'ma Zh. Eksp. Teor. Fiz. (1)

L. S. Vasilenko, V. P. Chebotaev, A. V. Shishaev, Pis'ma Zh. Eksp. Teor. Fiz. 12, 6 (1970)[JETP Lett. 12, 113 (1970)].

Other (3)

C. Moore, Atomic Energy Levels, Circ. 467 (U.S. National Bureau of Standards, Washington, D.C., 1949), Vol. 1.

D. C. Hanna, M. A. Yuratich, D. Cotter, in Nonlinear Optics of Free Atoms and Molecules, D. A. MacAdam, ed., Vol. 17 of Springer Series in Optical Sciences(Springer-Verlag, Berlin, 1979).

Note that in their derivation Dorschner et al.7 have assumed that Nj ≪ Ni, as in a four-level laser. Later in their paper they considered effects of pump rates on Nj variation and even suggested the possible use of squeeze states to reduce phase noise.

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Figures (3)

Fig. 1
Fig. 1

Partial energy-level diagram of Ne I. Note that the virtual Raman level is 15.6 cm−1 above the 2p8 level.

Fig. 2
Fig. 2

Small-signal gain profiles and mode structure of the pump and Raman lasers. The pump has a Gaussian-gain profile centered at 632.8 nm. The center of the Raman-gain profile is dependent on the cavity tuning but is always 417 cm−1 below the 632.8-nm laser's actual lasing frequency. The Raman gain is shown composed of two parts, a broad Gaussian part that is due to the counterpropagating pump and a narrow Lorentzian part that is due to the copropagating pump. The vertical lines labeled M, N … represent modes of the cavity.

Fig. 3
Fig. 3

Tuning range of the 650-nm laser as a function of discharge current. The theoretical curve is obtained by assuming a Gaussian-gain profile and linear dependence of the peak gain on current and has the form R = Δ[ln(i/i0]1/2, where Δ is the width of the composite 20Ne–22Ne gain line.

Equations (16)

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G = g I p = 3 ω s c 2 I p χ ( 3 ) ( ω s ; ω p , ω p , ω s ) ,
χ ( 3 ) = N μ f i 2 μ i g 2 6 h 3 ( Ω f g + ω s ω p + i Γ ) ( 1 Ω i g ω p ) 2
χ ( 3 ) ~ ( Ω f g + ω s k s v ω p + k p v + i Γ ) 1 ( Ω i g ω p + k p v ) 2 .
χ ( 3 ) ~ N ( Ω f g + ω s ω p + i Γ ) .
G + 2 π 2 r e 2 c 2 N ω s f g i f i f Ω g i Ω i f ( Ω g i ω p ) 2 { Γ I + Δ 2 + Γ 2 + Γ I υ G ( υ ) d υ [ Δ + ( 2 k p ) υ ] 2 + Γ 2 } ,
N c L = ν p , M c L = ν p Ω ± δ / 2 ,
M / N = r .
N + p M + p = ν p ν p Ω + δ .
p = δ ( c L ) ( 1 1 / r ) .
n ˙ r n ˙ s R = n α N i n β n α ( N i N j ) ,
n ˙ R = 1 τ N i ( N i N j ) per mode .
Δ ϕ 2 = ( E r E β ) 2 1 / 2 = 1 2 E r 2 E β 2 = 1 2 n β ,
Δ ϕ ( T ) rms = ( T τ N i N i N j 1 2 n β ) 1 / 2 .
Δ ω rms = 1 T Δ ϕ rms = ω 0 Q β ( h λ B P N i N i N j ) 1 / 2 ,
Δ ω rms = ω 0 Q β ( h ν B P 1 1 e / k T ) 1 / 2 ,
Δ ω RS = ω 0 Q a ( h ν B p N j N i N j ) 1 / 2 .

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