Abstract

We have investigated the use of stimulated Brillouin scattering (SBS) in a ring resonator to reduce the threshold of SBS phase conjugation for radiation from a frequency-narrowed Cr, Tm, Ho:YAG laser operating at 2.12 μm. Compared with an alternative scheme for threshold reduction, the loop scheme, we find that the ring resonator has a lower SBS threshold and a similar fidelity, but exhibits large fluctuations in output. We attribute these to fluctuations in the cavity length that detune the mode frequency from the center of the Brillouin gain bandwidth. Mode beating is occasionally observed with the beat frequency’s being strongly influenced by the effect of a Brillouin-induced phase shift.

© 1995 Optical Society of America

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References

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  1. B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
    [Crossref]
  2. S. R. Bowman, M. J. Winings, R. C. Y. Auyeung, J. E. Tucker, S. K. Searles, and B. J. Feldman, “Laser and spectral properties of Cr, Tm, Ho:YAG at 2.1 μ m,” IEEE J. Quantum Electron. 27, 2142 (1991).
    [Crossref]
  3. J. J. Ottusch and D. A. Rockwell, “Stimulated Brillouin scattering phase-conjugation fidelity fluctuations,” Opt. Lett. 16, 369 (1991); M. S. Mengir, J. J. Ottusch, D. C. Jones, and D. A. Rockwell, “Time-resolved measurements of stimulated Brillouin scattering phase jumps,” Phys. Rev. Lett. 68, 1702 (1992).
    [Crossref] [PubMed]
  4. I. Yu. Anikeev, D. A. Glazov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414 (1989).
    [Crossref]
  5. M. T. Duignan, B. J. Feldman, and W. T. Whitney, “Threshold reduction for stimulated Brillouin scattering using a multipass Herriott cell,” J. Opt. Soc. Am. B 9, 548 (1992).
    [Crossref]
  6. V. I. Odintsov and L. F. Rogacheva, “Efficient phase conjugation under parametric-feedback conditions,” Sov. Phys. JETP Lett. 36, 344 (1982).
  7. A. M. Scott, W. T. Whitney, and M. T. Duignan, “Stimulated Brillouin scattering and loop threshold reduction with a 2.1-μ m Cr, Tm, Ho:YAG laser,” J. Opt. Soc. Am. B 11, 2079 (1994).
    [Crossref]
  8. G. K. N. Wong and M. J. Damzen, “Investigations of optical feedback used to enhance stimulated scattering,” IEEE J. Quantum Electron. 26, 139 (1990).
    [Crossref]
  9. S. A. Shakir, “Increasing the efficiency of stimulated scattering phase conjugate mirrors,” in Southwest Conference on Optics ’85, R. S. McDowell and S. C. Stotlar, eds., Proc. Soc. Photo-Opt. Instrum. Eng.540, 303 (1985).
    [Crossref]
  10. S. Pfeifer, R. Johnson, and W. Carrion, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 50–51.
  11. A. M. Scott and P. Waggott, “Phase conjugation by self-pumped Brillouin-induced four-wave mixing,” Opt. Lett. 12, 835 (1987).
    [Crossref] [PubMed]
  12. K. D. Ridley and A. M. Scott, “Self-pumped Brillouin enhanced four-wave mixing in a medium with small phase mismatch,” Opt. Commun. 76, 406 (1990).
    [Crossref]
  13. K. D. Ridley and A. M. Scott, “Comparison between theory and experiment in self-pumped Brillouin-enhanced four-wave mixing,” J. Opt. Soc. Am. B 6, 1701 (1989).
    [Crossref]
  14. D. E. Watkins, K. D. Ridley, and A. M. Scott, “Self-pumped four-wave mixing using forward and backward Brillouin scattering,” J. Opt. Soc. Am. B 6, 1693 (1989).
    [Crossref]
  15. A. M. Scott and K. D. Ridley, “A review of Brillouin-enhanced four wave mixing,” IEEE J. Quantum Electron. 25, 438 (1989).
    [Crossref]
  16. G. Arfken, Mathematical Methods for Physicists (Academic, San Diego, 1985), Sect. 15.12.
  17. K. D. Ridley, A. M. Scott, and D. C. Jones, “Frequency detuning in Brillouin induced four-wave mixing,” Int. J. Nonlinear Opt. Phys. 1, 563 (1992).
    [Crossref]

