Abstract

Among known temporal–spatial light modulation methods, there is no realistic method that can precisely control a light pulse simultaneously in the temporal and spatial domains. By careful consideration of the symmetries and topological properties of electromagnetic waves, a novel spatial light modulator has been developed to create different far-field patterns for each wavelength of linearly polarized light composed of various wavelength components. The system consists of an optical rotatory dispersion device, which is like a Faraday rotator, and a spatial light modulator with parallel-alignment nematic liquid-crystal cells. Numerical simulation results show the effectiveness of this new spatial light modulation method.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. M. Kakehata, R. Ueda, H. Takada, K. Torizuka, M. Obara, “Generation of time-dependent polarization pulses by combinations of high-intensity femtosecond laser pulses,” Rev. Laser Eng. 28, 506–510 (2000).
    [CrossRef]
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  10. K. Midorikawa, Y. Nagata, S. Kubodera, M. Obara, K. Toyoda, “An optical field-induced ionization x-ray laser using a preformed plasma scheme,” IEEE J. Sel. Top. Quantum Electron. 1, 931–940 (1995).
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  15. K. Tanaka, H. Waki, Y. Ido, S. Akita, Y. Yoshida, T. Yoshida, “Protein and polymer analyses up to m/z 100 000 by laser ionization time-of-flight mass spectrometry,” Rapid Commun. Mass Spectrom. 2, 151–153 (1988).
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    [CrossRef]
  19. N. R. Heckenberg, R. Mcduff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
    [CrossRef]
  20. H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with high-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
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  23. P. A. M. Dirac, “The theory of magnetic poles,” Phys. Rev. 74, 817–830 (1948).
    [CrossRef]
  24. H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
    [CrossRef] [PubMed]
  25. M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
    [CrossRef] [PubMed]
  26. N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
    [CrossRef]
  27. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
    [CrossRef]
  28. K. T. Gahagan, G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
    [CrossRef] [PubMed]
  29. G. A. Swartzlander, “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497–499 (2001).
    [CrossRef]
  30. J. A. Davis, D. E. McNamara, D. M. Cottrell, T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39, 1549–1554 (2000).
    [CrossRef]
  31. I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201, 251–270 (2002).
    [CrossRef]
  32. S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chkalov, J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/ Gd3Ga5O12(111) films,” J. Appl. Phys. 91, 9556–9560 (2002).
    [CrossRef]
  33. P. Yeh, C. Gu, Optics of Liquid Crystal Displays (Wiley Interscience, 1999), pp. 5–10.
  34. M. Born, E. Wolf, Principles of Optics (Pergamon, 1975).
  35. J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
    [CrossRef]

2002 (3)

D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankovic, T. Tschudi, “Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%,” Opt. Lett. 27, 1351–1353 (2002).
[CrossRef]

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201, 251–270 (2002).
[CrossRef]

S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chkalov, J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/ Gd3Ga5O12(111) films,” J. Appl. Phys. 91, 9556–9560 (2002).
[CrossRef]

2001 (1)

2000 (6)

J. A. Davis, D. E. McNamara, D. M. Cottrell, T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39, 1549–1554 (2000).
[CrossRef]

F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, P. Tournois, “Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping,” Opt. Lett. 25, 575–577 (2000).
[CrossRef]

M. Kakehata, R. Ueda, H. Takada, K. Torizuka, M. Obara, “Generation of time-dependent polarization pulses by combinations of high-intensity femtosecond laser pulses,” Rev. Laser Eng. 28, 506–510 (2000).
[CrossRef]

T. Shirai, T. H. Barns, T. G. Haskell, “Adaptive wave-front correction by means of all-optical feedback interferometry,” Opt. Lett. 25, 773–775 (2000).
[CrossRef]

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

M. Dyba, T. A. Klar, S. Jakobs, S. W. Hell, “Ultrafast dynamics microscopy,” Appl. Phys. Lett. 77, 597–599 (2000).
[CrossRef]

1999 (1)

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

1997 (2)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245–249 (1997).
[CrossRef]

1996 (3)

