Abstract

We show that the contribution of the electric field components into the focal region can be controlled using binary phase structures. We discuss differently polarized incident waves, for each case suggesting easily implemented binary phase distributions that ensure a maximum contribution of a definite electric field component on the optical axis. A decrease in the size of the central focal spot produced by a high numerical aperture (NA) focusing system comes as the result of the spatial redistribution of the contribution of different electric field components into the focal region. Using a polarization conversion matrix of a high NA lens and the numerical simulation of the focusing system in Debye’s approximation, we demonstrate benefits of using asymmetric to polar angle ϕ binary phase distributions (such as arg[cos  ϕ] or arg[sin  2ϕ]) for generating a subwavelength focal spot in separate electric field components. Additional binary structure variations with respect to the azimuthal angle also make possible controlling the longitudinal distribution of light. In particular, the contribution of the transverse components in the focal plane can be reduced by the use of a simple axicon-like structure that serves to enhance the NA of the lens central part, redirecting the energy from focal plane. As compared with the superimposition of a narrow annular aperture, this approach is more energy efficient, and as compared with the Toraldo filters, it is easier to control when applied to three-dimensional focal shaping.

© 2010 Optical Society of America

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2010 (3)

2009 (6)

R. K. Singh, P. Senthilkumaran, and K. Singh, “Tight focusing of vortex beams in presence of primary astigmatism,” J. Opt. Soc. Am. A 26, 576–588 (2009).
[CrossRef]

Z. Zhou, Q. Tan, Q. Li, and G. Jin, “Achromatic generation of radially polarized beams in visible range using segmented subwavelength metal wire gratings,” Opt. Lett. 34, 3361–3363 (2009).
[CrossRef] [PubMed]

S. N. Khonina, S. A. Balalayev, R. V. Skidanov, V. V. Kotlyar, B. Paivanranta, and J. Turunen, “Encoded binary diffractive element to form hyper-geometric laser beams,” J. Opt. A, Pure Appl. Opt. 11, 065702 (2009).
[CrossRef]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[CrossRef]

B. R. Boruah and M. A. A. Neil, “Laser scanning confocal microscope with programmable amplitude, phase, and polarization of the illumination beam,” Rev. Sci. Instrum. 80, 013705 (2009).
[CrossRef] [PubMed]

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9, 1249–1254 (2009).
[CrossRef] [PubMed]

2008 (4)

J. Stadler, C. Stanciu, C. Stupperich, and A. J. Meixner, “Tighter focusing with a parabolic mirror,” Opt. Lett. 33, 681–683 (2008).
[CrossRef] [PubMed]

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[CrossRef]

G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16, 4567–4581 (2008).
[CrossRef] [PubMed]

2007 (5)

2006 (5)

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).
[CrossRef]

P. J. S. G. Ferreira and A. Kempf, “Superoscillations: faster than the Nyquist rate,” IEEE Trans. Signal Process. 54, 3732–3740 (2006).
[CrossRef]

T. Grosjean and D. Courjon, “Photopolymers as vectorial sensors of the electric field,” Opt. Express 14, 2203–2210 (2006).
[CrossRef] [PubMed]

M. R. Beversluis, L. Novotny, and S. J. Stranick, “Programmable vector point-spread function engineering,” Opt. Express 14, 2650–2656 (2006).
[CrossRef] [PubMed]

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265, 411–417 (2006).
[CrossRef]

2005 (1)

2004 (5)

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
[CrossRef]

L. E. Helseth, “Optical vortices in focal regions,” Opt. Commun. 229, 85–91 (2004).
[CrossRef]

N. Davidson and N. Bokor, “High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens,” Opt. Lett. 29, 1318–1320 (2004).
[CrossRef] [PubMed]

C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327 (2004).
[CrossRef] [PubMed]

S. F. Pereira and A. S. van de Nes, “Superresolution by means of polarisation, phase and amplitude pupil masks,” Opt. Commun. 234, 119–124 (2004).
[CrossRef]

2003 (3)

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

C.-C. Sun and C.-K. Liu, “Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation,” Opt. Lett. 28, 99–101 (2003).
[CrossRef] [PubMed]

G. S. Landsberg, Optics (Fizmatlit, 2003) (in Russian), p. 848.

2002 (1)

2001 (1)

N. Huse, A. Schonle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6, 273–276 (2001).
[CrossRef] [PubMed]

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[CrossRef]

R. Kant, “Superresolution and increased depth of focus: an inverse problem of vector diffraction,” J. Mod. Opt. 47, 905–916 (2000).

1999 (1)

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

1998 (1)

1997 (1)

1996 (1)

1994 (1)

X. S. Xie and R. C. Dunn, “Probing single molecule dynamics,” Science 265, 361–364 (1994).
[CrossRef] [PubMed]

1990 (1)

1972 (1)

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Courier Dover, 1972), p. 1046.

