Abstract

In this paper, the diffractive optical element (DOE) is used to realize beam smoothing with the smoothing by spectral dispersion (SSD) technique. The influences of the high and low frequency phase distortions on the DOE for beam smoothing are statistically analyzed based on the spatial frequency spectrum method. The amplitude and initial phase spectra of the far field intensity distribution are modulated by the characteristic of the phase distortion. The relationship between the performance parameters of the beam smoothing and the characteristic of the phase distortion is obtained. This can afford a theoretical tool to determine whether the characteristic of the phase distortion and the performance of the designed DOE for beam smoothing are able to satisfy the requirement of the light efficiency and the non-uniformity simultaneously or not.

©2004 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Performance of target irradiation in a high-power laser with a continuous phase plate and spectral dispersion

Xiujuan Jiang, Jinghui Li, Rong Wu, Zhengtao Zhu, Shenlei Zhou, and Zunqi Lin
J. Opt. Soc. Am. A 30(11) 2162-2168 (2013)

Influence of phase distortion on the propagation of vortex beams

Qianyi Xiao, Guodong Liu, and Rongzhu Zhang
Appl. Opt. 54(12) 3523-3529 (2015)

Analysis of illumination uniformity affected by small-scale self-focusing of a pump beam in the radial smoothing scheme

Xiaofeng Weng, Tengfei Li, Zheqiang Zhong, and Bin Zhang
Appl. Opt. 56(32) 8902-8907 (2017)

References

  • View by:
  • |
  • |
  • |

  1. S. N. Dixit, J. K. Lawson, K. R. Manes, H. T. Powell, and K. A. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Opt. Lett. 19, 417–419 (1994).
    [PubMed]
  2. R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).
  3. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  4. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982)
    [Crossref] [PubMed]
  5. J. S. Liu and M. R. Taghizadeh, “Iterative algorithm for the design of diffractive phase elements for laser beam shaping,” Opt. Lett. 27, 1463–1465 (2002).
    [Crossref]
  6. B. Y. Gu, G.Z. Yang, and B. Z. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).
    [Crossref] [PubMed]
  7. J. H. Zhai, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of continuous phase screens by Global/local united search algorithm for focal-plane irradiance profile control,” Chinese Journal of Lasers B7, 235–240 (1998).
  8. Q. F. Tan, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of diffractive optical element for true beam smoothing,” Opt. Commun. 189, 167–173 (2001).
    [Crossref]
  9. Q. F. Tan, Q. S. He, Y. B. Yan, G. F. Jin, and D. Y. Xu, “Spatial-frequency spectrum analysis of the performance of diffractive optical element for beam smoothing,” Optik 113, 163–166 (2002).
    [Crossref]
  10. “Two-dimensional SSD on OMEGA,” LLE Review69, 1–10 (1996), http://www.lle.rochester.edu/pub/review/v69/1-two.pdf.
  11. G. Miyaji, N. Miyanaga, S. Urushihara, K. Suzuki, S. Matsuoka, M. Nakatsuka, A. Morimoto, and T. Kobayashi, “Three-dimensional spectral dispersion for smoothing a laser irradiance profile,” Opt. Lett. 27, 725–727 (2002).
    [Crossref]
  12. K. R. Manes, R. A. London, S. B. Sutton, and L. E. Zapata, “Shot rate-thermal recovery,” in NIF Laser System Performance Ratings, J. M. Auerbach, E. S. Bliss, S. N. Dixit, M. D. Feit, D. M. Gold, S. W. Haan, M. A. Henesian, O. S. Jones, J. K. Lawson, R. A. London, K. R. Manes, D. Munro, J. R. Murray, S. M. Pollaine, P.A. Renard, J. E. Rothenberg, R. A. Sacks, and D. R. Speck, eds., Proc. SPIE3492(supplement), 136–149 (1999).
  13. Q. H. Deng, X. M. Zhang, F. Jing, and L. Q. Liu, “Research on the rule of laser beam’s low-frequency phase aberration superimposition,” High Power Laser and Particle Beams 14, 81–84 (2002).

2002 (4)

J. S. Liu and M. R. Taghizadeh, “Iterative algorithm for the design of diffractive phase elements for laser beam shaping,” Opt. Lett. 27, 1463–1465 (2002).
[Crossref]

Q. F. Tan, Q. S. He, Y. B. Yan, G. F. Jin, and D. Y. Xu, “Spatial-frequency spectrum analysis of the performance of diffractive optical element for beam smoothing,” Optik 113, 163–166 (2002).
[Crossref]

G. Miyaji, N. Miyanaga, S. Urushihara, K. Suzuki, S. Matsuoka, M. Nakatsuka, A. Morimoto, and T. Kobayashi, “Three-dimensional spectral dispersion for smoothing a laser irradiance profile,” Opt. Lett. 27, 725–727 (2002).
[Crossref]

Q. H. Deng, X. M. Zhang, F. Jing, and L. Q. Liu, “Research on the rule of laser beam’s low-frequency phase aberration superimposition,” High Power Laser and Particle Beams 14, 81–84 (2002).