K. T. Gahagan, G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
[CrossRef] [PubMed]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[CrossRef]

1995 (5)

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with high-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

M. M. Wefers, K. A. Nelson, “Analysis of programmable ultrashort waveform generation using liquid-crystal spatial light modulators,” J. Opt. Soc. Am. B 12, 1343–1362 (1995).
[CrossRef]

A. M. Weiner, “Femtosecond optical pulse shaping and processing,”Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

K. Midorikawa, Y. Nagata, S. Kubodera, M. Obara, K. Toyoda, “An optical field-induced ionization x-ray laser using a preformed plasma scheme,” IEEE J. Sel. Top. Quantum Electron. 1, 931–940 (1995).
[CrossRef]

1994 (1)

1993 (1)

C. E. Clayton, K. A. Marsh, A. Dyson, M. Everett, A. Lal, W. P. Leemans, R. Williams, C. Joshi, “Ultrahigh-gradient acceleration of injected electrons by laser-excited relativistic electron plasma waves,” Phys. Rev. Lett. 70, 37–40 (1993).
[CrossRef] [PubMed]

1992 (1)

N. R. Heckenberg, R. Mcduff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

1991 (1)

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. Mcduff, C. O. Weiss, Chr. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[CrossRef]

1990 (1)

L. R. Khundkar, A. H. Zewail, “Ultrafast molecular reaction dynamics in real-time: progress over a decade,” Annu. Rev. Phys. Chem. 41, 15–60 (1990).
[CrossRef]

1988 (2)

K. Tanaka, H. Waki, Y. Ido, S. Akita, Y. Yoshida, T. Yoshida, “Protein and polymer analyses up to m/z 100 000 by laser ionization time-of-flight mass spectrometry,” Rapid Commun. Mass Spectrom. 2, 151–153 (1988).
[CrossRef]

A. H. Zewail, “Laser femtochemistry,” Science 242, 1645–1653 (1988).
[CrossRef] [PubMed]

1985 (1)

T. Tajima, “High energy laser plasma accelerators,” Laser Part. Beams 3, 351–413 (1985).
[CrossRef]

1979 (1)

T. Tajima, J. M. Dawson, “Laser electron accelerator,” Phys. Rev. Lett. 43, 267–270 (1979).
[CrossRef]

1948 (1)

P. A. M. Dirac, “The theory of magnetic poles,” Phys. Rev. 74, 817–830 (1948).
[CrossRef]

1931 (1)

P. A. M. Dirac, “Quantised singularities in the electromagnetic field,”Proc. R. Soc. London Ser. A 133, 60–72 (1931).
[CrossRef]

Abell, J. S.

S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chkalov, J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/ Gd3Ga5O12(111) films,” J. Appl. Phys. 91, 9556–9560 (2002).
[CrossRef]

Akita, S.

K. Tanaka, H. Waki, Y. Ido, S. Akita, Y. Yoshida, T. Yoshida, “Protein and polymer analyses up to m/z 100 000 by laser ionization time-of-flight mass spectrometry,” Rapid Commun. Mass Spectrom. 2, 151–153 (1988).
[CrossRef]

Allen, L.

N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[CrossRef]

Amako, J.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Barns, T. H.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1975).

Cheng, Z.

Chkalov, R. A.

S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chkalov, J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/ Gd3Ga5O12(111) films,” J. Appl. Phys. 91, 9556–9560 (2002).
[CrossRef]

Clayton, C. E.

C. E. Clayton, K. A. Marsh, A. Dyson, M. Everett, A. Lal, W. P. Leemans, R. Williams, C. Joshi, “Ultrahigh-gradient acceleration of injected electrons by laser-excited relativistic electron plasma waves,” Phys. Rev. Lett. 70, 37–40 (1993).
[CrossRef] [PubMed]

Cottrell, D. M.

J. A. Davis, D. E. McNamara, D. M. Cottrell, T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39, 1549–1554 (2000).
[CrossRef]

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Davis, J. A.

J. A. Davis, D. E. McNamara, D. M. Cottrell, T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39, 1549–1554 (2000).
[CrossRef]

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Dawson, J. M.

