Abstract

Passive pulse shapers including Fabry-Perot etalons, double-etalons, and classical beam splitters are examined both theoretically and experimentally for their temporal behavior. For temporally and spatially overlapped pulses, interpulse interference effects determine the resulting pulse shapes. The output pulses from such devices are expected to be of great importance for laser fusion pulse shaping.

© 1976 Optical Society of America

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References

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  1. J. Nuckolls, L. Wood, A. Thiessen, G. Zimmerman, Nature (London) 239, 139 (1972).
    [CrossRef]
  2. R. J. Mason, Nucl. Fusion 15, 1031 (1975).
    [CrossRef]
  3. J. D. Lindl, W. C. Mead, Phys. Rev. Lett. 34, 1273 (1975).
    [CrossRef]
  4. J. Soures, S. Kumpan, J. Hoose, Appl. Opt. 13, 2081 (1974).
    [CrossRef] [PubMed]
  5. C. E. Thomas, L. D. Siebert, Appl. Opt. 15, 462 (1976).
    [CrossRef] [PubMed]
  6. J. L. Hughes, P. J. Donohue, Opt. Commun. 12, 302 (1974).
    [CrossRef]
  7. J. M. Thorne, T. R. Loree, G. H. McCall, J. Appl. Phys. 45, 3072 (1974).
    [CrossRef]
  8. E. S. Bliss, D. R. Speck, W. W. Simmons, Appl. Phys. Lett. 25, 728 (1974).
    [CrossRef]
  9. C. Roychoudhuri, J. Opt. Soc. Am. 65, 1418 (1975).
    [CrossRef]
  10. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), p. 379.
  11. L. Coleman, “Laser Fusion Program Semiannual Report, July–December 1973,” UCRL-50021-73-2, Lawrence Livermore Laboratory, p. 56 (unpublished).

1976 (1)

1975 (3)

C. Roychoudhuri, J. Opt. Soc. Am. 65, 1418 (1975).
[CrossRef]

R. J. Mason, Nucl. Fusion 15, 1031 (1975).
[CrossRef]

J. D. Lindl, W. C. Mead, Phys. Rev. Lett. 34, 1273 (1975).
[CrossRef]

1974 (4)

J. L. Hughes, P. J. Donohue, Opt. Commun. 12, 302 (1974).
[CrossRef]

J. M. Thorne, T. R. Loree, G. H. McCall, J. Appl. Phys. 45, 3072 (1974).
[CrossRef]

E. S. Bliss, D. R. Speck, W. W. Simmons, Appl. Phys. Lett. 25, 728 (1974).
[CrossRef]

J. Soures, S. Kumpan, J. Hoose, Appl. Opt. 13, 2081 (1974).
[CrossRef] [PubMed]

1972 (1)

J. Nuckolls, L. Wood, A. Thiessen, G. Zimmerman, Nature (London) 239, 139 (1972).
[CrossRef]

Bliss, E. S.

E. S. Bliss, D. R. Speck, W. W. Simmons, Appl. Phys. Lett. 25, 728 (1974).
[CrossRef]

Coleman, L.

L. Coleman, “Laser Fusion Program Semiannual Report, July–December 1973,” UCRL-50021-73-2, Lawrence Livermore Laboratory, p. 56 (unpublished).

Donohue, P. J.

J. L. Hughes, P. J. Donohue, Opt. Commun. 12, 302 (1974).
[CrossRef]

Hoose, J.

Hughes, J. L.

J. L. Hughes, P. J. Donohue, Opt. Commun. 12, 302 (1974).
[CrossRef]

Kumpan, S.

Lindl, J. D.

J. D. Lindl, W. C. Mead, Phys. Rev. Lett. 34, 1273 (1975).
[CrossRef]

Loree, T. R.

J. M. Thorne, T. R. Loree, G. H. McCall, J. Appl. Phys. 45, 3072 (1974).
[CrossRef]

Mason, R. J.

R. J. Mason, Nucl. Fusion 15, 1031 (1975).
[CrossRef]

McCall, G. H.

J. M. Thorne, T. R. Loree, G. H. McCall, J. Appl. Phys. 45, 3072 (1974).
[CrossRef]

Mead, W. C.

J. D. Lindl, W. C. Mead, Phys. Rev. Lett. 34, 1273 (1975).
[CrossRef]

Nuckolls, J.

J. Nuckolls, L. Wood, A. Thiessen, G. Zimmerman, Nature (London) 239, 139 (1972).
[CrossRef]

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), p. 379.

Roychoudhuri, C.

Siebert, L. D.

Simmons, W. W.

E. S. Bliss, D. R. Speck, W. W. Simmons, Appl. Phys. Lett. 25, 728 (1974).
[CrossRef]

Soures, J.

Speck, D. R.

E. S. Bliss, D. R. Speck, W. W. Simmons, Appl. Phys. Lett. 25, 728 (1974).
[CrossRef]

Thiessen, A.

