Abstract

We discuss the beam smoothing principle of a continuous phase plate (CPP) while the input light is varying. The analysis model of the process in which the laser beam with random phase noise propagates through a CPP has been established. With this model the beam smoothing mechanism of the CPP for the laser beam with a different phase aberrations can be described. A method to optimize the smoothing result is introduced.

© 2008 Optical Society of America

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References

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  1. Y. Kato, K. Mima, N. Miyanaga , S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057-1060 (1984).
    [CrossRef]
  2. 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]
  3. B. Chen, H.-z. Wang, H. Wei, Y.-k. Guo, and L.-r. Guo, “Design of fully continuous phase plates for beam smoothing in ICF,” Acta Opt. Sin. 21, 480-484 (2001) (in Chinese).
  4. X. Jiang, Q. Lin, and S. Wang, “Numerical analysis for smoothing of cw multimode beam transformed by time-varying random phase plate,” Opt. Laser Technol. 31, 381-385(1999).
    [CrossRef]
  5. Q. Tan, Y. Yan, G. Jin, and M. Wu, “Design of diffractive optical element for true beam smoothing,” Opt. Commun. 189, 167-173 (2001).
    [CrossRef]
  6. H. Hora, “Smoothing and stochastic pulsation at high power laser-plasma interaction,” Laser Part. Beams 24, 455-463(2006).
    [CrossRef]
  7. M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39-49 (2002).
    [CrossRef]

2006 (1)

H. Hora, “Smoothing and stochastic pulsation at high power laser-plasma interaction,” Laser Part. Beams 24, 455-463(2006).
[CrossRef]

2002 (1)

M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39-49 (2002).
[CrossRef]

2001 (2)

B. Chen, H.-z. Wang, H. Wei, Y.-k. Guo, and L.-r. Guo, “Design of fully continuous phase plates for beam smoothing in ICF,” Acta Opt. Sin. 21, 480-484 (2001) (in Chinese).

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

1999 (1)

X. Jiang, Q. Lin, and S. Wang, “Numerical analysis for smoothing of cw multimode beam transformed by time-varying random phase plate,” Opt. Laser Technol. 31, 381-385(1999).
[CrossRef]

1994 (1)

1984 (1)

Y. Kato, K. Mima, N. Miyanaga , S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057-1060 (1984).
[CrossRef]

Arinaga, S.

Y. Kato, K. Mima, N. Miyanaga , S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057-1060 (1984).
[CrossRef]

Chen, B.

B. Chen, H.-z. Wang, H. Wei, Y.-k. Guo, and L.-r. Guo, “Design of fully continuous phase plates for beam smoothing in ICF,” Acta Opt. Sin. 21, 480-484 (2001) (in Chinese).

Dixit, S. N.

Guo, L.-r.

B. Chen, H.-z. Wang, H. Wei, Y.-k. Guo, and L.-r. Guo, “Design of fully continuous phase plates for beam smoothing in ICF,” Acta Opt. Sin. 21, 480-484 (2001) (in Chinese).

Guo, Y.-k.

B. Chen, H.-z. Wang, H. Wei, Y.-k. Guo, and L.-r. Guo, “Design of fully continuous phase plates for beam smoothing in ICF,” Acta Opt. Sin. 21, 480-484 (2001) (in Chinese).

Hora, H.

H. Hora, “Smoothing and stochastic pulsation at high power laser-plasma interaction,” Laser Part. Beams 24, 455-463(2006).
[CrossRef]

Jiang, X.

X. Jiang, Q. Lin, and S. Wang, “Numerical analysis for smoothing of cw multimode beam transformed by time-varying random phase plate,” Opt. Laser Technol. 31, 381-385(1999).
[CrossRef]

Jin, G.

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

Kato, Y.

Y. Kato, K. Mima, N. Miyanaga , S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057-1060 (1984).
[CrossRef]

Kitagawa, Y.

Y. Kato, K. Mima, N. Miyanaga , S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057-1060 (1984).
[CrossRef]

Lawson, J. K.

Lin, Q.

X. Jiang, Q. Lin, and S. Wang, “Numerical analysis for smoothing of cw multimode beam transformed by time-varying random phase plate,” Opt. Laser Technol. 31, 381-385(1999).
[CrossRef]

Manes, K. R.

Meister, M.

M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39-49 (2002).
[CrossRef]

Mima, K.

Y. Kato, K. Mima, N. Miyanaga , S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057-1060 (1984).
[CrossRef]

Miyanaga, N.

Y. Kato, K. Mima, N. Miyanaga , S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057-1060 (1984).
[CrossRef]

Nakatsuka, M.