T. Tajima, J. M. Dawson, “Laser electron accelerator,” Phys. Rev. Lett. 43, 267–270 (1979).
[CrossRef]

Dirac, P. A. M.

P. A. M. Dirac, “The theory of magnetic poles,” Phys. Rev. 74, 817–830 (1948).
[CrossRef]

P. A. M. Dirac, “Quantised singularities in the electromagnetic field,”Proc. R. Soc. London Ser. A 133, 60–72 (1931).
[CrossRef]

Dyba, M.

M. Dyba, T. A. Klar, S. Jakobs, S. W. Hell, “Ultrafast dynamics microscopy,” Appl. Phys. Lett. 77, 597–599 (2000).
[CrossRef]

Dyson, A.

C. E. Clayton, K. A. Marsh, A. Dyson, M. Everett, A. Lal, W. P. Leemans, R. Williams, C. Joshi, “Ultrahigh-gradient acceleration of injected electrons by laser-excited relativistic electron plasma waves,” Phys. Rev. Lett. 70, 37–40 (1993).
[CrossRef] [PubMed]

Enger, J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

Everett, M.

C. E. Clayton, K. A. Marsh, A. Dyson, M. Everett, A. Lal, W. P. Leemans, R. Williams, C. Joshi, “Ultrahigh-gradient acceleration of injected electrons by laser-excited relativistic electron plasma waves,” Phys. Rev. Lett. 70, 37–40 (1993).
[CrossRef] [PubMed]

Freund, I.

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201, 251–270 (2002).
[CrossRef]

Friese, M. E. J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

Fukumoto, I.

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

Gahagan, K. T.

Gan, X.

Ganic, D.

Grishin, A. M.

S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chkalov, J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/ Gd3Ga5O12(111) films,” J. Appl. Phys. 91, 9556–9560 (2002).
[CrossRef]

Gu, C.

P. Yeh, C. Gu, Optics of Liquid Crystal Displays (Wiley Interscience, 1999), pp. 5–10.

Gu, M.

Hain, M.

Haskell, T. G.

He, H.

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with high-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with high-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

N. R. Heckenberg, R. Mcduff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. Mcduff, C. O. Weiss, Chr. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[CrossRef]

Hell, S. W.

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Hironaka, Y.

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

Ido, Y.

K. Tanaka, H. Waki, Y. Ido, S. Akita, Y. Yoshida, T. Yoshida, “Protein and polymer analyses up to m/z 100 000 by laser ionization time-of-flight mass spectrometry,” Rapid Commun. Mass Spectrom. 2, 151–153 (1988).
[CrossRef]

Jakobs, S.

M. Dyba, T. A. Klar, S. Jakobs, S. W. Hell, “Ultrafast dynamics microscopy,” Appl. Phys. Lett. 77, 597–599 (2000).
[CrossRef]

Joshi, C.

C. E. Clayton, K. A. Marsh, A. Dyson, M. Everett, A. Lal, W. P. Leemans, R. Williams, C. Joshi, “Ultrahigh-gradient acceleration of injected electrons by laser-excited relativistic electron plasma waves,” Phys. Rev. Lett. 70, 37–40 (1993).
[CrossRef] [PubMed]

Kahl, S.

S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chkalov, J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/ Gd3Ga5O12(111) films,” J. Appl. Phys. 91, 9556–9560 (2002).
[CrossRef]

Kakehata, M.

M. Kakehata, R. Ueda, H. Takada, K. Torizuka, M. Obara, “Generation of time-dependent polarization pulses by combinations of high-intensity femtosecond laser pulses,” Rev. Laser Eng. 28, 506–510 (2000).
[CrossRef]

Kawano, K.

S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chkalov, J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/ Gd3Ga5O12(111) films,” J. Appl. Phys. 91, 9556–9560 (2002).
[CrossRef]

Khartsev, S. I.

S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chkalov, J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/ Gd3Ga5O12(111) films,” J. Appl. Phys. 91, 9556–9560 (2002).
[CrossRef]

Khundkar, L. R.

