Abstract

Contrary to expectations based on mode spacing, single-mode operation in very large He-Ne ring lasers may be achieved at intracavity power levels up to ∼0.15 times the saturation intensity for the He-Ne transition. Homogeneous line broadening at a high total gas pressure of 4–6 Torr allows a single-peaked gain profile that suppresses closely spaced multiple modes. At startup, decay of initial multiple modes may take tens of seconds. The single remaining mode in each direction persists metastably as the cavity is detuned by many times the mode frequency spacing. A theoretical explanation requires the gain profile to be concave down and to satisfy an inequality related to slope and saturation at the operating frequency. Calculated metastable frequency ranges are >150 MHz at 6 Torr and depend strongly on pressure. Examples of unusual stable mode configurations are shown, with differently numbered modes in the two directions and with multiple modes at a spacing of ∼100 MHz.

© 2004 Optical Society of America

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References

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  1. W. M. Macek, D. T. M. Davis, R. W. Olthins, J. R. Schneider, G. R. White, “Ring laser rotation rate sensor,” in Optical Lasers, J. Fox, ed. (Polytechnic, Brooklyn, 1963), pp. 199–207.
  2. G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
    [CrossRef]
  3. U. K. Schreiber, C. H. Rowe, D. N. Wright, S. J. Cooper, G. E. Stedman, “Precision stabilization of the optical frequency in a large ring laser gyroscope,” Appl. Opt. 37, 8371–8381 (1998).
    [CrossRef]
  4. U. Schreiber, A. Velikoseltsev, T. Klügel, G. E. Stedman, W. Schlüter, “Advances in the stabilisation of large ring laser gyroscopes,” in Symposium Gyro Technology 2001, H. Sorg, ed. (Universität Stuttgart, Stuttgart, Germany, 2001), p. 8.0.
  5. R. W. Dunn, “Design of a triangular active ring laser 13 m on a side,” Appl. Opt. 37, 6405–6409 (1998).
    [CrossRef]
  6. R. W. Dunn, D. E. Shabalin, R. J. Thirkettle, G. J. MacDonald, G. E. Stedman, K. U. Schreiber, “Design and initial operation of a 367 m2 rectangular ring laser,” Appl. Opt. 41, 1685–1688 (2002).
    [CrossRef] [PubMed]
  7. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  8. T. D. Anh, W. Dietel, “Homogeneous broadening in a 0.63 μm single mode He-Ne laser,” Opto-electronics 5, 243–248 (1973).
    [CrossRef]
  9. P. W. Smith, “Cross-relaxation effects in the saturation of the 6328-A neon-laser line,” Phys. Rev. Lett. 26, 740–743 (1971).
    [CrossRef]
  10. We estimated ρ by noting the beam power level for the onset of multiple longitudinal mode operation and taking this to correspond to the limiting value of ρ for weak saturation, from the gain profile calculations. Other beam powers were then scaled appropriately.
  11. K. U. Schreiber, T. Klügel, G. E. Stedman, “Earth tide and tilt detection by a ring laser gyroscope,” J. Geophys. Res. 108, 2132–2137 (2003).
    [CrossRef]
  12. For a homogeneously broadened transition, f(ρ) = 1/(1 + ρ), and in the strong inhomogeneous limit f(ρ) = 1/(1 + ρ)1/2. Our case is intermediate, and in practice we evaluate f(ρ) and its derivative numerically.
  13. E. Kreyszig, Advanced Engineering Mathematics, 5th ed. (Wiley, New York, 1983), p. 360.
  14. G. E. Stedman, K. U. Schreiber, H. R. Bilger, “On the detectability of the Lense-Thirring field from rotating laboratory masses using ring laser gyroscope interferometers,” Class. Quantum Grav. 20, 2527–2540 (2003).
    [CrossRef]

2003 (2)

K. U. Schreiber, T. Klügel, G. E. Stedman, “Earth tide and tilt detection by a ring laser gyroscope,” J. Geophys. Res. 108, 2132–2137 (2003).
[CrossRef]

G. E. Stedman, K. U. Schreiber, H. R. Bilger, “On the detectability of the Lense-Thirring field from rotating laboratory masses using ring laser gyroscope interferometers,” Class. Quantum Grav. 20, 2527–2540 (2003).
[CrossRef]

2002 (1)

1998 (2)

1997 (1)

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[CrossRef]

1973 (1)

T. D. Anh, W. Dietel, “Homogeneous broadening in a 0.63 μm single mode He-Ne laser,” Opto-electronics 5, 243–248 (1973).
[CrossRef]

1971 (1)

P. W. Smith, “Cross-relaxation effects in the saturation of the 6328-A neon-laser line,” Phys. Rev. Lett. 26, 740–743 (1971).
[CrossRef]

Anh, T. D.

