Abstract

We propose and demonstrate the improvement of conventional Galilean refractive beam shaping system for accurately generating near-diffraction-limited flattop beam with arbitrary beam size. Based on the detailed study of the refractive beam shaping system, we found that the conventional Galilean beam shaper can only work well for the magnifying beam shaping. Taking the transformation of input beam with Gaussian irradiance distribution into target beam with high order Fermi-Dirac flattop profile as an example, the shaper can only work well at the condition that the size of input and target beam meets R 0≥1.3w 0. For the improvement, the shaper is regarded as the combination of magnifying and demagnifying beam shaping system. The surface and phase distributions of the improved Galilean beam shaping system are derived based on Geometric and Fourier Optics. By using the improved Galilean beam shaper, the accurate transformation of input beam with Gaussian irradiance distribution into target beam with flattop irradiance distribution is realized. The irradiance distribution of the output beam is coincident with that of the target beam and the corresponding phase distribution is maintained. The propagation performance of the output beam is greatly improved. Studies of the influences of beam size and beam order on the improved Galilean beam shaping system show that restriction of beam size has been greatly reduced. This improvement can also be used to redistribute the input beam with complicated irradiance distribution into output beam with complicated irradiance distribution.

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References

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2010 (2)

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18(8), 8251–8260 (2010).
[CrossRef] [PubMed]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12(4), 045704 (2010).
[CrossRef]

2008 (1)

2007 (1)

S. Zhang, “A simple bi-convex refractive laser beam shaper,” J. Opt. A, Pure Appl. Opt. 9(10), 945–950 (2007).
[CrossRef]

2006 (2)

2003 (1)

2001 (1)

2000 (1)

1998 (1)

1997 (1)

1994 (1)

1991 (1)

C. C. Aleksoff, K. K. Ellis, and B. D. Neagle, “Holographic conversion of a Gaussian-beam to a near-field uniform beam,” Opt. Eng. 30(5), 537–543 (1991).
[CrossRef]

1980 (1)

1965 (1)

Aleksoff, C. C.

C. C. Aleksoff, K. K. Ellis, and B. D. Neagle, “Holographic conversion of a Gaussian-beam to a near-field uniform beam,” Opt. Eng. 30(5), 537–543 (1991).
[CrossRef]

Arif, M.

Auerbach, J. M.

Awwal, A. A. S.

Burke, G. J.

Burnham, R. L.

Chan, Y. C.

Dowd, P.

Ellis, K. K.

C. C. Aleksoff, K. K. Ellis, and B. D. Neagle, “Holographic conversion of a Gaussian-beam to a near-field uniform beam,” Opt. Eng. 30(5), 537–543 (1991).
[CrossRef]

Frieden, B. R.

Hoffnagle, J. A.

Hossain, M. M.

Islam, M. N.

Jefferson, C. M.

Karpenko, V. P.

Kasinski, J. J.

Lam, Y. L.

Li, J. H.

Liu, C.

Liu, Z. J.

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18(8), 8251–8260 (2010).
[CrossRef] [PubMed]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12(4), 045704 (2010).
[CrossRef]

Ma, H. T.

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12(4), 045704 (2010).
[CrossRef]

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18(8), 8251–8260 (2010).
[CrossRef] [PubMed]

Ma, Y. X.

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18(8), 8251–8260 (2010).
[CrossRef] [PubMed]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12(4), 045704 (2010).
[CrossRef]

Neagle, B. D.

C. C. Aleksoff, K. K. Ellis, and B. D. Neagle, “Holographic conversion of a Gaussian-beam to a near-field uniform beam,” Opt. Eng. 30(5), 537–543 (1991).
[CrossRef]

Neil, G.

Rhodes, P. W.

Shealy, D. L.

Shinn, M.

Thompson, C. A.

Wang, X. L.

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18(8), 8251–8260 (2010).
[CrossRef] [PubMed]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12(4), 045704 (2010).
[CrossRef]

Webb, K. J.

White, D. A.

Xi, F. J.

Xu, X. J.

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18(8), 8251–8260 (2010).
[CrossRef] [PubMed]

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12(4), 045704 (2010).
[CrossRef]

Yuan, X.

Zhang, S.

Zhou, G.

Zhou, P.

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12(4), 045704 (2010).
[CrossRef]

H. T. Ma, P. Zhou, X. L. Wang, Y. X. Ma, F. J. Xi, X. J. Xu, and Z. J. Liu, “Near-diffraction-limited annular flattop beam shaping with dual phase only liquid crystal spatial light modulators,” Opt. Express 18(8), 8251–8260 (2010).
[CrossRef] [PubMed]

Appl. Opt. (6)

J. Opt. (1)

H. T. Ma, Z. J. Liu, P. Zhou, X. L. Wang, Y. X. Ma, and X. J. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12(4), 045704 (2010).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

S. Zhang, “A simple bi-convex refractive laser beam shaper,” J. Opt. A, Pure Appl. Opt. 9(10), 945–950 (2007).
[CrossRef]

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

Opt. Eng. (1)

C. C. Aleksoff, K. K. Ellis, and B. D. Neagle, “Holographic conversion of a Gaussian-beam to a near-field uniform beam,” Opt. Eng. 30(5), 537–543 (1991).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Other (3)

F. M. Dickey, S. C. Holswade, and D. L. Shealy, eds., Laser Beam Shaping Applications (CRC Press, 2005).

J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” U.S. patent 3,476,463 (4 November 1969).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, 2005).

