Abstract

Two interferometric techniques for converting a linearly polarized laser beam into a radially polarized beam with uniform azimuthal intensity are described. The techniques are based on the linear combination of orthogonally polarized beams, which have tailored intensity and phase profiles. Linearly polarized beams with intensity profiles tailored using a modified laser or an apodization filter are combined in separate experiments to produce radially polarized light. A beam with an extinction ratio of −21.7 dB and azimuthal intensity variations of less than ±12% is produced using the modified laser output. The second technique uses circularly polarized light and a unique spiral phase delay plate to produce the required phase profile. When focused, a radially polarized beam has a net longitudinal field useful for particle acceleration and, perhaps, other unique applications.

© 1990 Optical Society of America

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References

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  1. R. A. Chipman, “Polarization Analysis of Optical Systems,” Opt. Eng. 28, 90–99 (1989).
    [CrossRef]
  2. W. D. Kimura, R. D. Romea, S. C. Tidwell, D. H. Ford, “Progress on Inverse Cerenkov Laser Accelerator Experiment,” AIP Conf. Proc. 193, 203–216 (1989).
    [CrossRef]
  3. J. A. Edighoffer, W. D. Kimura, R. H. Pantell, M. A. Piestrup, D. Y. Wang, “Observation of Inverse Cerenkov Interaction Between Free Electrons and Laser Light,” Phys. Rev. A 23, 1848–1854 (1981).
    [CrossRef]
  4. J. R. Fontana, R. H. Pantell, “A High-Energy Laser Accelerator for Electrons Using the Inverse Cherenkov Effect,” J. Appl. Phys. 54, 4285 (1983).
    [CrossRef]
  5. P. J. Channell, C. J. Elliott, J. R. Fontana, “Laser Focusing of Particle Beams,” AIP Conf. Proc. 130, 407–417 (1985).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988), p. 172.
  15. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986), p. 689.
  16. Ref. 14, p. 182.
  17. Image-Pro II Image Processing System, Version 2.0, Media Cybernetics, Silver Springs, MD.
  18. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  19. S. C. Tidwell, D. H. Ford, W. D. Kimura, “Axicon Focusing of a Radially Polarized Laser Beam,” in preparation.

1989 (2)

R. A. Chipman, “Polarization Analysis of Optical Systems,” Opt. Eng. 28, 90–99 (1989).
[CrossRef]

W. D. Kimura, R. D. Romea, S. C. Tidwell, D. H. Ford, “Progress on Inverse Cerenkov Laser Accelerator Experiment,” AIP Conf. Proc. 193, 203–216 (1989).
[CrossRef]

1987 (1)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

1986 (1)

F. P. Schafer, “On Some Properties of Axicons,” Appl. Phys. B 39, 1–8 (1986).
[CrossRef]

1985 (1)

P. J. Channell, C. J. Elliott, J. R. Fontana, “Laser Focusing of Particle Beams,” AIP Conf. Proc. 130, 407–417 (1985).
[CrossRef]

1983 (1)

J. R. Fontana, R. H. Pantell, “A High-Energy Laser Accelerator for Electrons Using the Inverse Cherenkov Effect,” J. Appl. Phys. 54, 4285 (1983).
[CrossRef]

1982 (2)

1981 (1)

J. A. Edighoffer, W. D. Kimura, R. H. Pantell, M. A. Piestrup, D. Y. Wang, “Observation of Inverse Cerenkov Interaction Between Free Electrons and Laser Light,” Phys. Rev. A 23, 1848–1854 (1981).
[CrossRef]

1980 (1)

1979 (2)

1972 (1)

Y. Mushiake, K. Matsumura, N. Nakajima, “Generation of Radially Polarized Optical Beam Mode by Laser Oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[CrossRef]

Azzam, R. M. A.

Bigio, I. J.

T. Shimada, I. J. Bigio, N. A. Kurnit, R. F. Harrison, “Large-Volume High-Pressure CO2 Laser for Ultrashort Pulse Amplification,” in Technical Digest, Topical Meeting on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1988), p. 422.

Channell, P. J.

P. J. Channell, C. J. Elliott, J. R. Fontana, “Laser Focusing of Particle Beams,” AIP Conf. Proc. 130, 407–417 (1985).
[CrossRef]

Chipman, R. A.

R. A. Chipman, “Polarization Analysis of Optical Systems,” Opt. Eng. 28, 90–99 (1989).
[CrossRef]

Chodzko, R. A.

Dente, G. C.

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Edighoffer, J. A.

J. A. Edighoffer, W. D. Kimura, R. H. Pantell, M. A. Piestrup, D. Y. Wang, “Observation of Inverse Cerenkov Interaction Between Free Electrons and Laser Light,” Phys. Rev. A 23, 1848–1854 (1981).
[CrossRef]

Elliott, C. J.

P. J. Channell, C. J. Elliott, J. R. Fontana, “Laser Focusing of Particle Beams,” AIP Conf. Proc. 130, 407–417 (1985).
[CrossRef]

Fink, D.