T. D. Anh, W. Dietel, “Homogeneous broadening in a 0.63 μm single mode He-Ne laser,” Opto-electronics 5, 243–248 (1973).
[CrossRef]

Bilger, H. R.

G. E. Stedman, K. U. Schreiber, H. R. Bilger, “On the detectability of the Lense-Thirring field from rotating laboratory masses using ring laser gyroscope interferometers,” Class. Quantum Grav. 20, 2527–2540 (2003).
[CrossRef]

Cooper, S. J.

Davis, D. T. M.

W. M. Macek, D. T. M. Davis, R. W. Olthins, J. R. Schneider, G. R. White, “Ring laser rotation rate sensor,” in Optical Lasers, J. Fox, ed. (Polytechnic, Brooklyn, 1963), pp. 199–207.

Dietel, W.

T. D. Anh, W. Dietel, “Homogeneous broadening in a 0.63 μm single mode He-Ne laser,” Opto-electronics 5, 243–248 (1973).
[CrossRef]

Dunn, R. W.

Klügel, T.

K. U. Schreiber, T. Klügel, G. E. Stedman, “Earth tide and tilt detection by a ring laser gyroscope,” J. Geophys. Res. 108, 2132–2137 (2003).
[CrossRef]

U. Schreiber, A. Velikoseltsev, T. Klügel, G. E. Stedman, W. Schlüter, “Advances in the stabilisation of large ring laser gyroscopes,” in Symposium Gyro Technology 2001, H. Sorg, ed. (Universität Stuttgart, Stuttgart, Germany, 2001), p. 8.0.

Kreyszig, E.

E. Kreyszig, Advanced Engineering Mathematics, 5th ed. (Wiley, New York, 1983), p. 360.

MacDonald, G. J.

Macek, W. M.

W. M. Macek, D. T. M. Davis, R. W. Olthins, J. R. Schneider, G. R. White, “Ring laser rotation rate sensor,” in Optical Lasers, J. Fox, ed. (Polytechnic, Brooklyn, 1963), pp. 199–207.

Olthins, R. W.

W. M. Macek, D. T. M. Davis, R. W. Olthins, J. R. Schneider, G. R. White, “Ring laser rotation rate sensor,” in Optical Lasers, J. Fox, ed. (Polytechnic, Brooklyn, 1963), pp. 199–207.

Rowe, C. H.

Schlüter, W.

U. Schreiber, A. Velikoseltsev, T. Klügel, G. E. Stedman, W. Schlüter, “Advances in the stabilisation of large ring laser gyroscopes,” in Symposium Gyro Technology 2001, H. Sorg, ed. (Universität Stuttgart, Stuttgart, Germany, 2001), p. 8.0.

Schneider, J. R.

W. M. Macek, D. T. M. Davis, R. W. Olthins, J. R. Schneider, G. R. White, “Ring laser rotation rate sensor,” in Optical Lasers, J. Fox, ed. (Polytechnic, Brooklyn, 1963), pp. 199–207.

Schreiber, K. U.

G. E. Stedman, K. U. Schreiber, H. R. Bilger, “On the detectability of the Lense-Thirring field from rotating laboratory masses using ring laser gyroscope interferometers,” Class. Quantum Grav. 20, 2527–2540 (2003).
[CrossRef]

K. U. Schreiber, T. Klügel, G. E. Stedman, “Earth tide and tilt detection by a ring laser gyroscope,” J. Geophys. Res. 108, 2132–2137 (2003).
[CrossRef]

R. W. Dunn, D. E. Shabalin, R. J. Thirkettle, G. J. MacDonald, G. E. Stedman, K. U. Schreiber, “Design and initial operation of a 367 m2 rectangular ring laser,” Appl. Opt. 41, 1685–1688 (2002).
[CrossRef] [PubMed]

Schreiber, U.