L. R. Khundkar, A. H. Zewail, “Ultrafast molecular reaction dynamics in real-time: progress over a decade,” Annu. Rev. Phys. Chem. 41, 15–60 (1990).
[CrossRef]

Klar, T. A.

M. Dyba, T. A. Klar, S. Jakobs, S. W. Hell, “Ultrafast dynamics microscopy,” Appl. Phys. Lett. 77, 597–599 (2000).
[CrossRef]

Kondo, K.

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

Kong, G.

S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chkalov, J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/ Gd3Ga5O12(111) films,” J. Appl. Phys. 91, 9556–9560 (2002).
[CrossRef]

Kubodera, S.

K. Midorikawa, Y. Nagata, S. Kubodera, M. Obara, K. Toyoda, “An optical field-induced ionization x-ray laser using a preformed plasma scheme,” IEEE J. Sel. Top. Quantum Electron. 1, 931–940 (1995).
[CrossRef]

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Lal, A.

C. E. Clayton, K. A. Marsh, A. Dyson, M. Everett, A. Lal, W. P. Leemans, R. Williams, C. Joshi, “Ultrahigh-gradient acceleration of injected electrons by laser-excited relativistic electron plasma waves,” Phys. Rev. Lett. 70, 37–40 (1993).
[CrossRef] [PubMed]

Laude, V.

Leemans, W. P.

C. E. Clayton, K. A. Marsh, A. Dyson, M. Everett, A. Lal, W. P. Leemans, R. Williams, C. Joshi, “Ultrahigh-gradient acceleration of injected electrons by laser-excited relativistic electron plasma waves,” Phys. Rev. Lett. 70, 37–40 (1993).
[CrossRef] [PubMed]

Marsh, K. A.

C. E. Clayton, K. A. Marsh, A. Dyson, M. Everett, A. Lal, W. P. Leemans, R. Williams, C. Joshi, “Ultrahigh-gradient acceleration of injected electrons by laser-excited relativistic electron plasma waves,” Phys. Rev. Lett. 70, 37–40 (1993).
[CrossRef] [PubMed]

Mcduff, R.

N. R. Heckenberg, R. Mcduff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. Mcduff, C. O. Weiss, Chr. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[CrossRef]

McNamara, D. E.

Midorikawa, K.

K. Midorikawa, Y. Nagata, S. Kubodera, M. Obara, K. Toyoda, “An optical field-induced ionization x-ray laser using a preformed plasma scheme,” IEEE J. Sel. Top. Quantum Electron. 1, 931–940 (1995).
[CrossRef]

Nagata, Y.

K. Midorikawa, Y. Nagata, S. Kubodera, M. Obara, K. Toyoda, “An optical field-induced ionization x-ray laser using a preformed plasma scheme,” IEEE J. Sel. Top. Quantum Electron. 1, 931–940 (1995).
[CrossRef]

Nakamura, K. G.

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

Nelson, K. A.

Obara, M.

M. Kakehata, R. Ueda, H. Takada, K. Torizuka, M. Obara, “Generation of time-dependent polarization pulses by combinations of high-intensity femtosecond laser pulses,” Rev. Laser Eng. 28, 506–510 (2000).
[CrossRef]

K. Midorikawa, Y. Nagata, S. Kubodera, M. Obara, K. Toyoda, “An optical field-induced ionization x-ray laser using a preformed plasma scheme,” IEEE J. Sel. Top. Quantum Electron. 1, 931–940 (1995).
[CrossRef]

Padgett, M. J.

N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[CrossRef]

Rubinsztein-Dunlop, H.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with high-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

N. R. Heckenberg, R. Mcduff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. Mcduff, C. O. Weiss, Chr. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[CrossRef]

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Sasaki, A.

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

Sato, F.

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Shirai, T.

Simpson, N. B.

N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[CrossRef]

Smith, C. P.

N. R. Heckenberg, R. Mcduff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. Mcduff, C. O. Weiss, Chr. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[CrossRef]

Somalingam, S.

Sonehara, T.

