Abstract

Fresnel diffraction patterns by circular and serrated apertures under ultrashort pulsed-laser illumination are investigated in detail. A comparison of the diffraction patterns for pulsed and continuous wave illuminations reveals that an ultrashort pulsed beam of 10 fs can result in a significant effect on the distribution of the intensity. As a result a uniform intensity distribution in the transverse direction of the beam can be achieved as a result of the interference of the different frequency components within the pulsed beam. The interference fringes caused by the wavelets originating from the diffraction aperture can be further reduced when a serrated aperture is used.

© 1996 Optical Society of America

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References

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  15. M. S. Pshenichnikov, W. P. deBoeij, D. A. Wiersma, “Generation of 13-fs, 5-mW pulses from a cavity-damped Ti: sapphire laser,” Opt. Lett. 19, 572–574 (1994).
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1994 (5)

1992 (3)

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

C. J. R. Sheppard, M. Hrynevych, “Diffraction by a circular aperture: a generalization of Fresnel diffraction theory,” J. Opt. Soc. Am. A 9, 274–281 (1992).
[CrossRef]

M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 9, 1158–1159 (1992).
[CrossRef]

1989 (2)

1986 (1)

1982 (1)

1980 (1)

1976 (1)

A. Arimoto, “Intensity distribution of aberration-free diffraction pattern due to circular aperture in large F-number optical systems,” Opt. Acta 23, 245–250 (1976).
[CrossRef]

Arimoto, A.

A. Arimoto, “Intensity distribution of aberration-free diffraction pattern due to circular aperture in large F-number optical systems,” Opt. Acta 23, 245–250 (1976).
[CrossRef]

Auerbach, J. M.

Bibeau, C.

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

deBoeij, W. P.

Deng, X. M.

X. M. Deng, D. Fan, Qian Liejia, “Serrated aperture and its application in high power lasers,” in Collection of Theses on High Power Laser and Plasma Physics (National Laboratory on High Power Laser and Physics, Shanghai, 1993), pp. 45–47.

Ehrlich, R. B.

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

Fan, D.

X. M. Deng, D. Fan, Qian Liejia, “Serrated aperture and its application in high power lasers,” in Collection of Theses on High Power Laser and Plasma Physics (National Laboratory on High Power Laser and Physics, Shanghai, 1993), pp. 45–47.

George, N.

Gibson, S. F.

Goodman, W.

W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gu, M.

Henesian, M. A.

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

Hrynevych, M.

Huang, C.

Hunt, J.

J. Hunt, D. R. Speck, “Recent and future performance of the Nova laser system,” Opt. Eng. 28, 461–486 (1989).
[CrossRef]

Jacquinot, P.

P. Jacquinot, M. B. Roizen-Dossier, “Apodisation,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3.
[CrossRef]

Kapteyn, H. C.

Karpenko, V. P.

Kempe, M.

Krausz, F.

Kyrazis, D. T.

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

Lanni, F.

Laumann, C. W.

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

Lawson, J. K.

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

Liejia, Qian

X. M. Deng, D. Fan, Qian Liejia, “Serrated aperture and its application in high power lasers,” in Collection of Theses on High Power Laser and Plasma Physics (National Laboratory on High Power Laser and Physics, Shanghai, 1993), pp. 45–47.

Morris, G. M.

Murnane, M. M.

Perry, M. D.

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

Pshenichnikov, M. S.

Roizen-Dossier, M. B.

P. Jacquinot, M. B. Roizen-Dossier, “Apodisation,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3.
[CrossRef]

Rudolph, W.

Sheppard, C. J. R.

Speck, D. R.

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

J. Hunt, D. R. Speck, “Recent and future performance of the Nova laser system,” Opt. Eng. 28, 461–486 (1989).
[CrossRef]

Spielman, G.

Stamm, U.

Stingl, A.

Taft, G.

Wegner, P. J.

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

Weiland, T. L.

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

Wiersma, D. A.

Wilhelmi, B.

Wilson, T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Zhou, J.

Appl. Opt. (1)

Applied Opt. (1)

C. Bibeau, D. R. Speck, R. B. Ehrlich, C. W. Laumann, D. T. Kyrazis, M. A. Henesian, J. K. Lawson, M. D. Perry, P. J. Wegner, T. L. Weiland, “Power, energy, and temporal performance of the Nova laser facility with recent improvements to the amplifier system,” Applied Opt. 31, 5799–5809 (1992).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Opt. Soc. Am. B (1)

Opt. Acta (1)

A. Arimoto, “Intensity distribution of aberration-free diffraction pattern due to circular aperture in large F-number optical systems,” Opt. Acta 23, 245–250 (1976).
[CrossRef]

Opt. Eng. (1)

J. Hunt, D. R. Speck, “Recent and future performance of the Nova laser system,” Opt. Eng. 28, 461–486 (1989).
[CrossRef]

Opt. Lett. (3)

Other (4)

X. M. Deng, D. Fan, Qian Liejia, “Serrated aperture and its application in high power lasers,” in Collection of Theses on High Power Laser and Plasma Physics (National Laboratory on High Power Laser and Physics, Shanghai, 1993), pp. 45–47.