U. Schreiber, A. Velikoseltsev, T. Klügel, G. E. Stedman, W. Schlüter, “Advances in the stabilisation of large ring laser gyroscopes,” in Symposium Gyro Technology 2001, H. Sorg, ed. (Universität Stuttgart, Stuttgart, Germany, 2001), p. 8.0.

Schreiber, U. K.

Shabalin, D. E.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Smith, P. W.

P. W. Smith, “Cross-relaxation effects in the saturation of the 6328-A neon-laser line,” Phys. Rev. Lett. 26, 740–743 (1971).
[CrossRef]

Stedman, G. E.

K. U. Schreiber, T. Klügel, G. E. Stedman, “Earth tide and tilt detection by a ring laser gyroscope,” J. Geophys. Res. 108, 2132–2137 (2003).
[CrossRef]

G. E. Stedman, K. U. Schreiber, H. R. Bilger, “On the detectability of the Lense-Thirring field from rotating laboratory masses using ring laser gyroscope interferometers,” Class. Quantum Grav. 20, 2527–2540 (2003).
[CrossRef]

R. W. Dunn, D. E. Shabalin, R. J. Thirkettle, G. J. MacDonald, G. E. Stedman, K. U. Schreiber, “Design and initial operation of a 367 m2 rectangular ring laser,” Appl. Opt. 41, 1685–1688 (2002).
[CrossRef] [PubMed]

U. K. Schreiber, C. H. Rowe, D. N. Wright, S. J. Cooper, G. E. Stedman, “Precision stabilization of the optical frequency in a large ring laser gyroscope,” Appl. Opt. 37, 8371–8381 (1998).
[CrossRef]

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[CrossRef]

U. Schreiber, A. Velikoseltsev, T. Klügel, G. E. Stedman, W. Schlüter, “Advances in the stabilisation of large ring laser gyroscopes,” in Symposium Gyro Technology 2001, H. Sorg, ed. (Universität Stuttgart, Stuttgart, Germany, 2001), p. 8.0.

Thirkettle, R. J.

Velikoseltsev, A.

U. Schreiber, A. Velikoseltsev, T. Klügel, G. E. Stedman, W. Schlüter, “Advances in the stabilisation of large ring laser gyroscopes,” in Symposium Gyro Technology 2001, H. Sorg, ed. (Universität Stuttgart, Stuttgart, Germany, 2001), p. 8.0.

White, G. R.

W. M. Macek, D. T. M. Davis, R. W. Olthins, J. R. Schneider, G. R. White, “Ring laser rotation rate sensor,” in Optical Lasers, J. Fox, ed. (Polytechnic, Brooklyn, 1963), pp. 199–207.

Wright, D. N.

Appl. Opt. (3)

Class. Quantum Grav. (1)

G. E. Stedman, K. U. Schreiber, H. R. Bilger, “On the detectability of the Lense-Thirring field from rotating laboratory masses using ring laser gyroscope interferometers,” Class. Quantum Grav. 20, 2527–2540 (2003).
[CrossRef]

J. Geophys. Res. (1)

K. U. Schreiber, T. Klügel, G. E. Stedman, “Earth tide and tilt detection by a ring laser gyroscope,” J. Geophys. Res. 108, 2132–2137 (2003).
[CrossRef]

Opto-electronics (1)

T. D. Anh, W. Dietel, “Homogeneous broadening in a 0.63 μm single mode He-Ne laser,” Opto-electronics 5, 243–248 (1973).
[CrossRef]

Phys. Rev. Lett. (1)

P. W. Smith, “Cross-relaxation effects in the saturation of the 6328-A neon-laser line,” Phys. Rev. Lett. 26, 740–743 (1971).
[CrossRef]

Rep. Prog. Phys. (1)

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[CrossRef]

Other (6)

W. M. Macek, D. T. M. Davis, R. W. Olthins, J. R. Schneider, G. R. White, “Ring laser rotation rate sensor,” in Optical Lasers, J. Fox, ed. (Polytechnic, Brooklyn, 1963), pp. 199–207.

