Abstract

A procedure for global beam shaping by modifying some global spatial parameters characteristic of the beam is proposed. This method is based on the generation of a nonuniformly polarized beam using a Mach–Zehnder system with two suitably shaped intensity transmittances and orthogonal linear polarizers. The changes in beam quality and kurtosis parameters after a linear polarizer placed at the output of the system are investigated.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. J. Serna, R. Martínez-Herrero, and P. M. Mejías, "Parametric characterization of general partially coherent beams propagating through ABCD optical systems," J. Opt. Soc. Am. A 8, 1094-1098 (1991).
    [CrossRef]
  16. H. Weber, "Propagation of higher-order intensity moments in quadratic-index media," Opt. Quantum Electron. 24, 1027-1049 (1992).
    [CrossRef]
  17. G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "On the kurtosis parameter of laser beams," in Proceedings of the First Workshop on Laser Beam Characterization, P.M.Mejías, H.Weber, R.Martínez-Herrero, and A.GonzálezUreña, eds., (Sociedad Española de Óptica, 1993), pp. 141-148.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  20. G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "Sharpness changes of Gaussian beams induced by spherically aberrated lenses," Opt. Commun. 107, 179-83 (1994).
    [CrossRef]
  21. L. Shirong and B. Lu, "M2 factor and kurtosis parameter of super-Gaussian beams passing through an axicon," Optik 114, 193-198 (2003).
    [CrossRef]
  22. Q. Lü, S. Dong, and H. Weber, "Analysis of TEM00 laser beam degradation caused by a birefringent Nd:YAG rod," Opt. Quantum Electron. 27, 777-783 (1995).
    [CrossRef]
  23. V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D. 32, 1455-1461 (1999).
    [CrossRef]

2003

L. Shirong and B. Lu, "M2 factor and kurtosis parameter of super-Gaussian beams passing through an axicon," Optik 114, 193-198 (2003).
[CrossRef]

1999

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D. 32, 1455-1461 (1999).
[CrossRef]

1995

Q. Lü, S. Dong, and H. Weber, "Analysis of TEM00 laser beam degradation caused by a birefringent Nd:YAG rod," Opt. Quantum Electron. 27, 777-783 (1995).
[CrossRef]

1994

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "Sharpness changes of Gaussian beams induced by spherically aberrated lenses," Opt. Commun. 107, 179-83 (1994).
[CrossRef]

1993

1992

1991

1990

A. E. Siegman, "New developments in laser resonators," in Proc. SPIE 1224, 2-14 (1990).
[CrossRef]

K. Iwasaki, T. Hayashi, T. Goto, and S. Shimizu, "Square and uniform laser output device: theory and applications," Appl. Opt. 90, 1736-1744 (1990).
[CrossRef]

1989

M. J. Bastiaans, "Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems," Optik 82, 173-181 (1989).

1988

1982

1981

D. G. Burkhard and D. L. Shealy, "Simplified formula for the illuminance in an optical system," Appl. Opt. 20, 897-909 (1981).
[CrossRef] [PubMed]

W.-H. Lee, "Method for converting a Gaussian beam into a uniform beam," Opt. Commun. 36, 469-471 (1981).
[CrossRef]

1980

1977

L. W. Casperson, N. K. Kincheloe, and O. M. Stafsudd, "Phase plates for laser beam compensation," Opt. Commun. 21, 1-4 (1977).
[CrossRef]

1976

1974

1972

Bastiaans, M. J.

M. J. Bastiaans, "Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems," Optik 82, 173-181 (1989).

Burkhard, D. G.

Byer, R. L.

Casperson, L. W.

L. W. Casperson, N. K. Kincheloe, and O. M. Stafsudd, "Phase plates for laser beam compensation," Opt. Commun. 21, 1-4 (1977).
[CrossRef]

Dong, S.

Q. Lü, S. Dong, and H. Weber, "Analysis of TEM00 laser beam degradation caused by a birefringent Nd:YAG rod," Opt. Quantum Electron. 27, 777-783 (1995).
[CrossRef]

Feldman, B. J.