1994 (1)

1992 (2)

K. D. Ridley, A. M. Scott, and D. C. Jones, “Frequency detuning in Brillouin induced four-wave mixing,” Int. J. Nonlinear Opt. Phys. 1, 563 (1992).
[Crossref]

M. T. Duignan, B. J. Feldman, and W. T. Whitney, “Threshold reduction for stimulated Brillouin scattering using a multipass Herriott cell,” J. Opt. Soc. Am. B 9, 548 (1992).
[Crossref]

1991 (2)

1990 (2)

K. D. Ridley and A. M. Scott, “Self-pumped Brillouin enhanced four-wave mixing in a medium with small phase mismatch,” Opt. Commun. 76, 406 (1990).
[Crossref]

G. K. N. Wong and M. J. Damzen, “Investigations of optical feedback used to enhance stimulated scattering,” IEEE J. Quantum Electron. 26, 139 (1990).
[Crossref]

1989 (4)

K. D. Ridley and A. M. Scott, “Comparison between theory and experiment in self-pumped Brillouin-enhanced four-wave mixing,” J. Opt. Soc. Am. B 6, 1701 (1989).
[Crossref]

D. E. Watkins, K. D. Ridley, and A. M. Scott, “Self-pumped four-wave mixing using forward and backward Brillouin scattering,” J. Opt. Soc. Am. B 6, 1693 (1989).
[Crossref]

A. M. Scott and K. D. Ridley, “A review of Brillouin-enhanced four wave mixing,” IEEE J. Quantum Electron. 25, 438 (1989).
[Crossref]

I. Yu. Anikeev, D. A. Glazov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414 (1989).
[Crossref]

1987 (1)

1982 (1)

V. I. Odintsov and L. F. Rogacheva, “Efficient phase conjugation under parametric-feedback conditions,” Sov. Phys. JETP Lett. 36, 344 (1982).

Anikeev, I. Yu.

I. Yu. Anikeev, D. A. Glazov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414 (1989).
[Crossref]

Arfken, G.

G. Arfken, Mathematical Methods for Physicists (Academic, San Diego, 1985), Sect. 15.12.

Auyeung, R. C. Y.

S. R. Bowman, M. J. Winings, R. C. Y. Auyeung, J. E. Tucker, S. K. Searles, and B. J. Feldman, “Laser and spectral properties of Cr, Tm, Ho:YAG at 2.1 μ m,” IEEE J. Quantum Electron. 27, 2142 (1991).
[Crossref]

Bowman, S. R.

S. R. Bowman, M. J. Winings, R. C. Y. Auyeung, J. E. Tucker, S. K. Searles, and B. J. Feldman, “Laser and spectral properties of Cr, Tm, Ho:YAG at 2.1 μ m,” IEEE J. Quantum Electron. 27, 2142 (1991).
[Crossref]

Carrion, W.

S. Pfeifer, R. Johnson, and W. Carrion, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 50–51.

Damzen, M. J.

G. K. N. Wong and M. J. Damzen, “Investigations of optical feedback used to enhance stimulated scattering,” IEEE J. Quantum Electron. 26, 139 (1990).
[Crossref]

Duignan, M. T.

Feldman, B. J.

M. T. Duignan, B. J. Feldman, and W. T. Whitney, “Threshold reduction for stimulated Brillouin scattering using a multipass Herriott cell,” J. Opt. Soc. Am. B 9, 548 (1992).
[Crossref]

S. R. Bowman, M. J. Winings, R. C. Y. Auyeung, J. E. Tucker, S. K. Searles, and B. J. Feldman, “Laser and spectral properties of Cr, Tm, Ho:YAG at 2.1 μ m,” IEEE J. Quantum Electron. 27, 2142 (1991).
[Crossref]

Glazov, D. A.

I. Yu. Anikeev, D. A. Glazov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414 (1989).
[Crossref]

Gordeev, A. A.

I. Yu. Anikeev, D. A. Glazov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414 (1989).
[Crossref]

Johnson, R.

S. Pfeifer, R. Johnson, and W. Carrion, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 50–51.

Jones, D. C.

