Abstract

A matrix method for calculating the polarization aberrations of light beams is discussed in detail. The radiation is represented as a coherent collection of Hermite-Gauss modes with definite amplitude, phase, and polarization state, with the longitudinal component of the field being taken into account. The polarization aberrations of the beam as it passes through a thin lens are considered, taking into account the influence of a circular stop.

© 2008 Optical Society of America

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  1. I. B. Vitrishchak, L. N. Soms, and A. A. Tarasov, “Intrinsic polarizations of a resonator with a thermally strained active element,” Zh. Tekh. Fiz. 44, 1055 (1974) I. B. Vitrishchak, L. N. Soms, and A. A. Tarasov,[Sov. J. Nondestruct. Test. 19, 664 (1974)].
  2. A. M. Bel'skiĭ and A. P. Khapalyuk, “Refraction of laser radiation at the interface of isotropic insulators,” Opt. Spektrosk. 38, 154 (1975) A. M. Bel'skiĭ and A. P. Khapalyuk,[Opt. Spectrosc. 38, 85 (1975)].
  3. G. P. Ledneva and Yu. I. Chekalinskaya, “Calculating the eigentypes of vibrations of a ring cavity with anisotropy that varies in cross section,” Zh. Prikl. Spektrosk. 33, 430 (1980).
  4. N. F. Maksimova, “How the curvature of a refracting surface affects the polarization parameters of radiation,” Izv. Vyssh. Uchebn. Zaved. Prib. No. 6, 78 (1982).
  5. P. I. Lamekin, “Variation of the polarization structure of axial beams of polarized light by lens systems,” Opt. Spektrosk. 60, 137 (1986) P. I. Lamekin,[Opt. Spectrosc. 60, 85 (1986)].
  6. A. A. Livshits and A. L. Sokolov, “Variation of the ellipticity of light when it is transmitted through a stressed prism of variable thickness,” Sb. Nauchn. Trudov MÉI No. 164, 92 (1988).
  7. A. L. Sokolov, “Method of polarization-ray matrices,” Laz. Tekh. Optoélek. 3-4, 98 (1993).
  8. E. F. Ishchenko and A. L. Sokolov, Polarization Optics (Izd. Mosk. Élektron. Inst., Moscow, 2005).
  9. A. L. Sokolov, “Transformation of the polarization structure of laser radiation in optical systems,” Opt. Spektrosk. 95, 816 (2003) A. L. Sokolov,[Opt. Spectrosc. 95, 814 (2003)].
  10. A. L. Sokolov, “Polarization of spherical waves,” Opt. Spektrosk. 92, 1011 (2002) A. L. Sokolov,[Opt. Spectrosc. 92, 936 (2002)].
  11. J. P. McGuire and R. A. Chipman, “Polarization aberrations,” Appl. Opt. 33, 5080 (1994).
  12. A. L. Sokolov, “Polarization aberrations of laser radiation,” Opt. Spektrosk. 89, 518 (2000) A. L. Sokolov,[Opt. Spectrosc. 89, 469 (2000)].
  13. V. N. Kuryatov and A. L. Sokolov, “Polarization inhomogeneities of a ring resonator and nonreciprocity of counterpropagating waves,” Kvantovaya Elektron. (Moscow) 32, 324 (2002) V. N. Kuryatov and A. L. Sokolov,[Quantum Electron. 32, 324 (2002)].
  14. M. Shribak, S. Inoue, and R. Oldenbourg, “Polarization aberrations caused by differential transmission and phase shift in high-numerical-aperture lenses: theory, measurement and rectification,” Opt. Eng. (Bellingham) 41, 943 (2002).
    [CrossRef]
  15. V. Yu. Petrun'kin and N. M. Kozhevnikov, “A matrix method for designing spherical resonators with polarization anisotropy that is inhomogeneous in cross section,” Tr. LPI: Kvant. Élektronika No. 366, 12 (1979).
  16. A. L. Sokolov, “A technique for the calculation of the natural waves of a cavity with polarization nonuniform elements,” Opt. Spektrosk. 83, 1005 (1997) A. L. Sokolov,[Opt. Spectrosc. 83, 930 (1997)].
  17. A. V. Nesterov, V. G. Niz'ev, and A. L. Sokolov, “Transformation Problem for Radiation with Radial Polarization,” Opt. Spektrosk. 90, 1018 (2001) A. V. Nesterov, V. G. Niz'ev, and A. L. Sokolov,[Opt. Spectrosc. 90, 923 (2001)].
  18. Yu. A. Anan'ev, Optical Cavities and the Problem of the Divergence of Laser Radiation (Nauka, Moscow, 1979).
  19. A. L. Sokolov, “Polarization aberrations of the radiation at the focus of a lens,” Pis'ma Zh. Tekh. Fiz. 31, No. 17, 77 (2005) A. L. Sokolov,[Tech. Phys. 31, 756 (2005)].
  20. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef]