2001 (1)

Q. F. Tan, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of diffractive optical element for true beam smoothing,” Opt. Commun. 189, 167–173 (2001).
[Crossref]

1998 (1)

J. H. Zhai, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of continuous phase screens by Global/local united search algorithm for focal-plane irradiance profile control,” Chinese Journal of Lasers B7, 235–240 (1998).

1994 (1)

1986 (1)

1982 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1971 (1)

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Deng, Q. H.

Q. H. Deng, X. M. Zhang, F. Jing, and L. Q. Liu, “Research on the rule of laser beam’s low-frequency phase aberration superimposition,” High Power Laser and Particle Beams 14, 81–84 (2002).

Dixit, S. N.

Dong, B. Z.

Fienup, J. R.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Gu, B. Y.

He, Q. S.

Q. F. Tan, Q. S. He, Y. B. Yan, G. F. Jin, and D. Y. Xu, “Spatial-frequency spectrum analysis of the performance of diffractive optical element for beam smoothing,” Optik 113, 163–166 (2002).
[Crossref]

Jin, G. F.

Q. F. Tan, Q. S. He, Y. B. Yan, G. F. Jin, and D. Y. Xu, “Spatial-frequency spectrum analysis of the performance of diffractive optical element for beam smoothing,” Optik 113, 163–166 (2002).
[Crossref]

Q. F. Tan, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of diffractive optical element for true beam smoothing,” Opt. Commun. 189, 167–173 (2001).
[Crossref]

J. H. Zhai, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of continuous phase screens by Global/local united search algorithm for focal-plane irradiance profile control,” Chinese Journal of Lasers B7, 235–240 (1998).

Jing, F.

Q. H. Deng, X. M. Zhang, F. Jing, and L. Q. Liu, “Research on the rule of laser beam’s low-frequency phase aberration superimposition,” High Power Laser and Particle Beams 14, 81–84 (2002).

Kobayashi, T.

Lawson, J. K.

Liu, J. S.

Liu, L. Q.

Q. H. Deng, X. M. Zhang, F. Jing, and L. Q. Liu, “Research on the rule of laser beam’s low-frequency phase aberration superimposition,” High Power Laser and Particle Beams 14, 81–84 (2002).

London, R. A.

K. R. Manes, R. A. London, S. B. Sutton, and L. E. Zapata, “Shot rate-thermal recovery,” in NIF Laser System Performance Ratings, J. M. Auerbach, E. S. Bliss, S. N. Dixit, M. D. Feit, D. M. Gold, S. W. Haan, M. A. Henesian, O. S. Jones, J. K. Lawson, R. A. London, K. R. Manes, D. Munro, J. R. Murray, S. M. Pollaine, P.A. Renard, J. E. Rothenberg, R. A. Sacks, and D. R. Speck, eds., Proc. SPIE3492(supplement), 136–149 (1999).

Manes, K. R.

S. N. Dixit, J. K. Lawson, K. R. Manes, H. T. Powell, and K. A. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Opt. Lett. 19, 417–419 (1994).
[PubMed]

K. R. Manes, R. A. London, S. B. Sutton, and L. E. Zapata, “Shot rate-thermal recovery,” in NIF Laser System Performance Ratings, J. M. Auerbach, E. S. Bliss, S. N. Dixit, M. D. Feit, D. M. Gold, S. W. Haan, M. A. Henesian, O. S. Jones, J. K. Lawson, R. A. London, K. R. Manes, D. Munro, J. R. Murray, S. M. Pollaine, P.A. Renard, J. E. Rothenberg, R. A. Sacks, and D. R. Speck, eds., Proc. SPIE3492(supplement), 136–149 (1999).

Matsuoka, S.

Miyaji, G.

Miyanaga, N.

Morimoto, A.

Nakatsuka, M.

Nugent, K. A.

Powell, H. T.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Sutton, S. B.