K. D. Ridley, A. M. Scott, and D. C. Jones, “Frequency detuning in Brillouin induced four-wave mixing,” Int. J. Nonlinear Opt. Phys. 1, 563 (1992).
[Crossref]

Mikhailov, S. I.

I. Yu. Anikeev, D. A. Glazov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414 (1989).
[Crossref]

Mironov, A. B.

I. Yu. Anikeev, D. A. Glazov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414 (1989).
[Crossref]

Odintsov, V. I.

V. I. Odintsov and L. F. Rogacheva, “Efficient phase conjugation under parametric-feedback conditions,” Sov. Phys. JETP Lett. 36, 344 (1982).

Ottusch, J. J.

Pfeifer, S.

S. Pfeifer, R. Johnson, and W. Carrion, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 50–51.

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
[Crossref]

Ridley, K. D.

K. D. Ridley, A. M. Scott, and D. C. Jones, “Frequency detuning in Brillouin induced four-wave mixing,” Int. J. Nonlinear Opt. Phys. 1, 563 (1992).
[Crossref]

K. D. Ridley and A. M. Scott, “Self-pumped Brillouin enhanced four-wave mixing in a medium with small phase mismatch,” Opt. Commun. 76, 406 (1990).
[Crossref]

D. E. Watkins, K. D. Ridley, and A. M. Scott, “Self-pumped four-wave mixing using forward and backward Brillouin scattering,” J. Opt. Soc. Am. B 6, 1693 (1989).
[Crossref]

K. D. Ridley and A. M. Scott, “Comparison between theory and experiment in self-pumped Brillouin-enhanced four-wave mixing,” J. Opt. Soc. Am. B 6, 1701 (1989).
[Crossref]

A. M. Scott and K. D. Ridley, “A review of Brillouin-enhanced four wave mixing,” IEEE J. Quantum Electron. 25, 438 (1989).
[Crossref]

Rockwell, D. A.

Rogacheva, L. F.

V. I. Odintsov and L. F. Rogacheva, “Efficient phase conjugation under parametric-feedback conditions,” Sov. Phys. JETP Lett. 36, 344 (1982).

Scott, A. M.

Searles, S. K.

S. R. Bowman, M. J. Winings, R. C. Y. Auyeung, J. E. Tucker, S. K. Searles, and B. J. Feldman, “Laser and spectral properties of Cr, Tm, Ho:YAG at 2.1 μ m,” IEEE J. Quantum Electron. 27, 2142 (1991).
[Crossref]

Shakir, S. A.

S. A. Shakir, “Increasing the efficiency of stimulated scattering phase conjugate mirrors,” in Southwest Conference on Optics ’85, R. S. McDowell and S. C. Stotlar, eds., Proc. Soc. Photo-Opt. Instrum. Eng.540, 303 (1985).
[Crossref]

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
[Crossref]

Tucker, J. E.

S. R. Bowman, M. J. Winings, R. C. Y. Auyeung, J. E. Tucker, S. K. Searles, and B. J. Feldman, “Laser and spectral properties of Cr, Tm, Ho:YAG at 2.1 μ m,” IEEE J. Quantum Electron. 27, 2142 (1991).
[Crossref]

Waggott, P.

Watkins, D. E.

Whitney, W. T.

Winings, M. J.

S. R. Bowman, M. J. Winings, R. C. Y. Auyeung, J. E. Tucker, S. K. Searles, and B. J. Feldman, “Laser and spectral properties of Cr, Tm, Ho:YAG at 2.1 μ m,” IEEE J. Quantum Electron. 27, 2142 (1991).
[Crossref]

Wong, G. K. N.

G. K. N. Wong and M. J. Damzen, “Investigations of optical feedback used to enhance stimulated scattering,” IEEE J. Quantum Electron. 26, 139 (1990).
[Crossref]

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
[Crossref]

Zubarev, I. G.