U. Schreiber, A. Velikoseltsev, T. Klügel, G. E. Stedman, W. Schlüter, “Advances in the stabilisation of large ring laser gyroscopes,” in Symposium Gyro Technology 2001, H. Sorg, ed. (Universität Stuttgart, Stuttgart, Germany, 2001), p. 8.0.

We estimated ρ by noting the beam power level for the onset of multiple longitudinal mode operation and taking this to correspond to the limiting value of ρ for weak saturation, from the gain profile calculations. Other beam powers were then scaled appropriately.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

For a homogeneously broadened transition, f(ρ) = 1/(1 + ρ), and in the strong inhomogeneous limit f(ρ) = 1/(1 + ρ)1/2. Our case is intermediate, and in practice we evaluate f(ρ) and its derivative numerically.

E. Kreyszig, Advanced Engineering Mathematics, 5th ed. (Wiley, New York, 1983), p. 360.

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Figures (8)

Fig. 1
Fig. 1

Calculated gain profiles for a 50:50 mix of 20Ne and 22Ne, at different gas pressures and intracavity intensities: (a) 6 Torr pressure, I/ I sat = 0 (lower curve), 0.175 (middle curve), and 0.22; (b) 1.5 Torr pressure, I/ I sat = 0 (lower curve), 0.013 (middle curve), and 0.03.

Fig. 2
Fig. 2

Fabry-Perot (FP) spectrograms showing the slow collapse into single-mode operation, for the clockwise beam of laser UG-1. For details of the operating conditions, see text.

Fig. 3
Fig. 3

FP spectrogram of the output of laser AR-1, showing single modes in each of the clockwise and counterclockwise directions (b and c, respectively), but split by 26 MHz, equivalent to four mode numbers. The peaks at a and d are successive modes of a green laser, 440 MHz apart, used for calibration.

Fig. 4
Fig. 4

Optical frequency of the laser UG-1, measured at 30-min intervals over an 18-day period of continuous single-mode operation.

Fig. 5
Fig. 5

Sagnac frequency of laser UG-1 monitored with 30-min time resolution, over the same period as in Fig. 4.

Fig. 6
Fig. 6

Calculated boundaries of metastable single-frequency operation of a He-Ne laser, for a range of total gas pressures, and for 50:50 mix of 20Ne and 22Ne. The vertical ordinate is the ratio of the intracavity intensity to the saturation intensity for the He-Ne transition (itself a function of pressure).

Fig. 7
Fig. 7

FP spectrogram of a stable multimode configuration of (one beam of) laser UG-1. A strong central mode labeled a is flanked by modes labeled b, spaced at ±110 MHz. The two considerably weaker modes labeled c have been misplaced by wrap around in the Fabry-Perot spectrometer and are in reality at ±220 MHz relative to the central mode.

Fig. 8
Fig. 8

Sequence of gain profiles, proposed as an explanation of the multimode behavior shown in Fig. 7. a, Initial profile with I/ I sat = 0.12, allowing single-mode operation; b, transitional profile with I/ I sat = 0.225, above the single-frequency limit, allowing growth of modes on either side of the initial single mode; c, final profile, after modes have developed at ±110 MHz relative to the initial mode. Extra gain saturation modifies the profile so that the gain, averaged at ±110 MHz, is now equal to the gain at the origin.

Tables (1)

Tables Icon

Table 1 Parameters of the Three Large Ring Lasers

Equations (14)

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Δf=4AΩ cos θ/λp,
γ=8.5+59.5P
dI/dt=αI,
α=g-1/τr,
I=I01+a++a-*/a0 expiδt+complex conjugate,
gI=g0fρI/fρ0,
gI0+ΔI=1+ΔI/I0ρ0fρ0/fρ0.
αp=ΔI/I0ρ0fρ0/fρ0τr.
da+, da-=η/2a++a-*dt,
da+/dt=α+a+/2+ηa++a-*/2,
da-/dt=α-a-/2+ηa+*+a-/2.
ddta+a-*=12α++ηηηα-+ηa+a-*.
λ1, λ2=η+α++α-/2±α+-α-2/4+η21/2,
α++α-<0 and α+/η+1α-/η+1>1.

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