J. Nuckolls, L. Wood, A. Thiessen, G. Zimmerman, Nature (London) 239, 139 (1972).
[CrossRef]

Thomas, C. E.

Thorne, J. M.

J. M. Thorne, T. R. Loree, G. H. McCall, J. Appl. Phys. 45, 3072 (1974).
[CrossRef]

Wood, L.

J. Nuckolls, L. Wood, A. Thiessen, G. Zimmerman, Nature (London) 239, 139 (1972).
[CrossRef]

Zimmerman, G.

J. Nuckolls, L. Wood, A. Thiessen, G. Zimmerman, Nature (London) 239, 139 (1972).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

E. S. Bliss, D. R. Speck, W. W. Simmons, Appl. Phys. Lett. 25, 728 (1974).
[CrossRef]

J. Appl. Phys. (1)

J. M. Thorne, T. R. Loree, G. H. McCall, J. Appl. Phys. 45, 3072 (1974).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (London) (1)

J. Nuckolls, L. Wood, A. Thiessen, G. Zimmerman, Nature (London) 239, 139 (1972).
[CrossRef]

Nucl. Fusion (1)

R. J. Mason, Nucl. Fusion 15, 1031 (1975).
[CrossRef]

Opt. Commun. (1)

J. L. Hughes, P. J. Donohue, Opt. Commun. 12, 302 (1974).
[CrossRef]

Phys. Rev. Lett. (1)

J. D. Lindl, W. C. Mead, Phys. Rev. Lett. 34, 1273 (1975).
[CrossRef]

Other (2)

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), p. 379.

L. Coleman, “Laser Fusion Program Semiannual Report, July–December 1973,” UCRL-50021-73-2, Lawrence Livermore Laboratory, p. 56 (unpublished).

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Figures (16)

Fig. 1
Fig. 1

Calculated FP etalon output shapes for a Gaussian input pulse. Curves are labeled with the normalized delay time Δτ/ω. For these curves, R = 0.95.

Fig. 2
Fig. 2

Normalized energy and maximum intensity of an FP etalon as a function of Δτ/w and reflectivities. Bars at the right indicate energy and intensity at very large delays for R = 0.95.

Fig. 3
Fig. 3

A minimum element classical multiple beam splitter in unmodified form for square output pulses if 50/50 splitters are used. Attenuation is given by 2N for N beams.

Fig. 4
Fig. 4

Double etalon pulse stacker.5 Detailed device operation is given in the Appendix.

Fig. 5
Fig. 5

Normalized intensity as a function of the number of beams for square pulse outputs from a double-etalon stacker (DES) and a multiple beam splitter (MBS). No coherent pulse addition (widely separated pulses).

Fig. 6
Fig. 6

calculated output for a ten-beam double-etalon stacker with a Gaussian input pulse as a function of time and delay time, Δτ/w, for constructive interference.

Fig. 7
Fig. 7

Square pulse peak intensity for the double-etalon stacker as a function of number of beams N and pulse delay Δτ/w. R1 and R2 optimally chosen. Points labeled α are for exponentially rising pulses in a ten-beam stacker.

Fig. 8
Fig. 8

Normalized output energy (efficiency) for Fig. 7.

Fig. 9
Fig. 9

Calculated double-etalon stacker pulse shapes with Δτ/w = 1 for an exponentially rising pulse with various values of α.

Fig. 10
Fig. 10

Experimental configuration for measuring passive pulse shaper temporal behavior.

Fig. 11
Fig. 11

Streak camera trace of FP etalon output for constructive pulse addition (maximum in transmission). R = 0.95, Δτ = 33 psec, input pulse FWHM = 60 psec.

Fig. 12
Fig. 12

Streak camera trace of the input (dashed) and output pulse for the etalon of Fig. 11 adjusted to almost minimize cw throughput.

Fig. 13
Fig. 13

TPF densitometer trace of the output of FP etalon 2 adjusted for maximum cw transmission. Δτ = 16 psec; input pulse 60 psec FWHM. Contrast ratio 2.05 uncorrected for reciprocity.

Fig. 14
Fig. 14

Streak camera trace of the output pulse from the double-solid etalon stacker 2 of Table I for two different adjustments. The relative pulse heights are not significant.

Fig. 15
Fig. 15

Streak camera trace of the output pulse from the four-mirror stacker 1 of Table I. Fourteen beams, rising exponential (α = 1.34).

Fig. 16
Fig. 16

Streak camera trace of the output pulse from four-mirror stacker 2 of Table I. Fourteen beams, α = 1.53.