I. Yu. Anikeev, D. A. Glazov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414 (1989).
[Crossref]

IEEE J. Quantum Electron. (4)

S. R. Bowman, M. J. Winings, R. C. Y. Auyeung, J. E. Tucker, S. K. Searles, and B. J. Feldman, “Laser and spectral properties of Cr, Tm, Ho:YAG at 2.1 μ m,” IEEE J. Quantum Electron. 27, 2142 (1991).
[Crossref]

I. Yu. Anikeev, D. A. Glazov, A. A. Gordeev, I. G. Zubarev, A. B. Mironov, and S. I. Mikhailov, “The structure of the Stokes fields reflected in SBS in a light guide,” IEEE J. Quantum Electron. 25, 414 (1989).
[Crossref]

G. K. N. Wong and M. J. Damzen, “Investigations of optical feedback used to enhance stimulated scattering,” IEEE J. Quantum Electron. 26, 139 (1990).
[Crossref]

A. M. Scott and K. D. Ridley, “A review of Brillouin-enhanced four wave mixing,” IEEE J. Quantum Electron. 25, 438 (1989).
[Crossref]

Int. J. Nonlinear Opt. Phys. (1)

K. D. Ridley, A. M. Scott, and D. C. Jones, “Frequency detuning in Brillouin induced four-wave mixing,” Int. J. Nonlinear Opt. Phys. 1, 563 (1992).
[Crossref]

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

K. D. Ridley and A. M. Scott, “Self-pumped Brillouin enhanced four-wave mixing in a medium with small phase mismatch,” Opt. Commun. 76, 406 (1990).
[Crossref]

Opt. Lett. (2)

Sov. Phys. JETP Lett. (1)

V. I. Odintsov and L. F. Rogacheva, “Efficient phase conjugation under parametric-feedback conditions,” Sov. Phys. JETP Lett. 36, 344 (1982).

Other (4)

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
[Crossref]

S. A. Shakir, “Increasing the efficiency of stimulated scattering phase conjugate mirrors,” in Southwest Conference on Optics ’85, R. S. McDowell and S. C. Stotlar, eds., Proc. Soc. Photo-Opt. Instrum. Eng.540, 303 (1985).
[Crossref]

S. Pfeifer, R. Johnson, and W. Carrion, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 50–51.

G. Arfken, Mathematical Methods for Physicists (Academic, San Diego, 1985), Sect. 15.12.

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Figures (14)

Fig. 1
Fig. 1

Experimental arrangement for ring SBS.

Fig. 2
Fig. 2

Calculation of pump power transmitted through the Brillouin cell in ring resonator [in units of gI1(0)L]. All pump power is transmitted until the threshold power is reached. Above threshold, all power that is not transmitted is converted into the Stokes beam. Curve x = 0 is the case in which a resonator mode is tuned to the center of the Brillouin gain, i.e., ϕ20 = 0; curve x = 1 is the case in which the phase shift ϕ20 is nonzero and detuning occurs according to Eq. (15).

Fig. 3
Fig. 3

Comparison of instability threshold for a ring as a function of transmission, with equations for loop SBS7 and Eq. (16). The vertical scale is in gilbert units. Top two traces: calculated with loop SBS equations. (a) No gain enhancement, (b) with gain enhancement that is due to an aberrated pump beam. Lower two traces: calculated with Eq. (16); Brillouin gain equals round-trip loss. (c) Without gain enhancement, (d) with gain enhancement.

Fig. 4
Fig. 4

Experimental arrangement. The SBS assembly is as shown in Fig. 1: M’s, mirrors; Cal’s, calorimeters; Det’s, Au-doped Ge detectors; BS, beam splitter.

Fig. 5
Fig. 5

Stokes energy versus pump energy. Measurements for single-focus and two-focus SBS were obtained when the ring was blocked at different points and served to calibrate the degree of threshold reduction. Data sets recorded on different days are shown to illustrate the degree of reproducibility.

Fig. 6
Fig. 6

Typical measurements of input, throughput, and backscattered powers in a single pulse. When digitally summed, the throughput and the backscattered powers equal the input power at all times.

Fig. 7
Fig. 7

Throughput power measured for ring, single-focus, and two-focus SBS. Data points are measured from traces such as those in Fig. 6.

Fig. 8
Fig. 8

Shot-by-shot measurement of throughput power (as measured in Fig. 6) showing random fluctuations. Similar fluctuations were observed in the Stokes power and energy for a fixed input energy.

Fig. 9
Fig. 9

Measured onset energy (integrated pump power up to time at which the stokes beam is observed).7

Fig. 10
Fig. 10

Throughput power plotted versus peak input power. Different symbols indicate the laser’s being operated in different ways to influence the laser spectrum. Apart from a change in the resulting laser power, there was no apparent influence on the statistics of the SBS process.