K. R. Manes, R. A. London, S. B. Sutton, and L. E. Zapata, “Shot rate-thermal recovery,” in NIF Laser System Performance Ratings, J. M. Auerbach, E. S. Bliss, S. N. Dixit, M. D. Feit, D. M. Gold, S. W. Haan, M. A. Henesian, O. S. Jones, J. K. Lawson, R. A. London, K. R. Manes, D. Munro, J. R. Murray, S. M. Pollaine, P.A. Renard, J. E. Rothenberg, R. A. Sacks, and D. R. Speck, eds., Proc. SPIE3492(supplement), 136–149 (1999).

Suzuki, K.

Taghizadeh, M. R.

Tan, Q. F.

Q. F. Tan, Q. S. He, Y. B. Yan, G. F. Jin, and D. Y. Xu, “Spatial-frequency spectrum analysis of the performance of diffractive optical element for beam smoothing,” Optik 113, 163–166 (2002).
[Crossref]

Q. F. Tan, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of diffractive optical element for true beam smoothing,” Opt. Commun. 189, 167–173 (2001).
[Crossref]

Urushihara, S.

Wu, M. X.

Q. F. Tan, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of diffractive optical element for true beam smoothing,” Opt. Commun. 189, 167–173 (2001).
[Crossref]

J. H. Zhai, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of continuous phase screens by Global/local united search algorithm for focal-plane irradiance profile control,” Chinese Journal of Lasers B7, 235–240 (1998).

Xu, D. Y.

Q. F. Tan, Q. S. He, Y. B. Yan, G. F. Jin, and D. Y. Xu, “Spatial-frequency spectrum analysis of the performance of diffractive optical element for beam smoothing,” Optik 113, 163–166 (2002).
[Crossref]

Yan, Y. B.

Q. F. Tan, Q. S. He, Y. B. Yan, G. F. Jin, and D. Y. Xu, “Spatial-frequency spectrum analysis of the performance of diffractive optical element for beam smoothing,” Optik 113, 163–166 (2002).
[Crossref]

Q. F. Tan, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of diffractive optical element for true beam smoothing,” Opt. Commun. 189, 167–173 (2001).
[Crossref]

J. H. Zhai, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of continuous phase screens by Global/local united search algorithm for focal-plane irradiance profile control,” Chinese Journal of Lasers B7, 235–240 (1998).

Yang, G.Z.

Zapata, L. E.

K. R. Manes, R. A. London, S. B. Sutton, and L. E. Zapata, “Shot rate-thermal recovery,” in NIF Laser System Performance Ratings, J. M. Auerbach, E. S. Bliss, S. N. Dixit, M. D. Feit, D. M. Gold, S. W. Haan, M. A. Henesian, O. S. Jones, J. K. Lawson, R. A. London, K. R. Manes, D. Munro, J. R. Murray, S. M. Pollaine, P.A. Renard, J. E. Rothenberg, R. A. Sacks, and D. R. Speck, eds., Proc. SPIE3492(supplement), 136–149 (1999).

Zhai, J. H.

J. H. Zhai, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of continuous phase screens by Global/local united search algorithm for focal-plane irradiance profile control,” Chinese Journal of Lasers B7, 235–240 (1998).

Zhang, X. M.

Q. H. Deng, X. M. Zhang, F. Jing, and L. Q. Liu, “Research on the rule of laser beam’s low-frequency phase aberration superimposition,” High Power Laser and Particle Beams 14, 81–84 (2002).

Appl. Opt. (2)

Chinese Journal of Lasers (1)

J. H. Zhai, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of continuous phase screens by Global/local united search algorithm for focal-plane irradiance profile control,” Chinese Journal of Lasers B7, 235–240 (1998).

High Power Laser and Particle Beams (1)

Q. H. Deng, X. M. Zhang, F. Jing, and L. Q. Liu, “Research on the rule of laser beam’s low-frequency phase aberration superimposition,” High Power Laser and Particle Beams 14, 81–84 (2002).

Opt. Commun. (1)

Q. F. Tan, Y. B. Yan, G. F. Jin, and M. X. Wu, “Design of diffractive optical element for true beam smoothing,” Opt. Commun. 189, 167–173 (2001).
[Crossref]

Opt. Lett. (3)

Optik (3)

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Q. F. Tan, Q. S. He, Y. B. Yan, G. F. Jin, and D. Y. Xu, “Spatial-frequency spectrum analysis of the performance of diffractive optical element for beam smoothing,” Optik 113, 163–166 (2002).
[Crossref]

Other (2)

“Two-dimensional SSD on OMEGA,” LLE Review69, 1–10 (1996), http://www.lle.rochester.edu/pub/review/v69/1-two.pdf.

