Abstract

We describe experimental and theoretical investigations of beam cleanup with highly aberrated pump beams in the intensity-averaging regime. Distortion-free amplification of a diffraction-limited Stokes beam is demonstrated in a crossed-beam geometry with a pump beam aberrated to 120 times its diffraction limit, resulting in a brightness increase of 5000 times. Moderately aberrated pump beams produce off-axis Stokes components, while collinear interactions introduce distortion on the Stokes beam. Phase conjugation is combined with stimulated Raman scattering to remove both the aberrations of the pump beam and the aberrations on the Stokes beam itself.

© 1986 Optical Society of America

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  1. V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 21, 961 (1978).
  2. J. Goldhar and J. R. Murray, IEEE J. Quantum Electron. QE-18, 399 (1982).
    [Crossref]
  3. R. S. F. Chang, R. H. Lehmberg, M. T. Duignan, and N. Djeu, IEEE J. Quantum Electron. QE-21, 477 (1985).
    [Crossref]
  4. N. F. Andreev, V. I. Bespalov, A. M. Kiselev, and G. A. Pasmanik, Sov. J. Quantum Electron. 9, 585 (1979).
    [Crossref]
  5. R. S. F. Chang and N. Djeu, Opt. Lett. 8, 139 (1983).
    [Crossref] [PubMed]
  6. J. Reintjes, R. H. Lehmberg, G. Calame, R. S. F. Chang, and M. Duignan, J. Opt. Soc. Am. A 2(13), P3 (1985).
    [Crossref]
  7. J. Reintjes, presented at Lasers ’85, Las Vegas, Nev., December 1985.
  8. J. Goldhar, M. W. Taylor, and J. R. Murray, IEEE J. Quantum Electron. QE-20, 772 (1984).
    [Crossref]
  9. N. G. Basov and A. Z. Grasuik, in Lasers and Holographic Data Processing, N. G. Basov, ed. (Mir, Moscow, 1984), pp. 122–139.
  10. H. Komine, W. H. Long, E. A. Stappaerts, and S. J. Brosnan, J. Opt. Soc. Am. A 2(13), P3 (1985); see also J. Opt. Soc. Am. B 3, 1428–1447 (1986).
    [Crossref]

1985 (3)

R. S. F. Chang, R. H. Lehmberg, M. T. Duignan, and N. Djeu, IEEE J. Quantum Electron. QE-21, 477 (1985).
[Crossref]

J. Reintjes, R. H. Lehmberg, G. Calame, R. S. F. Chang, and M. Duignan, J. Opt. Soc. Am. A 2(13), P3 (1985).
[Crossref]

H. Komine, W. H. Long, E. A. Stappaerts, and S. J. Brosnan, J. Opt. Soc. Am. A 2(13), P3 (1985); see also J. Opt. Soc. Am. B 3, 1428–1447 (1986).
[Crossref]

1984 (1)

J. Goldhar, M. W. Taylor, and J. R. Murray, IEEE J. Quantum Electron. QE-20, 772 (1984).
[Crossref]

1983 (1)

1982 (1)

J. Goldhar and J. R. Murray, IEEE J. Quantum Electron. QE-18, 399 (1982).
[Crossref]

1979 (1)

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, and G. A. Pasmanik, Sov. J. Quantum Electron. 9, 585 (1979).
[Crossref]

1978 (1)

V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 21, 961 (1978).

Andreev, N. F.

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, and G. A. Pasmanik, Sov. J. Quantum Electron. 9, 585 (1979).
[Crossref]

Basov, N. G.

N. G. Basov and A. Z. Grasuik, in Lasers and Holographic Data Processing, N. G. Basov, ed. (Mir, Moscow, 1984), pp. 122–139.

Bespalov, V. I.

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, and G. A. Pasmanik, Sov. J. Quantum Electron. 9, 585 (1979).
[Crossref]

V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 21, 961 (1978).

Betin, A. A.

V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 21, 961 (1978).

Brosnan, S. J.

H. Komine, W. H. Long, E. A. Stappaerts, and S. J. Brosnan, J. Opt. Soc. Am. A 2(13), P3 (1985); see also J. Opt. Soc. Am. B 3, 1428–1447 (1986).
[Crossref]

Calame, G.

J. Reintjes, R. H. Lehmberg, G. Calame, R. S. F. Chang, and M. Duignan, J. Opt. Soc. Am. A 2(13), P3 (1985).
[Crossref]

Chang, R. S. F.

