Abstract

Phase locking of two beams of a Q-switched single-longitudinal-mode Nd:YAG laser is investigated. Phase locking and phase conjugation of these beams are achieved by mutual reflection in a Brillouin cell containing nitrogen at 75 bars. Phase locking is measured interferometrically as a function of the energy, the energy ratio, the separation in the far field, the separation in the near field, and the separation of the beam waists along the propagation path. The change of the relative phase from pulse to pulse of the two output beams is reduced to less than =λ/27 under optimized conditions (50% criterion). A strong influence of phase locking on the reflectivity of the Brillouin cell is observed.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. D. S. Sumida, D. C. Jones, and D. A. Rockwell, “An 8.2 J phase conjugate solid-state laser coherently combining eight parallel amplifiers,” IEEE J. Quantum Electron. 30, 2617–2627 (1994).
    [CrossRef]
  3. V. M. Leont’ev, V. G. Novoselov, Y. P. Rudnitskii, and L. V. Chernysheva, “Solid-state laser with a composite active element and diffraction-limit divergence,” Sov. J. Quantum Electron. 17, 220–223 (1987).
    [CrossRef]
  4. K. V. Gratsianov, A. F. Kornev, V. V. Lyubimov, and V. G. Pankov, “Laser beam phasing with phase conjugation in Brillouin scattering,” Opt. Spectrosc. 68, 360–361 (1990).
  5. N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhaǐlov, and M. B. Smirnov, “Inversion of wavefront in SMBS of a depolarized pump,” JETP Lett. 28, 197–200 (1979).
  6. D. L. Carroll, R. Johnson, S. J. Pfeifer, and R. H. Moyer, “Experimental investigations of stimulated Brillouin scattering beam combination,” J. Opt. Soc. Am. B 9, 2214–2224 (1992).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. Available from the Beuth Verlag GmbH, 10772 Berlin, Germany; D. Wright, P. Greeve, J. Fleischer, and L. Austin, “Laser beam width, divergence and beam propagation factor—an international standardization approach,” Opt. Quantum Electron. 24, 993–1000 (1992); D. Wright, “Beamwidths of a diffracted laser using four proposed methods,” Opt. Quantum Electron. 24, 1129–1135 (1992).
    [CrossRef]
  11. C. B. Dane, W. A. Neuman, and L. A. Hackel, “Pulse-shape dependence of stimulated-Brillouin-scattering phase conjugation fidelity for high input energies,” Opt. Lett. 17, 1271–1273 (1992).
    [CrossRef] [PubMed]
  12. The temporal and spatial evolution of SBS has been investigated, e.g., by the following: R. Menzel and H. J. Eichler, “Temporal and spatial reflectivity of focused beams in stimulated Brillouin scattering for phase conjugation,” Phys. Rev. A 46, 7139–7149 (1992). J. Munch, R. F. Wuerker, and M. J. LeFebvre, “Interaction length for optical phase conjugation by stimulated Brillouin scattering: an experimental investigation,” Appl. Opt. 28, 3099–3105 (1989).
    [CrossRef] [PubMed]
  13. In these experiments FFS=−2dσ, 0 resulted in the overlap volume being centered at −0.93zR behind the beam waist.
  14. M. S. Mangir and D. A. Rockwell, “4.5-J Brillouin phase-conjugate mirror producing excellent near- and far-field fidelity,” J. Opt. Soc. Am. B 10, 1396–1400 (1993).
    [CrossRef]

1994 (1)

D. S. Sumida, D. C. Jones, and D. A. Rockwell, “An 8.2 J phase conjugate solid-state laser coherently combining eight parallel amplifiers,” IEEE J. Quantum Electron. 30, 2617–2627 (1994).
[CrossRef]

1993 (1)

1992 (2)

1990 (2)

S. Sternklar, D. Chomsky, S. Jackel, and A. Zigler, “Misalignment sensitivity of beam combining by stimulated Brillouin scattering,” Opt. Lett. 15, 469–470 (1990).
[CrossRef] [PubMed]

K. V. Gratsianov, A. F. Kornev, V. V. Lyubimov, and V. G. Pankov, “Laser beam phasing with phase conjugation in Brillouin scattering,” Opt. Spectrosc. 68, 360–361 (1990).

1988 (2)

1987 (1)

V. M. Leont’ev, V. G. Novoselov, Y. P. Rudnitskii, and L. V. Chernysheva, “Solid-state laser with a composite active element and diffraction-limit divergence,” Sov. J. Quantum Electron. 17, 220–223 (1987).
[CrossRef]

1986 (1)

1979 (1)

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhaǐlov, and M. B. Smirnov, “Inversion of wavefront in SMBS of a depolarized pump,” JETP Lett. 28, 197–200 (1979).

IEEE J. Quantum Electron. (1)

D. S. Sumida, D. C. Jones, and D. A. Rockwell, “An 8.2 J phase conjugate solid-state laser coherently combining eight parallel amplifiers,” IEEE J. Quantum Electron. 30, 2617–2627 (1994).
[CrossRef]

J. Opt. Soc. Am. B (3)

JETP Lett. (1)

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, S. I. Mikhaǐlov, and M. B. Smirnov, “Inversion of wavefront in SMBS of a depolarized pump,” JETP Lett. 28, 197–200 (1979).

Opt. Lett. (4)

Opt. Spectrosc. (1)

K. V. Gratsianov, A. F. Kornev, V. V. Lyubimov, and V. G. Pankov, “Laser beam phasing with phase conjugation in Brillouin scattering,” Opt. Spectrosc. 68, 360–361 (1990).