2005 (1)

A. L. Sokolov, “Polarization aberrations of the radiation at the focus of a lens,” Pis'ma Zh. Tekh. Fiz. 31, No. 17, 77 (2005) A. L. Sokolov,[Tech. Phys. 31, 756 (2005)].

2003 (2)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

A. L. Sokolov, “Transformation of the polarization structure of laser radiation in optical systems,” Opt. Spektrosk. 95, 816 (2003) A. L. Sokolov,[Opt. Spectrosc. 95, 814 (2003)].

2002 (3)

A. L. Sokolov, “Polarization of spherical waves,” Opt. Spektrosk. 92, 1011 (2002) A. L. Sokolov,[Opt. Spectrosc. 92, 936 (2002)].

V. N. Kuryatov and A. L. Sokolov, “Polarization inhomogeneities of a ring resonator and nonreciprocity of counterpropagating waves,” Kvantovaya Elektron. (Moscow) 32, 324 (2002) V. N. Kuryatov and A. L. Sokolov,[Quantum Electron. 32, 324 (2002)].

M. Shribak, S. Inoue, and R. Oldenbourg, “Polarization aberrations caused by differential transmission and phase shift in high-numerical-aperture lenses: theory, measurement and rectification,” Opt. Eng. (Bellingham) 41, 943 (2002).
[CrossRef]

2001 (1)

A. V. Nesterov, V. G. Niz'ev, and A. L. Sokolov, “Transformation Problem for Radiation with Radial Polarization,” Opt. Spektrosk. 90, 1018 (2001) A. V. Nesterov, V. G. Niz'ev, and A. L. Sokolov,[Opt. Spectrosc. 90, 923 (2001)].

2000 (1)

A. L. Sokolov, “Polarization aberrations of laser radiation,” Opt. Spektrosk. 89, 518 (2000) A. L. Sokolov,[Opt. Spectrosc. 89, 469 (2000)].

1997 (1)

A. L. Sokolov, “A technique for the calculation of the natural waves of a cavity with polarization nonuniform elements,” Opt. Spektrosk. 83, 1005 (1997) A. L. Sokolov,[Opt. Spectrosc. 83, 930 (1997)].

1994 (1)

1993 (1)

A. L. Sokolov, “Method of polarization-ray matrices,” Laz. Tekh. Optoélek. 3-4, 98 (1993).

1986 (1)

P. I. Lamekin, “Variation of the polarization structure of axial beams of polarized light by lens systems,” Opt. Spektrosk. 60, 137 (1986) P. I. Lamekin,[Opt. Spectrosc. 60, 85 (1986)].

1980 (1)

G. P. Ledneva and Yu. I. Chekalinskaya, “Calculating the eigentypes of vibrations of a ring cavity with anisotropy that varies in cross section,” Zh. Prikl. Spektrosk. 33, 430 (1980).

1975 (1)

A. M. Bel'skiĭ and A. P. Khapalyuk, “Refraction of laser radiation at the interface of isotropic insulators,” Opt. Spektrosk. 38, 154 (1975) A. M. Bel'skiĭ and A. P. Khapalyuk,[Opt. Spectrosc. 38, 85 (1975)].

1974 (1)

I. B. Vitrishchak, L. N. Soms, and A. A. Tarasov, “Intrinsic polarizations of a resonator with a thermally strained active element,” Zh. Tekh. Fiz. 44, 1055 (1974) I. B. Vitrishchak, L. N. Soms, and A. A. Tarasov,[Sov. J. Nondestruct. Test. 19, 664 (1974)].

Appl. Opt. (1)

Kvantovaya Elektron. (Moscow) (1)

V. N. Kuryatov and A. L. Sokolov, “Polarization inhomogeneities of a ring resonator and nonreciprocity of counterpropagating waves,” Kvantovaya Elektron. (Moscow) 32, 324 (2002) V. N. Kuryatov and A. L. Sokolov,[Quantum Electron. 32, 324 (2002)].