J. A. Davis, D. E. McNamara, D. M. Cottrell, T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39, 1549–1554 (2000).
[CrossRef]

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Spielmann, Ch.

Stankovic, S.

Swartzlander, G. A.

Tajima, T.

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

T. Tajima, “High energy laser plasma accelerators,” Laser Part. Beams 3, 351–413 (1985).
[CrossRef]

T. Tajima, J. M. Dawson, “Laser electron accelerator,” Phys. Rev. Lett. 43, 267–270 (1979).
[CrossRef]

Takada, H.

M. Kakehata, R. Ueda, H. Takada, K. Torizuka, M. Obara, “Generation of time-dependent polarization pulses by combinations of high-intensity femtosecond laser pulses,” Rev. Laser Eng. 28, 506–510 (2000).
[CrossRef]

Tamm, Chr.

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. Mcduff, C. O. Weiss, Chr. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[CrossRef]

Tanaka, K.

K. Tanaka, H. Waki, Y. Ido, S. Akita, Y. Yoshida, T. Yoshida, “Protein and polymer analyses up to m/z 100 000 by laser ionization time-of-flight mass spectrometry,” Rapid Commun. Mass Spectrom. 2, 151–153 (1988).
[CrossRef]

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Torizuka, K.

M. Kakehata, R. Ueda, H. Takada, K. Torizuka, M. Obara, “Generation of time-dependent polarization pulses by combinations of high-intensity femtosecond laser pulses,” Rev. Laser Eng. 28, 506–510 (2000).
[CrossRef]

Tournois, P.

F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, P. Tournois, “Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping,” Opt. Lett. 25, 575–577 (2000).
[CrossRef]

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245–249 (1997).
[CrossRef]

Toyoda, K.

K. Midorikawa, Y. Nagata, S. Kubodera, M. Obara, K. Toyoda, “An optical field-induced ionization x-ray laser using a preformed plasma scheme,” IEEE J. Sel. Top. Quantum Electron. 1, 931–940 (1995).
[CrossRef]

Tsai, P.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Tschudi, T.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1998), pp. 210–222.

Ueda, R.

M. Kakehata, R. Ueda, H. Takada, K. Torizuka, M. Obara, “Generation of time-dependent polarization pulses by combinations of high-intensity femtosecond laser pulses,” Rev. Laser Eng. 28, 506–510 (2000).
[CrossRef]

Utsumi, T.

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

Verluise, F.

Waki, H.

K. Tanaka, H. Waki, Y. Ido, S. Akita, Y. Yoshida, T. Yoshida, “Protein and polymer analyses up to m/z 100 000 by laser ionization time-of-flight mass spectrometry,” Rapid Commun. Mass Spectrom. 2, 151–153 (1988).
[CrossRef]

Wefers, M. M.

Wegener, M. J.

N. R. Heckenberg, R. Mcduff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

Weiner, A. M.

A. M. Weiner, “Femtosecond optical pulse shaping and processing,”Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

Weiss, C. O.

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. Mcduff, C. O. Weiss, Chr. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[CrossRef]

White, A. G.

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. Mcduff, C. O. Weiss, Chr. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[CrossRef]

Wichmann, J.

Williams, R.

C. E. Clayton, K. A. Marsh, A. Dyson, M. Everett, A. Lal, W. P. Leemans, R. Williams, C. Joshi, “Ultrahigh-gradient acceleration of injected electrons by laser-excited relativistic electron plasma waves,” Phys. Rev. Lett. 70, 37–40 (1993).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1975).

Yeh, P.

P. Yeh, C. Gu, Optics of Liquid Crystal Displays (Wiley Interscience, 1999), pp. 5–10.

Yoshida, M.

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

Yoshida, T.

K. Tanaka, H. Waki, Y. Ido, S. Akita, Y. Yoshida, T. Yoshida, “Protein and polymer analyses up to m/z 100 000 by laser ionization time-of-flight mass spectrometry,” Rapid Commun. Mass Spectrom. 2, 151–153 (1988).
[CrossRef]

Yoshida, Y.