Gitomer, S. J.

Giuliani, G.

Goto, T.

K. Iwasaki, T. Hayashi, T. Goto, and S. Shimizu, "Square and uniform laser output device: theory and applications," Appl. Opt. 90, 1736-1744 (1990).
[CrossRef]

Hayashi, T.

K. Iwasaki, T. Hayashi, T. Goto, and S. Shimizu, "Square and uniform laser output device: theory and applications," Appl. Opt. 90, 1736-1744 (1990).
[CrossRef]

Ih, C. S.

Iwasaki, K.

K. Iwasaki, T. Hayashi, T. Goto, and S. Shimizu, "Square and uniform laser output device: theory and applications," Appl. Opt. 90, 1736-1744 (1990).
[CrossRef]

Johnson, B. C.

Keren, E.

Kincheloe, N. K.

L. W. Casperson, N. K. Kincheloe, and O. M. Stafsudd, "Phase plates for laser beam compensation," Opt. Commun. 21, 1-4 (1977).
[CrossRef]

Lavi, S.

Lee, W.-H.

W.-H. Lee, "Method for converting a Gaussian beam into a uniform beam," Opt. Commun. 36, 469-471 (1981).
[CrossRef]

Leppelmeier, G. W.

Lu, B.

L. Shirong and B. Lu, "M2 factor and kurtosis parameter of super-Gaussian beams passing through an axicon," Optik 114, 193-198 (2003).
[CrossRef]

Lü, Q.

Q. Lü, S. Dong, and H. Weber, "Analysis of TEM00 laser beam degradation caused by a birefringent Nd:YAG rod," Opt. Quantum Electron. 27, 777-783 (1995).
[CrossRef]

Martínez-Herrero, R.

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "Sharpness changes of Gaussian beams induced by spherically aberrated lenses," Opt. Commun. 107, 179-83 (1994).
[CrossRef]

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "Linear Gaussian intensity distributions synthesized by reflection on elliptic cylinders: a proposal," Appl. Opt. 31, 2970-2971 (1992).
[CrossRef] [PubMed]

R. Martínez-Herrero, P. M. Mejías, and G. Piquero, "Quality improvement of partially coherent symmetric-intensity beams caused by quartic phase distorsions," Opt. Lett. 17, 1650-1651 (1992).
[CrossRef] [PubMed]

J. Serna, R. Martínez-Herrero, and P. M. Mejías, "Parametric characterization of general partially coherent beams propagating through ABCD optical systems," J. Opt. Soc. Am. A 8, 1094-1098 (1991).
[CrossRef]

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "On the kurtosis parameter of laser beams," in Proceedings of the First Workshop on Laser Beam Characterization, P.M.Mejías, H.Weber, R.Martínez-Herrero, and A.GonzálezUreña, eds., (Sociedad Española de Óptica, 1993), pp. 141-148.

Mejías, P. M.

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "Sharpness changes of Gaussian beams induced by spherically aberrated lenses," Opt. Commun. 107, 179-83 (1994).
[CrossRef]

R. Martínez-Herrero, P. M. Mejías, and G. Piquero, "Quality improvement of partially coherent symmetric-intensity beams caused by quartic phase distorsions," Opt. Lett. 17, 1650-1651 (1992).
[CrossRef] [PubMed]

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "Linear Gaussian intensity distributions synthesized by reflection on elliptic cylinders: a proposal," Appl. Opt. 31, 2970-2971 (1992).
[CrossRef] [PubMed]

J. Serna, R. Martínez-Herrero, and P. M. Mejías, "Parametric characterization of general partially coherent beams propagating through ABCD optical systems," J. Opt. Soc. Am. A 8, 1094-1098 (1991).
[CrossRef]

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "On the kurtosis parameter of laser beams," in Proceedings of the First Workshop on Laser Beam Characterization, P.M.Mejías, H.Weber, R.Martínez-Herrero, and A.GonzálezUreña, eds., (Sociedad Española de Óptica, 1993), pp. 141-148.

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D. 32, 1455-1461 (1999).
[CrossRef]

Niziev, V. G.