Y. Kato, K. Mima, N. Miyanaga , S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057-1060 (1984).
[CrossRef]

Nugent, K. A.

Powell, H. T.

Tan, Q.

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

Wang, H.-z.

B. Chen, H.-z. Wang, H. Wei, Y.-k. Guo, and L.-r. Guo, “Design of fully continuous phase plates for beam smoothing in ICF,” Acta Opt. Sin. 21, 480-484 (2001) (in Chinese).

Wang, S.

X. Jiang, Q. Lin, and S. Wang, “Numerical analysis for smoothing of cw multimode beam transformed by time-varying random phase plate,” Opt. Laser Technol. 31, 381-385(1999).
[CrossRef]

Wei, H.

B. Chen, H.-z. Wang, H. Wei, Y.-k. Guo, and L.-r. Guo, “Design of fully continuous phase plates for beam smoothing in ICF,” Acta Opt. Sin. 21, 480-484 (2001) (in Chinese).

Winfield, R. J.

M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39-49 (2002).
[CrossRef]

Wu, M.

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

Yamanaka, C.

Y. Kato, K. Mima, N. Miyanaga , S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057-1060 (1984).
[CrossRef]

Yan, Y.

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

Acta Opt. Sin. (1)

B. Chen, H.-z. Wang, H. Wei, Y.-k. Guo, and L.-r. Guo, “Design of fully continuous phase plates for beam smoothing in ICF,” Acta Opt. Sin. 21, 480-484 (2001) (in Chinese).

Laser Part. Beams (1)

H. Hora, “Smoothing and stochastic pulsation at high power laser-plasma interaction,” Laser Part. Beams 24, 455-463(2006).
[CrossRef]

Opt. Commun. (2)

M. Meister and R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39-49 (2002).
[CrossRef]

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

Opt. Laser Technol. (1)

X. Jiang, Q. Lin, and S. Wang, “Numerical analysis for smoothing of cw multimode beam transformed by time-varying random phase plate,” Opt. Laser Technol. 31, 381-385(1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

Y. Kato, K. Mima, N. Miyanaga , S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057-1060 (1984).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Principle of the phase plate in the optical system.

Fig. 2
Fig. 2

The two different surface figures of the beam wavefront: s = 0.1 m , c = 0.002 and s = 0.1 m , c = 0.008 .

Fig. 3
Fig. 3

Far-field distribution of the two different input lasers. I,  s = 0.1 m , c = 0.002 ; II,  s = 0.1 m , c = 0.008 .

Fig. 4
Fig. 4

Surface figure of two different continuous phase plates.

Fig. 5
Fig. 5

The Fourier spectral distribution of the continuous phase plates.

Fig. 6
Fig. 6

Far-field distribution of light after the smoothing operation. Far-field distribution of laser I (solid curve) and laser II (dashed curve) after the different CPPs.

Equations (10)

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u ( x ) = exp [ j k α ( x ) ] ,
t ( x ) = exp [ j k β ( x ) ] ,
U inf ( f ) = F { u ( x ) t ( x ) } = ± u ( x ) t ( x ) exp [ j k f x ] d x ,
E { U inf ( f ) ¯ U inf ( f ) } = E { F { u ( x ) t ( x ) ¯ * u ( x ) t ( x ) } } = F { E { u ( y ) ¯ · u ( x y ) } ± t ( y ) ¯ t ( x y ) d y } = F { B u ( x ) R t ( x ) } ,
E { U inf ( f ) } = E { F { u ( x ) t ( x ) } } = F { E { u ( x ) } t ( x ) } = F { u 0 ( x ) } * T ( f ) ,
D [ U inf ( f ) ] = E { U inf ( f ) ¯ U inf ( f ) } E { U inf ( f ) } ¯ E { U inf ( f ) } = F { B u ( x ) R t ( x ) } | F { u 0 ( x ) } * T ( f ) | 2 = F { B u ( x ) } * | T ( f ) | 2 | F { u 0 ( x ) } * T ( f ) | 2 .
E [ u ( x ) ] = e k 2 σ α 2 / 2 = u 0 ,
B α ( s ) = E [ e j k [ A ( x + s ) A ( x ) ] ] = e k 2 σ α 2 / 2 = e 2 k 2 ( σ α 2 B α ( s ) ) .
D [ U inf ( f ) ] ( M u 0 2 ) · | T ( f ) | 2 .
α ( x ) = c s · random ( 1 , 1 ) * exp [ ( x 2 s 2 ) ] ,

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