Tables (1)

Tables Icon

Table I Pulse Stacker Test Configurations

Equations (32)

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B ˜ ( ω ) = H ( ω ) A ˜ ( ω ) ,
H ( ω ) = t 1 t 2 n = 0 ( r 1 r 2 ) n exp ( - i ω n Δ τ ) ,
A ( t ) = exp ( - i ω o t ) f ( t ) ,
B ( t ) = t 1 t 2 exp ( i ω o t ) n = 0 ( r 1 r 2 ) n exp ( - i ω o n Δ τ ) f ( t - n Δ τ ) .
I ( t ) = B ( t ) · B * ( t ) = ( t 1 t 2 ) 2 [ n = 0 ( r 1 r 2 ) n f ( t - n Δ τ ) ] 2 ;
I ( t ) = ( 1 - R 1 ) ( 1 - R 2 ) [ n = 0 ( R 1 R 2 ) n / 2 f ( t - n Δ τ ) ] 2 .
lim Δ τ 0 I ( t ) = f 2 ( t ) ,
E o = - f 2 ( t ) d t .
lim Δ τ I ( t ) = ( 1 - R ) 2 n = 0 R 2 n f 2 ( t - n Δ τ ) , and E = ( 1 - R ) 2 1 - R 2 - f 2 ( t ) d t .
f ( t ) = exp [ - ( 2 L n 2 ) ( t / w ) 2 ] .
H ( ω ) = t 1 t 2 r 2 N r 1 n = 1 N ( r 1 r 2 ) n exp ( - i ω n Δ τ ) ,
B ( t ) = t 1 t 2 exp ( - i ω o t ) r 2 N r 1 n = 1 N ( r 1 r 2 ) n exp ( - i ω o n Δ τ ) f ( t - n Δ τ ) .
I ( t ) = ( 1 - R 1 ) ( 1 - R 2 ) ( R 2 R 1 ) N [ n = 1 N ( R 1 R 2 ) n / 2 f ( t - n Δ τ ) ] 2 .
lim Δ τ 0 I ( t ) = ( 2 N N + 1 ) 2 ( N - 1 N + 1 ) N - 1 f 2 ( t ) ,
lim Δ τ I ( t ) = ( 2 N + 1 ) 2 ( N - 1 N + 1 ) N - 1 n = 1 N f 2 ( t - n Δ τ ) , E = N ( 2 N + 1 ) 2 ( N - 1 N + 1 ) N - 1 - f 2 ( t ) d t .
f ( t ) = 1 1 + 4 ( 2 - 1 ) ( t / w ) 2 .
A 1 = exp ( - d t 2 ) exp [ i ( ω o t + ½ b t 2 ) ]
A 2 = exp [ - d ( t - Δ τ ) 2 ] exp { i [ ω o ( t - Δ τ ) + ½ b ( t - Δ τ ) 2 ] } ,
I ( t ) = exp ( - 2 d t 2 ) + exp [ - 2 d ( t - Δ τ ) 2 ] + 2 exp ( - d t 2 ) × exp [ - d ( t - Δ τ ) 2 ] cos ( ω o Δ τ + b t Δ τ - b Δ τ 2 2 ) .
2 exp ( - d t 2 ) exp [ - d ( t - Δ τ ) 2 ] cos ( b t Δ τ + ϕ ) ,
b Δ τ 2 π · 10 12 sec - 1 .
b 10 23 sec - 2 .
Δ ν b Δ τ π 2 · 10 - 12 sec - 1 .
Δ λ = ( λ 2 / c ) Δ ν 7 nm .
b 2 π / Δ τ 2 10 21 sec - 2 ,
Δ λ 0.07 mm .
R 2 = N ( α + 1 ) - [ N 2 ( α - 1 ) 2 + 4 α ] 1 / 2 2 α ( N + 1 ) .
S = 2 d 1 n 3 sin θ 1 cos θ 1 ( n 1 2 - n 3 2 sin 2 θ 1 ) 1 / 2 .
c Δ τ = 2 n 1 d 1 ( n 1 2 - n 3 2 sin 2 θ 1 ) 1 / 2 - 2 n 2 d 2 ( n 2 2 - n 4 2 sin 2 θ 2 ) 1 / 2 + 2 n 3 d 1 sin θ 1 [ sin θ 2 ( n 4 2 - n 3 2 sin 2 θ 1 ) 1 / 2 - n 3 cos θ 2 sin θ 1 ] n 4 cos θ 2 ( n 1 2 - n 3 2 sin 2 θ 1 ) 1 / 2 .
2 d 2 n 4 sin θ 2 ( n 2 2 - n 4 2 sin 2 θ 2 ) 1 / 2 = 2 d 1 n 3 sin θ 1 ( n 4 2 - n 3 2 sin 2 θ 1 ) 1 / 2 n 4 cos θ 2 ( n 1 2 - n 3 2 sin 2 θ 1 ) 1 / 2 .
c Δ τ = 2 n d 1 ( n 2 - sin 2 θ 1 ) 1 / 2 { 1 - sin θ 1 cos θ 2 [ cos θ 1 sin θ 2 - sin ( θ 2 - θ 1 ) ] } , d 2 = d 1 sin θ 1 cos θ 1 ( n 2 - sin 2 θ 2 ) 1 / 2 sin θ 2 cos θ 2 ( n 2 - sin 2 θ 1 ) 1 / 2 .
δ l ( n - 1 ) [ 2 n 2 d 2 cos ( θ 2 + 2 ϕ ) - 2 n 2 d 2 cos θ 2 ] ,

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