Abstract

This paper uses the integral Rayleigh–Sommerfeld transformation of the first type and an expansion in plane waves to investigate the nonparaxial phenomena that appear when optical elements are combined (using the lensacon as an example) even with a low numerical aperture. The contribution of various components of the vector field when high-aperture optical elements are used in tandem was also taken into account. Based on our studies, it is shown that, in the case of radial polarization, supplementing a lens with an axicon makes it possible to substantially strengthen the contribution of the longitudinal component and to overcome the diffraction limit in the overall intensity by a method that is an alternative to using an annular stop.

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  1. V. P. Koronkevich, I. A. Mikhaltsova, E. G. Churin, and Yu. I. Yurlov, “Lensacon,” Appl. Opt. 34, 5761 (1993).
    [Crossref]
  2. S. N. Khonina and S. G. Volotovskiĭ, “The fraxicon—a diffraction optical element with a conical focal region,” Komp. Opt. 33, 401 (2009).
  3. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Cambridge University Press, Cambridge, 1999).
  4. M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Wave Theory (Nauka, Moscow, 1979).
  5. A. V. Ustinov, “Fast method of computing the Rayleigh–Sommerfeld integral of the first type,” Comp. Opt. 33, 412 (2009).
  6. M. Totzeck, “Validity of the scalar Kirchhoff and Rayleigh–Sommerfeld diffraction theories in the near field of small phase objects,” J. Opt. Soc. Am. A 8, 27 (1991).
    [Crossref]
  7. V. I. Tsoy and L. A. Melnikov, “The use of Kirchhoff approach for the calculation of the near-field amplitudes of electromagnetic field,” Opt. Commun. 256, 1 (2005).
    [Crossref]
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968; Mir, Moscow, 1970).
  9. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am 44, 592 (1954).
    [Crossref]
  10. Z. Zhao, K. Duan, and B. Lu, “Focusing and diffraction by an optical lens and a small circular aperture,” Optik 117, 253 (2006).
    [Crossref]
  11. A. A. Kovalev and V. V. Kotlyar, “Nonparaxial propagation of a vector Gaussian optical vortex with initial radial polarization,” Komp. Opt. 33, 226 (2009).
  12. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [Crossref] [PubMed]

2009 (3)

S. N. Khonina and S. G. Volotovskiĭ, “The fraxicon—a diffraction optical element with a conical focal region,” Komp. Opt. 33, 401 (2009).

A. V. Ustinov, “Fast method of computing the Rayleigh–Sommerfeld integral of the first type,” Comp. Opt. 33, 412 (2009).

A. A. Kovalev and V. V. Kotlyar, “Nonparaxial propagation of a vector Gaussian optical vortex with initial radial polarization,” Komp. Opt. 33, 226 (2009).

2006 (1)

Z. Zhao, K. Duan, and B. Lu, “Focusing and diffraction by an optical lens and a small circular aperture,” Optik 117, 253 (2006).
[Crossref]

2005 (1)

V. I. Tsoy and L. A. Melnikov, “The use of Kirchhoff approach for the calculation of the near-field amplitudes of electromagnetic field,” Opt. Commun. 256, 1 (2005).
[Crossref]

2003 (1)

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

1993 (1)

1991 (1)

1954 (1)

J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am 44, 592 (1954).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Cambridge University Press, Cambridge, 1999).

Churin, E. G.

Dorn, R.

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

Duan, K.

Z. Zhao, K. Duan, and B. Lu, “Focusing and diffraction by an optical lens and a small circular aperture,” Optik 117, 253 (2006).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968; Mir, Moscow, 1970).

Khonina, S. N.

S. N. Khonina and S. G. Volotovskiĭ, “The fraxicon—a diffraction optical element with a conical focal region,” Komp. Opt. 33, 401 (2009).

Koronkevich, V. P.

Kotlyar, V. V.

A. A. Kovalev and V. V. Kotlyar, “Nonparaxial propagation of a vector Gaussian optical vortex with initial radial polarization,” Komp. Opt. 33, 226 (2009).

Kovalev, A. A.

A. A. Kovalev and V. V. Kotlyar, “Nonparaxial propagation of a vector Gaussian optical vortex with initial radial polarization,” Komp. Opt. 33, 226 (2009).

Leuchs, G.

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

Lu, B.

Z. Zhao, K. Duan, and B. Lu, “Focusing and diffraction by an optical lens and a small circular aperture,” Optik 117, 253 (2006).
[Crossref]

McLeod, J. H.

J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am 44, 592 (1954).
[Crossref]

Melnikov, L. A.

V. I. Tsoy and L. A. Melnikov, “The use of Kirchhoff approach for the calculation of the near-field amplitudes of electromagnetic field,” Opt. Commun. 256, 1 (2005).
[Crossref]

Mikhaltsova, I. A.

Quabis, S.

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

Rudenko, O. V.

M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Wave Theory (Nauka, Moscow, 1979).

Sukhorukov, A. P.

M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Wave Theory (Nauka, Moscow, 1979).

Totzeck, M.

Tsoy, V. I.

V. I. Tsoy and L. A. Melnikov, “The use of Kirchhoff approach for the calculation of the near-field amplitudes of electromagnetic field,” Opt. Commun. 256, 1 (2005).
[Crossref]

Ustinov, A. V.

A. V. Ustinov, “Fast method of computing the Rayleigh–Sommerfeld integral of the first type,” Comp. Opt. 33, 412 (2009).

Vinogradova, M. B.

M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Wave Theory (Nauka, Moscow, 1979).

Volotovskii, S. G.

S. N. Khonina and S. G. Volotovskiĭ, “The fraxicon—a diffraction optical element with a conical focal region,” Komp. Opt. 33, 401 (2009).

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Cambridge University Press, Cambridge, 1999).

Yurlov, Yu. I.

Zhao, Z.

Z. Zhao, K. Duan, and B. Lu, “Focusing and diffraction by an optical lens and a small circular aperture,” Optik 117, 253 (2006).
[Crossref]

Appl. Opt. (1)

Comp. Opt. (1)

A. V. Ustinov, “Fast method of computing the Rayleigh–Sommerfeld integral of the first type,” Comp. Opt. 33, 412 (2009).

J. Opt. Soc. Am (1)

J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am 44, 592 (1954).
[Crossref]

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

Komp. Opt. (2)

S. N. Khonina and S. G. Volotovskiĭ, “The fraxicon—a diffraction optical element with a conical focal region,” Komp. Opt. 33, 401 (2009).

A. A. Kovalev and V. V. Kotlyar, “Nonparaxial propagation of a vector Gaussian optical vortex with initial radial polarization,” Komp. Opt. 33, 226 (2009).

Opt. Commun. (1)

V. I. Tsoy and L. A. Melnikov, “The use of Kirchhoff approach for the calculation of the near-field amplitudes of electromagnetic field,” Opt. Commun. 256, 1 (2005).
[Crossref]

Optik (1)

Z. Zhao, K. Duan, and B. Lu, “Focusing and diffraction by an optical lens and a small circular aperture,” Optik 117, 253 (2006).
[Crossref]

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] [PubMed]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968; Mir, Moscow, 1970).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Cambridge University Press, Cambridge, 1999).

M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Wave Theory (Nauka, Moscow, 1979).

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