K. Tanaka, H. Waki, Y. Ido, S. Akita, Y. Yoshida, T. Yoshida, “Protein and polymer analyses up to m/z 100 000 by laser ionization time-of-flight mass spectrometry,” Rapid Commun. Mass Spectrom. 2, 151–153 (1988).
[CrossRef]

Zewail, A. H.

L. R. Khundkar, A. H. Zewail, “Ultrafast molecular reaction dynamics in real-time: progress over a decade,” Annu. Rev. Phys. Chem. 41, 15–60 (1990).
[CrossRef]

A. H. Zewail, “Laser femtochemistry,” Science 242, 1645–1653 (1988).
[CrossRef] [PubMed]

Zhidkov, A.

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

Annu. Rev. Phys. Chem. (1)

L. R. Khundkar, A. H. Zewail, “Ultrafast molecular reaction dynamics in real-time: progress over a decade,” Annu. Rev. Phys. Chem. 41, 15–60 (1990).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Dyba, T. A. Klar, S. Jakobs, S. W. Hell, “Ultrafast dynamics microscopy,” Appl. Phys. Lett. 77, 597–599 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

K. Midorikawa, Y. Nagata, S. Kubodera, M. Obara, K. Toyoda, “An optical field-induced ionization x-ray laser using a preformed plasma scheme,” IEEE J. Sel. Top. Quantum Electron. 1, 931–940 (1995).
[CrossRef]

J. Appl. Phys. (1)

S. Kahl, S. I. Khartsev, A. M. Grishin, K. Kawano, G. Kong, R. A. Chkalov, J. S. Abell, “Structure, microstructure, and magneto-optical properties of laser deposited Bi3Fe5O12/ Gd3Ga5O12(111) films,” J. Appl. Phys. 91, 9556–9560 (2002).
[CrossRef]

J. Mod. Opt. (3)

A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. Mcduff, C. O. Weiss, Chr. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991).
[CrossRef]

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with high-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

N. B. Simpson, L. Allen, M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[CrossRef]

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

Laser Part. Beams (1)

T. Tajima, “High energy laser plasma accelerators,” Laser Part. Beams 3, 351–413 (1985).
[CrossRef]

Opt. Commun. (2)

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245–249 (1997).
[CrossRef]

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201, 251–270 (2002).
[CrossRef]

Opt. Eng. (1)

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Opt. Lett. (6)

Opt. Quantum Electron. (1)

N. R. Heckenberg, R. Mcduff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

Phys. Rev. (1)

P. A. M. Dirac, “The theory of magnetic poles,” Phys. Rev. 74, 817–830 (1948).
[CrossRef]

Phys. Rev. A (1)

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

Phys. Rev. E (1)

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Sato, Y. Hironaka, K. G. Nakamura, K. Kondo, M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E 62, 7232–7240 (2000).
[CrossRef]

Phys. Rev. Lett. (4)

T. Tajima, J. M. Dawson, “Laser electron accelerator,” Phys. Rev. Lett. 43, 267–270 (1979).
[CrossRef]

C. E. Clayton, K. A. Marsh, A. Dyson, M. Everett, A. Lal, W. P. Leemans, R. Williams, C. Joshi, “Ultrahigh-gradient acceleration of injected electrons by laser-excited relativistic electron plasma waves,” Phys. Rev. Lett. 70, 37–40 (1993).
[CrossRef] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef] [PubMed]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

P. A. M. Dirac, “Quantised singularities in the electromagnetic field,”Proc. R. Soc. London Ser. A 133, 60–72 (1931).
[CrossRef]

Prog. Quantum Electron. (1)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,”Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

Rapid Commun. Mass Spectrom. (1)

K. Tanaka, H. Waki, Y. Ido, S. Akita, Y. Yoshida, T. Yoshida, “Protein and polymer analyses up to m/z 100 000 by laser ionization time-of-flight mass spectrometry,” Rapid Commun. Mass Spectrom. 2, 151–153 (1988).
[CrossRef]

Rev. Laser Eng. (1)

M. Kakehata, R. Ueda, H. Takada, K. Torizuka, M. Obara, “Generation of time-dependent polarization pulses by combinations of high-intensity femtosecond laser pulses,” Rev. Laser Eng. 28, 506–510 (2000).
[CrossRef]

Science (1)

A. H. Zewail, “Laser femtochemistry,” Science 242, 1645–1653 (1988).
[CrossRef] [PubMed]

Other (3)

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1998), pp. 210–222.