Fig. 11
Fig. 11

Mode beating in Stokes and transmitted beams at 50 MHz. The conventional mode separation is 167 MHz and the low beat frequency is due to the effect of the Brillouin-induced phase shift.

Fig. 12
Fig. 12

Near-field beam profile of input beam (i/p), Stokes return beam, and aberrated input beam. Data points are measured transmission through calibrated apertures. Curves are for an ideal Gaussian beam.

Fig. 13
Fig. 13

Far-field beam profile measured at a focus of 4-m focal-length mirror showing input beam, Stokes beam, and Stokes beam when the aberrator is placed between the input and the ring system.

Fig. 14
Fig. 14

Shot-by-shot transmission through a fixed aperture in the far field. This shows that fidelity fluctuates randomly on a shot-by-shot basis.

Equations (24)

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E j ( r , t ) = ½ E j ( r , t ) exp [ i ( ω j t - k j · r ) ] + c . c . ; j = 1 , 2 ;             ω 2 = ω 1 - Δ ω ;         k 2 - k 1 .
( 1 + i x ) u 1 + 1 δ ω 0 δ u 1 t = - β E 1 E 2 * .
E 1 r = g 2 β h 1 E 2 u 1 ,             E 2 r = g 2 β h 1 E 1 u 1 *
x = ( Δ ω - ω s ) / δ ω 0 .
δ ω 0 = ½ α s v s = 1 2 τ B ,
E 1 r = - g 2 ( 1 + i x ) E 2 2 E 1 , E 2 * r = - g 2 ( 1 + i x ) E 1 2 E 2 * ,
I 1 r = - g 1 + x 2 I 1 I 2 = I 2 r .
I 2 ( r ) = I 2 ( 0 ) [ I 1 ( 0 ) - I 2 ( 0 ) ] I 1 ( 0 ) exp { g ( 1 + x 2 ) [ I 1 ( 0 ) - I 2 ( 0 ) ] r } - I 2 ( 0 ) .
E 2 * ( 0 ) = E 2 * ( L ) exp [ g ( C L + J ) 2 ( 1 + x 2 ) ] exp [ - i x g ( C L + J ) 2 ( 1 + x 2 ) ] ,
J = ln [ I 1 ( 0 ) exp ( g C L 1 + x 2 ) - I 2 ( 0 ) I 1 ( 0 ) - I 2 ( 0 ) ] .
E 2 * ( 0 ) = E 2 * ( L ) γ 2 exp ( i ϕ B 2 ) ,
E 2 ( L ) = r E 2 ( 0 ) exp ( i ϕ S ) .
g ( C L + J ) 2 ( 1 + x 2 ) = ln ( 1 / r )
ϕ S = k 2 L R = ϕ 20 - x δ ω 0 L R / c
ϕ 20 - x [ δ ω 0 L R / c - log ( 1 / r ) ] = 2 n π ,
x = 2 n π - ϕ 20 [ δ ω 0 L R / c - log ( 1 / r ) ] .
γ 2 2 = 1 r 2 = ln ( I 1 ( 0 ) exp { g [ I 1 ( 0 ) - I 2 ( 0 ) ] L 1 + x 2 } - I 2 ( 0 ) I 1 ( 0 ) - I 2 ( 0 ) ) .
[ δ ω 0 ( 1 + i x ) + s ] u ¯ = - β E 1 E ¯ 2 * δ ω 0 ,
E ¯ 2 * r = - g h 1 E 1 2 δ ω 0 2 [ δ ω 0 ( 1 + i x ) + s ] .
E ¯ 2 * ( 0 ) = E ¯ 2 * ( L ) exp { g h 1 E 1 2 L δ ω 0 2 [ δ ω 0 ( 1 + i x ) + s ] } ,
r exp { g h 1 E 1 2 L δ ω 0 [ δ ω 0 ( 1 + i x ) + s ] + i ϕ 20 - i x δ ω 0 L R c } = 1.
E 2 * ( 0 , t ) = m b m exp ( s m t ) + C ,
s δ ω 0 = [ g h 1 E 1 2 L ln ( r ) - 1 ] .
I 2 ( t ) ~ exp [ - δ ω 0 t + ( h 1 g B I 1 L δ ω 0 t ) 1 / 2 ] .

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