J. Reintjes, R. H. Lehmberg, G. Calame, R. S. F. Chang, and M. Duignan, J. Opt. Soc. Am. A 2(13), P3 (1985).
[Crossref]

R. S. F. Chang, R. H. Lehmberg, M. T. Duignan, and N. Djeu, IEEE J. Quantum Electron. QE-21, 477 (1985).
[Crossref]

R. S. F. Chang and N. Djeu, Opt. Lett. 8, 139 (1983).
[Crossref] [PubMed]

Djeu, N.

R. S. F. Chang, R. H. Lehmberg, M. T. Duignan, and N. Djeu, IEEE J. Quantum Electron. QE-21, 477 (1985).
[Crossref]

R. S. F. Chang and N. Djeu, Opt. Lett. 8, 139 (1983).
[Crossref] [PubMed]

Duignan, M.

J. Reintjes, R. H. Lehmberg, G. Calame, R. S. F. Chang, and M. Duignan, J. Opt. Soc. Am. A 2(13), P3 (1985).
[Crossref]

Duignan, M. T.

R. S. F. Chang, R. H. Lehmberg, M. T. Duignan, and N. Djeu, IEEE J. Quantum Electron. QE-21, 477 (1985).
[Crossref]

Goldhar, J.

J. Goldhar, M. W. Taylor, and J. R. Murray, IEEE J. Quantum Electron. QE-20, 772 (1984).
[Crossref]

J. Goldhar and J. R. Murray, IEEE J. Quantum Electron. QE-18, 399 (1982).
[Crossref]

Grasuik, A. Z.

N. G. Basov and A. Z. Grasuik, in Lasers and Holographic Data Processing, N. G. Basov, ed. (Mir, Moscow, 1984), pp. 122–139.

Kiselev, A. M.

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, and G. A. Pasmanik, Sov. J. Quantum Electron. 9, 585 (1979).
[Crossref]

Komine, H.

H. Komine, W. H. Long, E. A. Stappaerts, and S. J. Brosnan, J. Opt. Soc. Am. A 2(13), P3 (1985); see also J. Opt. Soc. Am. B 3, 1428–1447 (1986).
[Crossref]

Lehmberg, R. H.

J. Reintjes, R. H. Lehmberg, G. Calame, R. S. F. Chang, and M. Duignan, J. Opt. Soc. Am. A 2(13), P3 (1985).
[Crossref]

R. S. F. Chang, R. H. Lehmberg, M. T. Duignan, and N. Djeu, IEEE J. Quantum Electron. QE-21, 477 (1985).
[Crossref]

Long, W. H.

H. Komine, W. H. Long, E. A. Stappaerts, and S. J. Brosnan, J. Opt. Soc. Am. A 2(13), P3 (1985); see also J. Opt. Soc. Am. B 3, 1428–1447 (1986).
[Crossref]

Murray, J. R.

J. Goldhar, M. W. Taylor, and J. R. Murray, IEEE J. Quantum Electron. QE-20, 772 (1984).
[Crossref]

J. Goldhar and J. R. Murray, IEEE J. Quantum Electron. QE-18, 399 (1982).
[Crossref]

Pasmanik, G. A.

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, and G. A. Pasmanik, Sov. J. Quantum Electron. 9, 585 (1979).
[Crossref]

V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 21, 961 (1978).

Reintjes, J.

J. Reintjes, R. H. Lehmberg, G. Calame, R. S. F. Chang, and M. Duignan, J. Opt. Soc. Am. A 2(13), P3 (1985).
[Crossref]

J. Reintjes, presented at Lasers ’85, Las Vegas, Nev., December 1985.

Stappaerts, E. A.

H. Komine, W. H. Long, E. A. Stappaerts, and S. J. Brosnan, J. Opt. Soc. Am. A 2(13), P3 (1985); see also J. Opt. Soc. Am. B 3, 1428–1447 (1986).
[Crossref]

Taylor, M. W.

J. Goldhar, M. W. Taylor, and J. R. Murray, IEEE J. Quantum Electron. QE-20, 772 (1984).
[Crossref]

IEEE J. Quantum Electron. (3)

J. Goldhar and J. R. Murray, IEEE J. Quantum Electron. QE-18, 399 (1982).
[Crossref]

R. S. F. Chang, R. H. Lehmberg, M. T. Duignan, and N. Djeu, IEEE J. Quantum Electron. QE-21, 477 (1985).
[Crossref]

J. Goldhar, M. W. Taylor, and J. R. Murray, IEEE J. Quantum Electron. QE-20, 772 (1984).
[Crossref]

Izv. Vyssh. Uchebn. Zaved. Radiofiz. (1)

V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 21, 961 (1978).