Laz. Tekh. Optoélek. (1)

A. L. Sokolov, “Method of polarization-ray matrices,” Laz. Tekh. Optoélek. 3-4, 98 (1993).

Opt. Eng. (Bellingham) (1)

M. Shribak, S. Inoue, and R. Oldenbourg, “Polarization aberrations caused by differential transmission and phase shift in high-numerical-aperture lenses: theory, measurement and rectification,” Opt. Eng. (Bellingham) 41, 943 (2002).
[CrossRef]

Opt. Spektrosk. (7)

A. L. Sokolov, “A technique for the calculation of the natural waves of a cavity with polarization nonuniform elements,” Opt. Spektrosk. 83, 1005 (1997) A. L. Sokolov,[Opt. Spectrosc. 83, 930 (1997)].

A. V. Nesterov, V. G. Niz'ev, and A. L. Sokolov, “Transformation Problem for Radiation with Radial Polarization,” Opt. Spektrosk. 90, 1018 (2001) A. V. Nesterov, V. G. Niz'ev, and A. L. Sokolov,[Opt. Spectrosc. 90, 923 (2001)].

A. L. Sokolov, “Transformation of the polarization structure of laser radiation in optical systems,” Opt. Spektrosk. 95, 816 (2003) A. L. Sokolov,[Opt. Spectrosc. 95, 814 (2003)].

A. L. Sokolov, “Polarization of spherical waves,” Opt. Spektrosk. 92, 1011 (2002) A. L. Sokolov,[Opt. Spectrosc. 92, 936 (2002)].

A. L. Sokolov, “Polarization aberrations of laser radiation,” Opt. Spektrosk. 89, 518 (2000) A. L. Sokolov,[Opt. Spectrosc. 89, 469 (2000)].

A. M. Bel'skiĭ and A. P. Khapalyuk, “Refraction of laser radiation at the interface of isotropic insulators,” Opt. Spektrosk. 38, 154 (1975) A. M. Bel'skiĭ and A. P. Khapalyuk,[Opt. Spectrosc. 38, 85 (1975)].

P. I. Lamekin, “Variation of the polarization structure of axial beams of polarized light by lens systems,” Opt. Spektrosk. 60, 137 (1986) P. I. Lamekin,[Opt. Spectrosc. 60, 85 (1986)].

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Pis'ma Zh. Tekh. Fiz. (1)

A. L. Sokolov, “Polarization aberrations of the radiation at the focus of a lens,” Pis'ma Zh. Tekh. Fiz. 31, No. 17, 77 (2005) A. L. Sokolov,[Tech. Phys. 31, 756 (2005)].

Zh. Prikl. Spektrosk. (1)

G. P. Ledneva and Yu. I. Chekalinskaya, “Calculating the eigentypes of vibrations of a ring cavity with anisotropy that varies in cross section,” Zh. Prikl. Spektrosk. 33, 430 (1980).

Zh. Tekh. Fiz. (1)

I. B. Vitrishchak, L. N. Soms, and A. A. Tarasov, “Intrinsic polarizations of a resonator with a thermally strained active element,” Zh. Tekh. Fiz. 44, 1055 (1974) I. B. Vitrishchak, L. N. Soms, and A. A. Tarasov,[Sov. J. Nondestruct. Test. 19, 664 (1974)].

Other (5)

Yu. A. Anan'ev, Optical Cavities and the Problem of the Divergence of Laser Radiation (Nauka, Moscow, 1979).

V. Yu. Petrun'kin and N. M. Kozhevnikov, “A matrix method for designing spherical resonators with polarization anisotropy that is inhomogeneous in cross section,” Tr. LPI: Kvant. Élektronika No. 366, 12 (1979).

N. F. Maksimova, “How the curvature of a refracting surface affects the polarization parameters of radiation,” Izv. Vyssh. Uchebn. Zaved. Prib. No. 6, 78 (1982).

A. A. Livshits and A. L. Sokolov, “Variation of the ellipticity of light when it is transmitted through a stressed prism of variable thickness,” Sb. Nauchn. Trudov MÉI No. 164, 92 (1988).

E. F. Ishchenko and A. L. Sokolov, Polarization Optics (Izd. Mosk. Élektron. Inst., Moscow, 2005).

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