P. Yeh, C. Gu, Optics of Liquid Crystal Displays (Wiley Interscience, 1999), pp. 5–10.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1975).

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Figures (18)

Fig. 1
Fig. 1

Concept and fundamental configuration of the optical rotatory-dispersion-type spatial light modulator.

Fig. 2
Fig. 2

Molecular alignment of nematic LCs in the SLPM.

Fig. 3
Fig. 3

Coordinates for the calculation of diffraction.

Fig. 4
Fig. 4

Phase distribution in near field m = 1.

Fig. 5
Fig. 5

Far-field pattern of the uniform incident beam (topological charge m = 1, polarization angle 0°, wavelength 400 nm).

Fig. 6
Fig. 6

Cross section of far-field patterns (m = 1, 2, 3, 4) (uniform beam intensity distribution, polarization angle 0°, wavelength 400 nm).

Fig. 7
Fig. 7

Cross section of far-field patterns, x axis (m = 0, 0.2, 0.4, 0.6, 0.8, 1.0; uniform beam intensity distribution, polarization angle 0°, wavelength 400 nm).

Fig. 8
Fig. 8

Cross section of far-field patterns, y axis (m = 0, 0.2, 0.4, 0.6, 0.8, 1.0; uniform beam intensity distribution, polarization angle 0°, wavelength 400 nm).

Fig. 9
Fig. 9

Cross section of far field patterns, x axis (m = 1.0, 1.2, 1.4, 1.6, 1.8, 2.0; uniform beam intensity distribution, polarization angle 0°, wavelength 400 nm).

Fig. 10
Fig. 10

Cross section of far field patterns, y axis (m = 1.0, 1.2, 1.4, 1.6, 1.8, 2.0; uniform beam intensity distribution, polarization angle 0°, wavelength 400 nm).

Fig. 11
Fig. 11

Characteristic of far-field pattern cross section, x axis for various polarization angles (uniform beam intensity distribution, m = 1, wavelength 400–800 nm).

Fig. 12
Fig. 12

Characteristic of far-field pattern cross section, y axis, for various polarization angles (uniform beam intensity distribution, m = 1, wavelength 400–800 nm).

Fig. 13
Fig. 13

Characteristic of far-field pattern cross section in x axis for various polarization angles (uniform beam intensity distribution, m = 1, wavelength 400–800 nm).

Fig. 14
Fig. 14

Characteristic of far-field pattern cross section, y axis, for various polarization angles (uniform beam intensity distribution, m = 1, wavelength 400–800 nm).

Fig. 15
Fig. 15

Characteristic of far-field pattern cross section, x axis, for various polarization angles (uniform beam intensity distribution, m = 1, wavelength 800–400 nm).

Fig. 16
Fig. 16

Characteristic of far-field pattern cross section, y axis, for various polarization angles (uniform beam intensity distribution, m = 1, wavelength 800–400 nm).

Fig. 17
Fig. 17

Characteristic of far-field pattern cross section, x axis, for various polarization angles (uniform beam intensity distribution, m = 1, wavelength 800–400 nm).

Fig. 18
Fig. 18

Characteristic of far-field pattern cross section, y axis, for various polarization angles (uniform beam intensity distribution, m = 1, wavelength 800–400 nm).

Equations (6)

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

A x = 1 i λ A x 0 R exp [ i ( 2 π λ R + ϕ ) ] d x d y ,
A y = 1 i λ A y 0 R exp [ i ( 2 π λ R ) ] d x d y ,
A x 0 = A cos ( θ λ ) ,
A y 0 = A sin ( θ λ ) ,
ϕ = 2 π [ n e ( θ ) n o ] d λ ,
I = | A x | 2 + | A y | 2 ,

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