J. Opt. Soc. Am. A (2)

J. Reintjes, R. H. Lehmberg, G. Calame, R. S. F. Chang, and M. Duignan, J. Opt. Soc. Am. A 2(13), P3 (1985).
[Crossref]

H. Komine, W. H. Long, E. A. Stappaerts, and S. J. Brosnan, J. Opt. Soc. Am. A 2(13), P3 (1985); see also J. Opt. Soc. Am. B 3, 1428–1447 (1986).
[Crossref]

Opt. Lett. (1)

Sov. J. Quantum Electron. (1)

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, and G. A. Pasmanik, Sov. J. Quantum Electron. 9, 585 (1979).
[Crossref]

Other (2)

J. Reintjes, presented at Lasers ’85, Las Vegas, Nev., December 1985.

N. G. Basov and A. Z. Grasuik, in Lasers and Holographic Data Processing, N. G. Basov, ed. (Mir, Moscow, 1984), pp. 122–139.

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Figures (27)

Fig. 1
Fig. 1

Schematic illustration of Raman beam cleanup with collinear propagation.

Fig. 2
Fig. 2

Schematic illustration of Raman beam cleanup with crossing pump beams.

Fig. 3
Fig. 3

Geometry used to model collinear beam-cleanup interactions.

Fig. 4
Fig. 4

Typical theoretical result for collinear interactions. (a) Pump intensity distribution at the lens plane, (b) pump intensity (solid curve) and Stokes intensity (dashed curve) at the entrance to the amplifier, (c) pump intensity (solid curve) and Stokes intensity (dashed curve) at the exit of the amplifier, (d) far-field distnbutions of the incident Stokes (dotted curve) and amplified Stokes (dashed curve). For these calculations the pump-beam divergence was 1.3 mrad, corresponding to 43 times the diffraction limit. The total Raman gain was GL = 5.4, and 70% of the amplified Stokes energy was contained in the far-field sidebands.

Fig. 5
Fig. 5

Geometry used to model crossed-beam-cleanup interactions.

Fig. 6
Fig. 6

Intensity distributions of pump and Stokes beams in various planes for crossed-beam amplification with four pump beams. (a) Geometry, (b) pump (solid curve) and Stokes (dashed curve) at amplifier entrance, (c) pump (solid curve) and Stokes (dashed curve) at amplifier exit, (d) far field of incident Stokes (dotted curve) and amplified Stokes (dashed curve).

Fig. 7
Fig. 7

Intensity distribution of pump and Stokes beams in various planes for crossed-beam amplification with the center pump beam restored. (a) Geometry, (b) pump (solid curve) and Stokes (dashed curve) at amplifier entrance, (c) pump (solid curve) and Stokes (dashed curve) at amplifier exit, (d) far field of incident Stokes (dotted curve) and amplified Stokes (dashed curve).

Fig. 8
Fig. 8

Schematic diagram of system used to generate narrow-band 308-nm radiation for amplification, showing the cw Ar laser, the ring dye laser, the dye-amplifier chain pumped by a XeCl laser, the direct-vision prisms (DVP’s), the spatial filters, and the KDP-doubling crystal.

Fig. 9
Fig. 9

(a) Schematic diagram of a two-pass XeCl amplifier and spatial filter for the input beam. The second pass, following reflection from mirror M3, is above the plane of the paper. (b) Typical UV input (left) and amplified (right) pulses from a two-pass amplifier system.

Fig. 10
Fig. 10

Schematic illustration of apparatus used for collinear beam-cleanup experiments. The lens focal length was 2 m, and the aberrator produced a beam at 120 XDL. Ten percent of the incident pump beam was used to drive the Stokes seed generator, C1, and the remaining 90% was used to pump the Raman amplifier, C2.

Fig. 11
Fig. 11

Far-field distribution of an amplified Stokes beam obtained with collinear geometry. Pattern shows a broad skirt in addition to a central peak. Stokes energy measurement is shown in the lower trace.

Fig. 12
Fig. 12

Experimental diagram of apparatus used for crossed-beam geometry.

Fig. 13
Fig. 13

Diagram of optical integrator. Top, side view showing reflection and focusing of beams. Bottom, front view showing 5 × 5 array with hole for Stokes beam.

Fig. 14
Fig. 14

Far-field diode-array traces of incident Stokes (top left) and amplified Stokes (bottom left) obtained with crossed-beam geometry and a H2 pressure of 13 atm. Pulse shapes for unamplified (top right) and amplified (bottom right) Stokes beams are also shown. The input Stokes pulse is on the left; the output Stokes pulse is on the right. Scale for diode-array trace is 0.5 mm/division, and the time scale is 10 nsec/division.

Fig. 15
Fig. 15

Intensity pattern of the first-Stokes radiation obtained at a H2 pressure of 4.4 atm with a pump beam aberrated to a level of 20 XDL with a gas aberrator.