W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

P. Jacquinot, M. B. Roizen-Dossier, “Apodisation,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Serrated aperture with maximum and minimum radii, a + δa and aδa, respectively. The ratio of δa/a is chosen to be 0.05, giving a range of the Fresnel number ΔN = 10 for N0 = 100.

Fig. 2
Fig. 2

On-axis intensity distribution of the Fresnel diffraction pattern: (a) circular aperture with CW illumination; (b) circular aperture with pulsed illumination; (c) serrated aperture with CW illumination; (d) serrated aperture with pulsed illumination.

Fig. 3
Fig. 3

Intensity distribution in a vertical plane for N0 = 100: (a) circular aperture with CW illumination; (b) circular aperture with pulsed illumination (ΔN = 29); (c) serrated aperture (ΔN = 10) with CW illumination; (d) serrated aperture (ΔN = 10) with pulsed illumination (ΔN = 29).

Fig. 4
Fig. 4

Cross section of the intensity distribution in a vertical plane for N0 = 100: (a) circular aperture with CW illumination; (b) circular aperture with pulsed illumination; (c) serrated aperture with CW illumination; (d) serrated aperture with pulsed illumination.

Fig. 5
Fig. 5

Intensity distribution in a horizontal plane along the z axis. The plotted range of Z is from 0.005 to 2, corresponding to N0 in the range from 200 to 2: (a) circular aperture with CW illumination; (b) circular aperture with pulsed illumination; (c) serrated aperture with CW illumination; (d) serrated aperture with pulsed illumination.

Equations (26)

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U ( x , y , z , ω ) = i exp ( - i 2 π z / λ ) λ z exp [ - i π λ z ( x 2 + y 2 ) ] × - + - + U 1 ( x 1 , y 1 , ω ) × exp [ i 2 π λ z ( x 1 x + y 1 y ) ] × exp [ - i π λ z ( x 1 2 + y 1 2 ) ] d x 1 d y 1 ,
I ( x , y , z ) = C - V ( Δ ω ) U ( x , y , z , ω ) 2 d ω ,
U 0 ( t ) = exp ( - i ω 0 t ) exp ( - t 2 T 2 ) ,
T = Δ τ 2 ln 2 .
V ( Δ ω ) = π T exp [ - T 2 ( ω - ω 0 ) 2 4 ] = π T exp [ T 2 ω 0 2 4 ( ω ω 0 - 1 ) 2 ] .
ρ 1 = r 1 / a
ρ = r / a ,
U ( ρ , z , ω ) = 2 π i a 2 exp ( - i 2 π z / λ ) exp ( - i N ρ 2 ) λ z × 0 1 U 1 ( ρ 1 , ω ) J 0 ( 2 N ρ 1 ρ ) × exp ( - i N ρ 1 2 ) ρ 1 d ρ 1 .
N = π a 2 λ z ,
N = a 2 ω 0 2 z c ω ω 0 = N 0 ω ω 0 ,
N 0 = π a 2 λ 0 z
I ( ρ , z ) = C 0 + 1 N 0 | N exp [ - T 2 ω 0 2 4 ( N N 0 - 1 ) 2 ] × 0 1 J 0 ( 2 N ρ 1 ρ ) exp ( - i N ρ 1 2 ) ρ 1 d ρ 1 | 2 d N .
I ( N 0 ) = 4 sin 2 ( N 0 / 2 ) ,
Z = 1 N 0 = λ 0 z π a 2 .
I ( N 0 ) = C 0 + 1 N 0 | exp [ - T 2 ω 0 2 4 ( N N 0 - 1 ) 2 ] × sin ( N / 2 ) | 2 d N ,
I ( N 0 ) = 2 [ 1 - exp ( - N 0 2 2 T 2 ω 0 2 ) cos ( N 0 ) ] .
Δ N = N 0 Δ Ω ω 0 .
r = a [ 1 + α sin ( m 1 θ ) sin ( m 2 θ ) ] ,
U ( ρ , θ , z , ω 0 ) = i a 2 exp ( - i 2 π z / λ 0 ) exp ( - i N 0 ρ 2 ) λ 0 z × 0 2 π 0 r / a exp [ i 2 N 0 ρ 1 ρ cos ( θ 1 - θ ) ] × exp ( - i N 0 ρ 1 2 ) ρ 1 d ρ 1 d θ 1 ,
I ( ρ , θ , z ) = C 0 1 N 0 | N exp [ - ω 0 2 4 α ( N N 0 - 1 ) 2 ] × 0 2 π 0 r / a exp [ i 2 N ρ 1 ρ cos ( θ 1 - θ ) ] × exp ( - i N ρ 1 2 ) ρ 1 d ρ 1 d θ 1 | 2 d N .
r = a [ 1 + α ( m θ π + 1 - 2 n ) ] ,             2 ( n - 1 ) π m θ 2 n π m ,
I ( N 0 ) = C | 2 π - m 0 2 π / m exp ( - i N 0 r 2 ) d θ | 2 ,
I ( N 0 ) = { 1 - 2 cos ( N 0 ) sin ( 2 α N 0 ) 2 α N 0 + [ sin ( 2 α N 0 ) 2 α N 0 ] 2 } ,
N 0 2 > 10 ( ω 0 T ) 2 ,
z < a 2 40 c T ,
Δ N > 3 π .

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