K. R. Manes, R. A. London, S. B. Sutton, and L. E. Zapata, “Shot rate-thermal recovery,” in NIF Laser System Performance Ratings, J. M. Auerbach, E. S. Bliss, S. N. Dixit, M. D. Feit, D. M. Gold, S. W. Haan, M. A. Henesian, O. S. Jones, J. K. Lawson, R. A. London, K. R. Manes, D. Munro, J. R. Murray, S. M. Pollaine, P.A. Renard, J. E. Rothenberg, R. A. Sacks, and D. R. Speck, eds., Proc. SPIE3492(supplement), 136–149 (1999).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. The design results of the DOE for beam smoothing
Fig. 2.
Fig. 2. Spatial-frequency spectrum of the designed DOE for beam smoothing
Fig. 3.
Fig. 3. Relationship between η, rms and σ
Fig. 4.
Fig. 4. Relationship between η, rms and a
Fig. 5.
Fig. 5. Relationship between η, rms and a

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

T ( x ) = p = 1 K exp ( i φ p ) rect ( x p D / K D / K ) ,
rect ( x ) = { 1 when x 1 2 . 0 else
I ( x ) = p = 1 K exp ( i φ p ) exp ( i 2 π p D K λ f x ) 2 ,
I ( y ) = p = 1 K q = 1 K cos [ φ p φ q + ( p q ) y ] = K + 2 m = 1 K 1 A m cos ( my + B m ) ,
I total = y 1 y 2 I ( y ) dy = K ( y 2 y 1 ) + 2 m = 1 K 1 A m m [ sin ( my 2 + B m ) sin ( my 1 + B m ) ] ,
η = I total 2 π K .
rms = y 1 y 2 ( I ( y ) I ¯ ) 2 dy ( y 2 y 1 ) I ¯ 2 ,
I ( y ) = p = 1 K exp [ i ( φ p + Δ φ p ) ] exp ( i py ) 2 .
I ¯ L ( y ) = l = 1 L p = 1 K exp [ i ( φ p + Δ φ p l ) ] exp ( i py ) 2 / L ,
I ¯ L ( y ) = 1 L l = 1 L [ p = 1 K q = 1 K exp [ i ( φ p φ q + ( p q ) y ] exp [ i ( Δ ϕ p l Δ ϕ q l ) ] ]
= K + p = 1 K q = 1 , q p K exp [ i ( φ p φ q + ( P q ) ) y ] 1 L l = 1 L [ exp [ i ( Δ ϕ p l Δ ϕ q l ) ] ]
Δ ϕ H = N [ 0 , σ ] ,
Δ ϕ L = a · rand ( 1 , 1 ) * exp ( ( x / x s ) 2 ) ,
Δ ϕ p l = Δ ϕ p , H l + Δ ϕ p , L l ,
E ( exp [ i ( Δ ϕ p Δ ϕ q ) ] ) = E ( exp [ i ( Δ ϕ p , H Δ ϕ q , H ) ] ) · E ( exp [ i ( Δ ϕ p , L Δ ϕ q , L ) ] ) .
Δ ϕ p , H l Δ ϕ q , H l = N [ 0 , 2 σ ] ,
E ( exp [ i ( Δ ϕ p , H Δ ϕ q , H ) ] ) = + exp [ i ϕ ] 1 2 σ π exp ( ϕ 2 4 σ 2 ) d ϕ = exp ( σ 2 ) .
Δ ϕ p , L l Δ ϕ q , L l = a · k = 1 K R k l · { exp { [ ( k p ) D K / x s ] 2 } exp { [ ( k q ) D K / x s ] 2 } } ,
= k = 1 K F ( k , p , q ) R k l
E ( exp [ i ( Δ ϕ p , L Δ ϕ q , L ) ] ) = E ( exp ( i k = 1 K F ( k , p , q ) ) R k ) = k = 1 K E ( exp ( i F ( k , p , q ) R k ) ) .
E ( exp ( i F ( k , p , q ) R k ) ) = 1 1 exp ( i F ( k , p , q ) ϕ ) 1 2 d ϕ = sin c ( F ( k , p , q ) ) ,
I ( y ) = K + exp ( σ 2 ) p = 1 K q = 1 , q p K k = 1 K sin c ( F ( k , p , q ) ) exp [ i ( φ p φ q + ( p q ) y ) ]
= K + 2 exp ( σ 2 ) m = 1 K 1 A m cos ( m y + B m )
D m = p = m + 1 K k = 1 K sin c ( F ( k , p , p m ) ) cos ( φ p φ p m ) ,
D m = p = m + 1 K k = 1 K sin c ( F ( k , p , p m ) ) sin ( φ p φ p m ) .

Metrics