1969 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Courier Dover, 1972), p. 1046.

Balalayev, S. A.

S. N. Khonina, S. A. Balalayev, R. V. Skidanov, V. V. Kotlyar, B. Paivanranta, and J. Turunen, “Encoded binary diffractive element to form hyper-geometric laser beams,” J. Opt. A, Pure Appl. Opt. 11, 065702 (2009).
[CrossRef]

Beijersbergen, M. W.

Berry, M. V.

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).
[CrossRef]

Beversluis, M. R.

Biener, G.

Bokor, N.

Bomzon, Z.

Boruah, B. R.

B. R. Boruah and M. A. A. Neil, “Laser scanning confocal microscope with programmable amplitude, phase, and polarization of the illumination beam,” Rev. Sci. Instrum. 80, 013705 (2009).
[CrossRef] [PubMed]

Bouwmeester, D.

Chen, W.

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265, 411–417 (2006).
[CrossRef]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[CrossRef]

Choudhury, A.

Courjon, D.

Davidson, N.

Dedecker, P.

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]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[CrossRef]

Dunn, R. C.

X. S. Xie and R. C. Dunn, “Probing single molecule dynamics,” Science 265, 361–364 (1994).
[CrossRef] [PubMed]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[CrossRef]

Enderlein, J.

Ferreira, P. J. S. G.

P. J. S. G. Ferreira and A. Kempf, “Superoscillations: faster than the Nyquist rate,” IEEE Trans. Signal Process. 54, 3732–3740 (2006).
[CrossRef]

Ford, D. H.

Gao, X.

X. Gao, J. Wang, H. Gu, and W. Xu, “Focusing properties of concentric piecewise cylindrical vector beam,” Optik 118, 257–265 (2007).
[CrossRef]

Glockl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[CrossRef]

Golub, I.

Grosjean, T.

Gu, H.

X. Gao, J. Wang, H. Gu, and W. Xu, “Focusing properties of concentric piecewise cylindrical vector beam,” Optik 118, 257–265 (2007).
[CrossRef]

Hasman, E.

Hell, S. W.

N. Huse, A. Schonle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6, 273–276 (2001).
[CrossRef] [PubMed]

Helseth, L. E.

L. E. Helseth, “Optical vortices in focal regions,” Opt. Commun. 229, 85–91 (2004).
[CrossRef]

Hofkens, J.

Honkanen, M.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

Hotta, J. -I.

Huang, F. M.

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9, 1249–1254 (2009).
[CrossRef] [PubMed]

Huang, K.

Huse, N.

N. Huse, A. Schonle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6, 273–276 (2001).
[CrossRef] [PubMed]

Jin, G.

Kalosha, V. P.

Kang, X. -L.

Kant, R.

R. Kant, “Superresolution and increased depth of focus: an inverse problem of vector diffraction,” J. Mod. Opt. 47, 905–916 (2000).

Karman, G. P.

Karpeev, S. V.

Kempf, A.

P. J. S. G. Ferreira and A. Kempf, “Superoscillations: faster than the Nyquist rate,” IEEE Trans. Signal Process. 54, 3732–3740 (2006).
[CrossRef]

Khonina, S. N.

S. N. Khonina and S. V. Karpeev, “Grating-based optical scheme for the universal generation of inhomogeneously polarized laser beams,” Appl. Opt. 49, 1734–1738 (2010).
[CrossRef] [PubMed]

S. N. Khonina and S. G. Volotovsky, “Investigation of axicon application in high-aperture focusing system,” Computer Optics 34, 35–51 (2010) (in Russian).

S. N. Khonina, S. A. Balalayev, R. V. Skidanov, V. V. Kotlyar, B. Paivanranta, and J. Turunen, “Encoded binary diffractive element to form hyper-geometric laser beams,” J. Opt. A, Pure Appl. Opt. 11, 065702 (2009).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

Kimura, W. D.

Kleiner, V.

Kotlyar, V. V.

S. N. Khonina, S. A. Balalayev, R. V. Skidanov, V. V. Kotlyar, B. Paivanranta, and J. Turunen, “Encoded binary diffractive element to form hyper-geometric laser beams,” J. Opt. A, Pure Appl. Opt. 11, 065702 (2009).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

Kozawa, Y.

Landsberg, G. S.

G. S. Landsberg, Optics (Fizmatlit, 2003) (in Russian), p. 848.

Lautanen, J.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

Lerman, G. M.

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]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[CrossRef]

Levy, U.

Li, Q.

Li, Y. -P.

Liu, C. -K.

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[CrossRef]

Meixner, A. J.

Morris, G. M.