Fontana, J. R.

P. J. Channell, C. J. Elliott, J. R. Fontana, “Laser Focusing of Particle Beams,” AIP Conf. Proc. 130, 407–417 (1985).
[CrossRef]

J. R. Fontana, R. H. Pantell, “A High-Energy Laser Accelerator for Electrons Using the Inverse Cherenkov Effect,” J. Appl. Phys. 54, 4285 (1983).
[CrossRef]

Ford, D. H.

W. D. Kimura, R. D. Romea, S. C. Tidwell, D. H. Ford, “Progress on Inverse Cerenkov Laser Accelerator Experiment,” AIP Conf. Proc. 193, 203–216 (1989).
[CrossRef]

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Axicon Focusing of a Radially Polarized Laser Beam,” in preparation.

Harrison, R. F.

T. Shimada, I. J. Bigio, N. A. Kurnit, R. F. Harrison, “Large-Volume High-Pressure CO2 Laser for Ultrashort Pulse Amplification,” in Technical Digest, Topical Meeting on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1988), p. 422.

Kahn, M. E. R.

Kimura, W. D.

W. D. Kimura, R. D. Romea, S. C. Tidwell, D. H. Ford, “Progress on Inverse Cerenkov Laser Accelerator Experiment,” AIP Conf. Proc. 193, 203–216 (1989).
[CrossRef]

J. A. Edighoffer, W. D. Kimura, R. H. Pantell, M. A. Piestrup, D. Y. Wang, “Observation of Inverse Cerenkov Interaction Between Free Electrons and Laser Light,” Phys. Rev. A 23, 1848–1854 (1981).
[CrossRef]

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Axicon Focusing of a Radially Polarized Laser Beam,” in preparation.

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988), p. 172.

Kurnit, N. A.

T. Shimada, I. J. Bigio, N. A. Kurnit, R. F. Harrison, “Large-Volume High-Pressure CO2 Laser for Ultrashort Pulse Amplification,” in Technical Digest, Topical Meeting on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1988), p. 422.

Mason, S. B.

Matsumura, K.

Y. Mushiake, K. Matsumura, N. Nakajima, “Generation of Radially Polarized Optical Beam Mode by Laser Oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Mushiake, Y.

Y. Mushiake, K. Matsumura, N. Nakajima, “Generation of Radially Polarized Optical Beam Mode by Laser Oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[CrossRef]

Nakajima, N.

Y. Mushiake, K. Matsumura, N. Nakajima, “Generation of Radially Polarized Optical Beam Mode by Laser Oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[CrossRef]

Pantell, R. H.

J. R. Fontana, R. H. Pantell, “A High-Energy Laser Accelerator for Electrons Using the Inverse Cherenkov Effect,” J. Appl. Phys. 54, 4285 (1983).
[CrossRef]

J. A. Edighoffer, W. D. Kimura, R. H. Pantell, M. A. Piestrup, D. Y. Wang, “Observation of Inverse Cerenkov Interaction Between Free Electrons and Laser Light,” Phys. Rev. A 23, 1848–1854 (1981).
[CrossRef]

Piestrup, M. A.

J. A. Edighoffer, W. D. Kimura, R. H. Pantell, M. A. Piestrup, D. Y. Wang, “Observation of Inverse Cerenkov Interaction Between Free Electrons and Laser Light,” Phys. Rev. A 23, 1848–1854 (1981).
[CrossRef]

Plummer, W. W.

Romea, R. D.

W. D. Kimura, R. D. Romea, S. C. Tidwell, D. H. Ford, “Progress on Inverse Cerenkov Laser Accelerator Experiment,” AIP Conf. Proc. 193, 203–216 (1989).
[CrossRef]

Schafer, F. P.

F. P. Schafer, “On Some Properties of Axicons,” Appl. Phys. B 39, 1–8 (1986).
[CrossRef]

Shimada, T.

T. Shimada, I. J. Bigio, N. A. Kurnit, R. F. Harrison, “Large-Volume High-Pressure CO2 Laser for Ultrashort Pulse Amplification,” in Technical Digest, Topical Meeting on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1988), p. 422.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986), p. 689.

Tidwell, S. C.

W. D. Kimura, R. D. Romea, S. C. Tidwell, D. H. Ford, “Progress on Inverse Cerenkov Laser Accelerator Experiment,” AIP Conf. Proc. 193, 203–216 (1989).
[CrossRef]

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Axicon Focusing of a Radially Polarized Laser Beam,” in preparation.

Turner, E. B.

Wang, D. Y.