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D. 32, 1455-1461 (1999).
[CrossRef]

Park, Y. K.

Piquero, G.

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "Sharpness changes of Gaussian beams induced by spherically aberrated lenses," Opt. Commun. 107, 179-83 (1994).
[CrossRef]

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "Linear Gaussian intensity distributions synthesized by reflection on elliptic cylinders: a proposal," Appl. Opt. 31, 2970-2971 (1992).
[CrossRef] [PubMed]

R. Martínez-Herrero, P. M. Mejías, and G. Piquero, "Quality improvement of partially coherent symmetric-intensity beams caused by quartic phase distorsions," Opt. Lett. 17, 1650-1651 (1992).
[CrossRef] [PubMed]

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "On the kurtosis parameter of laser beams," in Proceedings of the First Workshop on Laser Beam Characterization, P.M.Mejías, H.Weber, R.Martínez-Herrero, and A.GonzálezUreña, eds., (Sociedad Española de Óptica, 1993), pp. 141-148.

Prochaska, R.

Rhodes, P. W.

Serna, J.

Shealy, D. L.

Shimizu, S.

K. Iwasaki, T. Hayashi, T. Goto, and S. Shimizu, "Square and uniform laser output device: theory and applications," Appl. Opt. 90, 1736-1744 (1990).
[CrossRef]

Shirong, L.

L. Shirong and B. Lu, "M2 factor and kurtosis parameter of super-Gaussian beams passing through an axicon," Optik 114, 193-198 (2003).
[CrossRef]

Siegman, A. E.

Simmons, W. W.

Stafsudd, O. M.

L. W. Casperson, N. K. Kincheloe, and O. M. Stafsudd, "Phase plates for laser beam compensation," Opt. Commun. 21, 1-4 (1977).
[CrossRef]

Veldkamp, W. B.

Weber, H.

Q. Lü, S. Dong, and H. Weber, "Analysis of TEM00 laser beam degradation caused by a birefringent Nd:YAG rod," Opt. Quantum Electron. 27, 777-783 (1995).
[CrossRef]

H. Weber, "Propagation of higher-order intensity moments in quadratic-index media," Opt. Quantum Electron. 24, 1027-1049 (1992).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

J. Phys. D.

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D. 32, 1455-1461 (1999).
[CrossRef]

Opt. Commun.

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "Sharpness changes of Gaussian beams induced by spherically aberrated lenses," Opt. Commun. 107, 179-83 (1994).
[CrossRef]

L. W. Casperson, N. K. Kincheloe, and O. M. Stafsudd, "Phase plates for laser beam compensation," Opt. Commun. 21, 1-4 (1977).
[CrossRef]

W.-H. Lee, "Method for converting a Gaussian beam into a uniform beam," Opt. Commun. 36, 469-471 (1981).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

H. Weber, "Propagation of higher-order intensity moments in quadratic-index media," Opt. Quantum Electron. 24, 1027-1049 (1992).
[CrossRef]

Q. Lü, S. Dong, and H. Weber, "Analysis of TEM00 laser beam degradation caused by a birefringent Nd:YAG rod," Opt. Quantum Electron. 27, 777-783 (1995).
[CrossRef]

Optik

L. Shirong and B. Lu, "M2 factor and kurtosis parameter of super-Gaussian beams passing through an axicon," Optik 114, 193-198 (2003).
[CrossRef]

M. J. Bastiaans, "Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems," Optik 82, 173-181 (1989).

Proc. SPIE

A. E. Siegman, "New developments in laser resonators," in Proc. SPIE 1224, 2-14 (1990).
[CrossRef]

Other

G. Piquero, P. M. Mejías, and R. Martínez-Herrero, "On the kurtosis parameter of laser beams," in Proceedings of the First Workshop on Laser Beam Characterization, P.M.Mejías, H.Weber, R.Martínez-Herrero, and A.GonzálezUreña, eds., (Sociedad Española de Óptica, 1993), pp. 141-148.