Sov. J. Quantum Electron. (1)

V. M. Leont’ev, V. G. Novoselov, Y. P. Rudnitskii, and L. V. Chernysheva, “Solid-state laser with a composite active element and diffraction-limit divergence,” Sov. J. Quantum Electron. 17, 220–223 (1987).
[CrossRef]

Other (3)

Available from the Beuth Verlag GmbH, 10772 Berlin, Germany; D. Wright, P. Greeve, J. Fleischer, and L. Austin, “Laser beam width, divergence and beam propagation factor—an international standardization approach,” Opt. Quantum Electron. 24, 993–1000 (1992); D. Wright, “Beamwidths of a diffracted laser using four proposed methods,” Opt. Quantum Electron. 24, 1129–1135 (1992).
[CrossRef]

The temporal and spatial evolution of SBS has been investigated, e.g., by the following: R. Menzel and H. J. Eichler, “Temporal and spatial reflectivity of focused beams in stimulated Brillouin scattering for phase conjugation,” Phys. Rev. A 46, 7139–7149 (1992). J. Munch, R. F. Wuerker, and M. J. LeFebvre, “Interaction length for optical phase conjugation by stimulated Brillouin scattering: an experimental investigation,” Appl. Opt. 28, 3099–3105 (1989).
[CrossRef] [PubMed]

In these experiments FFS=−2dσ, 0 resulted in the overlap volume being centered at −0.93zR behind the beam waist.

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Figures (13)

Fig. 1
Fig. 1

Experimental setup used in this investigation. Circled inset, beam overlap region viewed from above; quadratic inset, cross section of the beam waist. BS, beam splitter with 50% reflectivity; TFP’s, thin-film polarizers.

Fig. 2
Fig. 2

Typical result of 1000 interferometrical measurements of the change of the relative phase difference δ of the two output beams from pulse to pulse. For 50% of all pulses, δ is smaller than . Here is a measure of the quality of the phase locking (here =λ/31 corresponding to K=0.87). This measurement corresponds to the marked data point in Fig. 7.

Fig. 3
Fig. 3

The pump beams E1, E3, the phase conjugated beams E2, E4,4WM, E4, the unit vectors Ŝ, Ĝ, , and the angles between them.

Fig. 4
Fig. 4

Phase locking as a function of the energy of the beams at an energy ratio of W3/W1=1.0 and FFS=0. This graph shows the average of a number of data sets with NFS’s ranging from 2dσ(0) to 4dσ(0). Each individual data set shows a similar function.

Fig. 5
Fig. 5

Phase locking as a function of the energy ratio of the beams at FFS=0, NFS=2.2dσ(0), and W1=7Wth. Similar dependencies were obtained for other FFS’s, too.

Fig. 6
Fig. 6

Phase locking as a function of NFS at an energy ratio of W3/W1=1.0 and FFS=0. NFS=dσ(0) corresponds to an angle of 2α=5.7 mrad between the pump beams. This graph shows the average of a number of data sets with W1 ranging from 1.2Wth to 9.2Wth. Each individual data set shows a similar function.

Fig. 7
Fig. 7

Phase locking as a function of FFS at an energy ratio of W3/W1=1.0, NFS=2.2dσ(0), and W1=7.8Wth. Filled and open circles represent two individual data sets.

Fig. 8
Fig. 8

Phase locking as a function of FFS at an energy ratio of W3/W1=0.3, NFS=2.2dσ(0), and W1=7.8Wth. An FFS of -2dσ,0 results in the overlap volume being centered at -0.93zR behind the beam waists. Filled and open circles represent two individual data sets. The measurement of p(δ) that corresponds to the marked data point is shown in Fig. 2.

Fig. 9
Fig. 9

Phase locking as a function of the separation of the beam waists in the beam propagation direction (BWS) at an energy ratio of W3/W1=0.3. The overlap volume is centered at the beam waist of beam b, NFS=2.2dσ(0), and W1=7.8Wth. For positive BWS the beam waist of beam a is behind the beam crossing. Filled and open circles represent two individual data sets.

Fig. 10
Fig. 10

Phase locking as a function of FFS at an energy ratio of W3/W1=0.3 at FFS=0, NFS=2.2dσ(0), and W1=7.8Wth. Filled and open circles represent two individual data sets.

Fig. 11
Fig. 11

Transmission of the SBS cell as a function of FFS at an energy ratio of W3/W1=0.3, FFS=0, NFS=2.2dσ(0), and W1=7.8Wth. The filled circles represent the data of beam a, the open circles that of beam b.

Fig. 12
Fig. 12

Transmission of the SBS cell as a function of BWS for the conditions of the measurements presented in Fig. 9. The filled circles represent the data of beam a, the open circles that of beam b.

Fig. 13
Fig. 13

Delay of the pump pulse and the signal pulse of beam b against BWS for the conditions of the measurements presented in Fig. 9. The origin of the time scale is chosen arbitrarily.

Equations (9)

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0p(δ)dδ=πp(δ)dδ,
K=1-2/π,
E1(r, t)=e^PE1 expiωt-ωc Pˆr-ϕP(r),
E2(r, t)=e^PE2 expi(ω-ωB)t+ω-ωBc Pˆr+ϕP(r)+ϕ1,
E3(r, t)=e^SE1 expiωt-ωc Sˆr-ϕS(r),
E4(r, t)=e^SE2 expi(ω-ωB)t+ω-ωBc Sˆr+ϕS(r)+ϕ2,
I2,3(r, t)=½0cn(ω)|E2+E3|2E22+E32+2(ePeS)E2E3×cosωBt-ωc (Pˆr+Sˆr)+ωBc Pˆr-ϕP(r)-ϕS(r)-ϕ1,
λgrating,2,3λ(ω)/2 cos α,
vgrating,2,3cωB/2ω cos α

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