Fig. 16
Fig. 16

Phase-matching diagram for four-wave mixing process leading to off-axis Stokes components.

Fig. 17
Fig. 17

Far-field pattern of amplified Stokes beam calculated for four crossing pump beams without aberration, showing generation of off-axis components that reproduce the pump distribution. The far-field pattern of the incident Stokes beam contained only a single central peak (dotted curve overlapping central component of amplified Stokes pattern).

Fig. 18
Fig. 18

Schematic illustration of combination of phase conjugation and Raman beam cleanup to compensate for distortions in the Stokes-beam path as well as for pump-beam aberrations.

Fig. 19
Fig. 19

Characteristics of incident Stokes beam used for Raman beam-cleanup–phase-conjugation calculations. (a) Intensity profile, (b) phase distribution, (c) far-field intensity, (d) integrated far field over width required to account for 63% of Stokes energy.

Fig. 20
Fig. 20

Characteristics of Stokes beam in Raman beam-cleanup–phase-conjugation calculations after the first pass through the aberrator. (a) Intensity profile, (b) phase distribution, (c) far-field intensity, (d) integrated far field over width required to account for 63% of Stokes energy.

Fig. 21
Fig. 21

Characteristics of Stokes beam in Raman beam-cleanup–phase-conjugation calculations after phase conjugation and the second pass through Raman amplifier but before the second pass through the aberrator. (a) Intensity profile, (b) phase distribution, (c) far-field intensity, (d) integrated far field over width required to account for 63% of Stokes energy.

Fig. 22
Fig. 22

Characteristics of the Stokes beam in Raman beam-cleanup–phase-conjugation calculations after the second pass through the aberrator. (a) Intensity profile, (b) phase distribution, (c) far-field intensity, (d) integrated far field over width required to account for 63% of Stokes energy.

Fig. 23
Fig. 23

Characteristics of the renormalized reference beam used for comparison with amplified Stokes beam in Raman beam-cleanup–phase-conjugation calculations. (a) Intensity profile, (b) phase distribution, (c) far-field intensity, (d) integrated far field over width required to account for 63% of Stokes energy.

Fig. 24
Fig. 24

Schematic diagram of the apparatus used for Raman beam-cleanup–phase-conjugation experiments.

Fig. 25
Fig. 25

Interferogram of the input Stokes beam showing aberration imposed by He jet.

Fig. 26
Fig. 26

Near-field measurements of the Stokes beam obtained with the Raman amplifier on. Top left, conjugate mirror, no aberrator; top right, conjugate mirror, aberrator on; bottom left, normal mirror, no aberrator; bottom right, normal mirror, aberrator on.

Fig. 27
Fig. 27

Calculated distributions for the Stokes beam after two passes through a He-jet aberrator in the Raman beam-cleanup–phase-conjugation interaction with the Raman amplifier on. (a) Near-field intensity with a conjugate mirror in place, (b) far-field intensity with a conjugate mirror in place, (c) near-field intensity distribution with a normal mirror in place, (d) far-field intensity distribution with a normal mirror in place, (e) near-field phase distribution with the conjugate mirror in place.

Tables (5)

Tables Icon

Table 1 Raman Beam-Cleanup Configurations

Tables Icon

Table 2 Raman Beam-Cleanup Theoretical Results with Collinear Geometry

Tables Icon

Table 3 Raman Beam-Cleanup Theoretical Results with Crossed Beams

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Table 4 Raman Beam-Cleanup Experimental Results with Crossed Beams

Tables Icon

Table 5 Raman Beam-Cleanup–Phase-Conjugation Theoretical Results

Equations (8)

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d A S ( r , z ) / d z = ( g / 2 ) | A L ( r , z ) | 2 A S ,
d A L ( r , z ) / d z = ( ω L / ω S ) ( g / 2 ) | A S ( r , z , ) | 2 A L .
E i ( r , z , t ) = 1 / 2 [ | A i ( r , z ) | exp [ i ϕ i ( r , z ) ] exp [ i ( ω i t k i z ) ] + c . c . ] .
A S ( r , z ) = A S ( r , 0 ) exp [ ( g / 2 ) 0 z | A L ( r , z ) | 2 d z ] .
Δ θ 2 G [ L / k ] 1 / 2 .
( 1 / 2 i k S ) 2 A S / x 2 + A S / z = ( g / 2 ) | A L | 2 A S ,
( 1 / 2 i k L ) 2 A L / x 2 + A L / z = ( ω L / ω S ) ( g / 2 ) | A S | 2 A L .
ω S , 2 = ω L , 1 ω L , 2 + ω S , 1 ,

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