J. A. Edighoffer, W. D. Kimura, R. H. Pantell, M. A. Piestrup, D. Y. Wang, “Observation of Inverse Cerenkov Interaction Between Free Electrons and Laser Light,” Phys. Rev. A 23, 1848–1854 (1981).
[CrossRef]

AIP Conf. Proc. (2)

W. D. Kimura, R. D. Romea, S. C. Tidwell, D. H. Ford, “Progress on Inverse Cerenkov Laser Accelerator Experiment,” AIP Conf. Proc. 193, 203–216 (1989).
[CrossRef]

P. J. Channell, C. J. Elliott, J. R. Fontana, “Laser Focusing of Particle Beams,” AIP Conf. Proc. 130, 407–417 (1985).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. B (1)

F. P. Schafer, “On Some Properties of Axicons,” Appl. Phys. B 39, 1–8 (1986).
[CrossRef]

J. Appl. Phys. (1)

J. R. Fontana, R. H. Pantell, “A High-Energy Laser Accelerator for Electrons Using the Inverse Cherenkov Effect,” J. Appl. Phys. 54, 4285 (1983).
[CrossRef]

Opt. Eng. (1)

R. A. Chipman, “Polarization Analysis of Optical Systems,” Opt. Eng. 28, 90–99 (1989).
[CrossRef]

Phys. Rev. A (1)

J. A. Edighoffer, W. D. Kimura, R. H. Pantell, M. A. Piestrup, D. Y. Wang, “Observation of Inverse Cerenkov Interaction Between Free Electrons and Laser Light,” Phys. Rev. A 23, 1848–1854 (1981).
[CrossRef]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Proc. IEEE (1)

Y. Mushiake, K. Matsumura, N. Nakajima, “Generation of Radially Polarized Optical Beam Mode by Laser Oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[CrossRef]

Other (6)

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988), p. 172.

A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986), p. 689.

Ref. 14, p. 182.

Image-Pro II Image Processing System, Version 2.0, Media Cybernetics, Silver Springs, MD.

T. Shimada, I. J. Bigio, N. A. Kurnit, R. F. Harrison, “Large-Volume High-Pressure CO2 Laser for Ultrashort Pulse Amplification,” in Technical Digest, Topical Meeting on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1988), p. 422.

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Axicon Focusing of a Radially Polarized Laser Beam,” in preparation.

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Figures (6)

Fig. 1
Fig. 1

Synthesis of different polarization configurations by combining linearly polarized TEM10 and TEM01 modes. (From Ref. 14.)

Fig. 2
Fig. 2

Mach-Zehnder interferometer configurations used to produce radially polarized beams: (a) 90° rotational shear interferometer that converts a sinusoidally varying linearly polarized beam; (b) conventional Mach-Zehnder for converting a general linearly polarized beam using spiral delay of circularly polarized light. (M = mirror, BS = beam splitter, P = polarizer, PS = periscope, and SPDP = spiral phase delay plate).

Fig. 3
Fig. 3

Schematic of output beam diagnostic system used to characterize the beam quality, intensity profile, and state of polarization.

Fig. 4
Fig. 4

Intensity profiles of a radially polarized beam produced by combining TEM01 modes after passing through an analyzer [see Fig. 2(a)]. The arrows indicate the analyzer transmission axis.

Fig. 5
Fig. 5

Intensity profiles, produced by the linear polarization combining technique, decomposed into their radial and azimuthal polarization components. Produced with TEM01 beams: (a) radial component; (b) azimuthal component (×10). Produced with apodized beams: (c) radial component; and (d) azimuthal component (×10).

Fig. 6
Fig. 6

Intensity profiles of the beam produced through spiral delay of circularly polarized beams: (a) the intensity profile before the analyzer; (b) the ideal intensity profile after transmission through an analyzer as predicted by theory (the arrow indicates the analyzer transmission axis); (c) and (d) the actual intensity profile as seen through an analyzer in orthogonal orientations.

Equations (14)

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E 1 ( r , θ ) = E o ( r ) cos ( θ ) x ^ ,
E 2 ( r , θ ) = E o ( r ) sin ( θ ) y ^ ,
E 1 + 2 ( r , θ ) = E o ( r ) [ cos ( θ ) x ^ + sin ( θ ) y ^ ] .
I ( r ) = E o ( r ) 2 ,
ψ ( θ ) = tan - 1 [ sin ( θ ) / cos ( θ ) ] = θ .
I ( r , θ ) = I o cos 2 ( θ ) ( r / w ) 2 exp [ - 2 ( r / w ) 2 ] ,
E ( r , θ ) = E o cos ( θ ) ( r / w ) exp [ - ( r / w ) 2 ] .
T ( r , θ ) = I ( r ) cos 2 ( θ ) I ( r , θ ) ,
T ( r , θ ) = T ( θ ) = T o cos 2 ( θ ) .
E 1 ( r , θ ) = E o ( r , θ ) 2 ( x ^ - i y ^ ) ,
E 2 ( r , θ ) = E o ( r , θ ) 2 ( x ^ + i y ^ ) ,
E 1 ( r , θ ) = E o ( r , θ ) 2 ( x ^ - i y ^ ) exp ( i θ ) ,
E 2 ( r , θ ) = E o ( r , θ ) 2 ( x ^ + i y ^ ) exp ( i θ ) .
E 1 + 2 ( r , θ ) = E o ( r , θ ) [ cos ( θ ) x ^ + sin ( θ ) y ^ ] .

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