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Figures (16)

Fig. 1
Fig. 1

Configuration of the refractive beam shaping system, (a). Galilean system; (b) Keplerian system.

Fig. 2
Fig. 2

Phase distributions of dual aspheric lenses, (a) aspheric lens 1, (b) aspheric lens 2.

Fig. 3
Fig. 3

The change of irradiance and phase distribution of the output beam along with target beam size (R 0), (a) irradiance distribution, (b) phase distribution.

Fig. 4
Fig. 4

The change of shaping error and PIB curve along with target beam size (R 0), (a) shaping error, (b) PIB curve.

Fig. 5
Fig. 5

Phase distributions of the dual aspheric lenses, (a) aspheric lens 1, (b) aspheric lens 2.

Fig. 6
Fig. 6

The change of irradiance and phase distribution of the output beam along with target beam order (β), (a) irradiance distribution, (b) phase distribution.

Fig. 7
Fig. 7

The change of shaping error along with target beam order (β).

Fig. 8
Fig. 8

Configuration of the Galilean beam shaping system, (a) magnifying beam shaping system, (b) demagnifying beam shaping system consisted of one magnifying and one demagnifying systems.

Fig. 9
Fig. 9

Configuration of the demagnifying beam shaping system consisted of only one demagnifying system.

Fig. 10
Fig. 10

Surface and phase distributions of the improved Galilean beam shaping system, (a) surface distributions, (b) phase distributions.

Fig. 11
Fig. 11

Irradiance and phase distributions of the output beam, (a) Irradiance distribution, (b) phase distribution.

Fig. 12
Fig. 12

Dependence of rms intensity variation of the output beam on efficiency compared with that of the target beam.

Fig. 13
Fig. 13

Far field irradiance distributions of the output and target beam.

Fig. 14
Fig. 14

The change of the irradiance distribution of the output beam along with the propagation distance, (a) generated by the improved Galilean beam shaping system, (b) generated by the conventional Galilean beam shaping system.

Fig. 15
Fig. 15

The change of shaping error along with beam size (R 0) and beam order (β), (a) with beam size (R 0), (b) with beam order (β).

Fig. 16
Fig. 16

The irradiance and phase distribution of the output beam, (a) near field irradiance distribution, (b) phase distribution, (c) far field irradiance distribution.

Equations (13)

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z ( r ) = 0 r { ( n 2 1 ) + [ ( n 1 ) d h ( x ) x ] 2 } 1 / 2 d x
Z ( R ) = 0 R { ( n 2 1 ) + [ ( n 1 ) d h 1 ( x ) x ] 2 } 1 / 2 d x ,
f p h a s e 1 ( r ) = 2 π [ z e d g e z ( r ) + n z ( r ) ] λ
f p h a s e 2 ( R ) = 2 π [ n Z e d g e n Z ( R ) + Z ( R ) ] λ ,
P i n p u t ( r ) = exp ( 2 r 2 w 0 2 )
P o u t p u t ( r ) = { 1 + exp [ β ( r R 0 1 ) ] } 1 ,
E r r o r = [ I o u t p u t ( x , y ) I t arg e t ( x , y ) ] 2 d x d y ,
{ z ( r 1 ) = 0 r 1 { ( n 2 1 ) + [ ( n 1 ) d h ( x ) x ] 2 } 1 / 2 d x                             0 < r 1 < h 1 z ( r 2 ) = z ( h 1 ) h 1 r 2 { ( n 2 1 ) + [ ( n 1 ) d h ( x ) x ] 2 } 1 / 2 d x           h 1 < r 2 < h 2
{       Z ( R 1 ) = 0 R 1 { ( n 2 1 ) + [ ( n 1 ) d h 1 ( x ) x ] 2 } 1 / 2 d x                                       0 < R 1 < H 1 Z ( R 2 ) = Z ( H 1 ) H 1 R 2 { ( n 2 1 ) + [ ( n 1 ) d h 1 ( x ) x ] 2 } 1 / 2 d x                     H 1 < R 1 < H 2 ,
f p h a s e 1 ( r ) = 2 π [ z max z ( r ) + n z ( r ) ] λ
f p h a s e 2 ( R ) = 2 π [ n Z max n Z ( R ) + Z ( R ) ] λ ,
S E = a { 0 a [ P o u t p u t ( r ) 2 a 2 0 a P o u t p u t ( r ) r d r ] 2 r d r } 1 2 2 0 a P o u t p u t ( r ) r d r
η = 2 π 0 a P o u t p u t ( r ) r d r W i n p u t ,

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