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Figures (3)

Fig. 1
Fig. 1

Squared profiles of the transmittances, t m 2 ( x ) and t n 2 ( x ) , for a = b = 1 m m 1 and m = 10 and n = 0.6 .

Fig. 2
Fig. 2

Beam quality parameter at the output of the polarizer normalized to the beam quality of a Gaussian beam with the same wavelength, Q / Q g , versus the angle of the polarizer θ.

Fig. 3
Fig. 3

Kurtosis parameter at the output of the polarizer normalized to the kurtosis of a Gaussian beam with the same wavelength, K / K g , versus the angle of the polarizer θ.

Equations (77)

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

E ( x ; z ) = [ E s ( x ; z ) , E p ( x ; z ) ] .
αβ j = 1 I j αβ E j ( x + s / 2 , z ) E j ( x s / 2 , z ) ¯ × exp ( i k s u ) d s d x d u ,
α , β = x , u
Q = I s 2 I 2 Q s + I p 2 I 2 Q p + I s I p I 2 Q s p ,
Q = x 2 u 2 ,
Q s = x 2 s u 2 s ,
Q p = x 2 p u 2 p ,
Q s p = x 2 s u 2 p + x 2 p u 2 s ,
I s
I p
I = I s + I p
x 2
u 2
x = u = 0
Q g = 1 / 4 k 2
k = 2 π / λ
M 2
( M 2 ) 2 = k 2 Q
K = x 4 x 2 2 ,
x 4 = I s I x 4 s + I p I x 4 p ,
x 2 = I s I x 2 s + I p I x 2 p .
( K g )
t m ( x ) = exp [ 1 2 ( a x ) 2 m ] ,
t n ( x ) = exp [ 1 2 ( b x ) 2 n ] ,
E ( o ) ( x ) = ( t m ( x ) E s ( i ) ( x ) t n ( x ) E p ( i ) ( x ) ) ,
E ( o )
E ( o )
Q = [ a 3 2 m Γ ( 3 2 m ) + b 3 2 n Γ ( 3 2 n ) ] [ m a 2 Γ ( 2 1 2 m ) + n b 2 Γ ( 2 1 2 n ) ] k 2 [ a 1 2 m Γ ( 1 2 m ) + b 1 2 n Γ ( 1 2 n ) ] 2 ,
K = [ a 5 2 m Γ ( 5 2 m ) + b 5 2 n Γ ( 5 2 n ) ] [ a 1 2 m Γ ( 1 2 m ) + b 1 2 n Γ ( 1 2 n ) ] [ a 3 2 m Γ ( 3 2 m ) + b 3 2 n Γ ( 3 2 n ) ] 2 ,
m = n
a = b
E ( o ) ( x ) = [ E s ( i ) ( x ) t m ( x ) cos θ + E p ( i ) ( x ) t n ( x ) sin θ ] × ( cos θ sin θ ) ,
E ( o ) ( x )
θ = 0 °
90 °
Q l = l 2 k 2 Γ ( 3 / 2 l ) Γ ( 2 1 / 2 l ) Γ ( 1 / 2 l ) 2 ,
K l = Γ ( 5 / 2 l ) Γ ( 1 / 2 l ) Γ ( 3 / 2 l ) 2 ,
θ = 0 °
θ = 90 °
Q
K
m = 10
n = 0.6
a = b = 1 mm 1
Q g
K g
Q / Q g = 8.02
K / K g = 2.02
Q / Q g
K / K g
θ = 0 °
Q 0 ° / Q g = 6.43
θ = 90 °
Q 90 ° / Q g = 1.394
Q / Q g
θ = 88.81 °
( Q / Q g = 1.390 )
( Q / Q g = 190.178 )
θ = 134.65 °
K / K g
θ = 0 °
θ = 90 °
K 0 ° / K g = 0.61
K 90 ° / K g = 1.58
θ = 10.31 °
111.15 °
142.95 °
171.42 °
( K / K g = 1 )
T E M 00
t m 2 ( x )
t n 2 ( x )
a = b = 1 m m 1
m = 10
n = 0.6
Q / Q g
K / K g

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