Muls, B.

Neil, M. A. A.

B. R. Boruah and M. A. A. Neil, “Laser scanning confocal microscope with programmable amplitude, phase, and polarization of the illumination beam,” Rev. Sci. Instrum. 80, 013705 (2009).
[CrossRef] [PubMed]

Novotny, L.

Paivanranta, B.

S. N. Khonina, S. A. Balalayev, R. V. Skidanov, V. V. Kotlyar, B. Paivanranta, and J. Turunen, “Encoded binary diffractive element to form hyper-geometric laser beams,” J. Opt. A, Pure Appl. Opt. 11, 065702 (2009).
[CrossRef]

Pereira, S. F.

S. F. Pereira and A. S. van de Nes, “Superresolution by means of polarisation, phase and amplitude pupil masks,” Opt. Commun. 234, 119–124 (2004).
[CrossRef]

Petrov, D.

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
[CrossRef]

Popescu, S.

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).
[CrossRef]

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]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[CrossRef]

Ramsay, E.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Reid, D. T.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

Sales, T. R. M.

Sato, S.

Schadt, M.

Schonle, A.

N. Huse, A. Schonle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6, 273–276 (2001).
[CrossRef] [PubMed]

Senthilkumaran, P.

Serrels, K. A.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[CrossRef]

Sheppard, C. J. R.

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[CrossRef]

Shi, P.

Singh, K.

Singh, R. K.

Skidanov, R. V.

S. N. Khonina, S. A. Balalayev, R. V. Skidanov, V. V. Kotlyar, B. Paivanranta, and J. Turunen, “Encoded binary diffractive element to form hyper-geometric laser beams,” J. Opt. A, Pure Appl. Opt. 11, 065702 (2009).
[CrossRef]

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

Stadler, J.

Stalder, M.

Stanciu, C.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Courier Dover, 1972), p. 1046.

Stranick, S. J.

Stupperich, C.

Sun, C. -C.

Tan, Q.

Tidwell, S. C.

Toraldo di Francia, G.

Turunen, J.

S. N. Khonina, S. A. Balalayev, R. V. Skidanov, V. V. Kotlyar, B. Paivanranta, and J. Turunen, “Encoded binary diffractive element to form hyper-geometric laser beams,” J. Opt. A, Pure Appl. Opt. 11, 065702 (2009).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

van de Nes, A. S.

S. F. Pereira and A. S. van de Nes, “Superresolution by means of polarisation, phase and amplitude pupil masks,” Opt. Commun. 234, 119–124 (2004).
[CrossRef]

van Duijl, A.

Volotovsky, S. G.

S. N. Khonina and S. G. Volotovsky, “Investigation of axicon application in high-aperture focusing system,” Computer Optics 34, 35–51 (2010) (in Russian).

Volpe, G.

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
[CrossRef]

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[CrossRef]

Wang, J.

X. Gao, J. Wang, H. Gu, and W. Xu, “Focusing properties of concentric piecewise cylindrical vector beam,” Optik 118, 257–265 (2007).
[CrossRef]

Warburton, R. J.

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

Woerdman, J. P.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

Xie, X. S.

X. S. Xie and R. C. Dunn, “Probing single molecule dynamics,” Science 265, 361–364 (1994).
[CrossRef] [PubMed]

Xu, W.

X. Gao, J. Wang, H. Gu, and W. Xu, “Focusing properties of concentric piecewise cylindrical vector beam,” Optik 118, 257–265 (2007).
[CrossRef]

Yonezawa, K.

K. Yonezawa, Y. Kozawa, and S. Sato, “Compact laser with radial polarization using birefringent laser medium,” Jpn. J. Appl. Phys., Part 1 46, 5160–5163 (2007).
[CrossRef]

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[CrossRef]

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265, 411–417 (2006).
[CrossRef]

Zhang, X.

Zheludev, N. I.

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9, 1249–1254 (2009).
[CrossRef] [PubMed]

Zhou, Z.

Adv. Opt. Photon. (1)

Appl. Opt. (3)

Computer Optics (1)

S. N. Khonina and S. G. Volotovsky, “Investigation of axicon application in high-aperture focusing system,” Computer Optics 34, 35–51 (2010) (in Russian).

IEEE Trans. Signal Process. (1)

P. J. S. G. Ferreira and A. Kempf, “Superoscillations: faster than the Nyquist rate,” IEEE Trans. Signal Process. 54, 3732–3740 (2006).
[CrossRef]

J. Biomed. Opt. (1)

N. Huse, A. Schonle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6, 273–276 (2001).
[CrossRef] [PubMed]

J. Mod. Opt. (2)

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

R. Kant, “Superresolution and increased depth of focus: an inverse problem of vector diffraction,” J. Mod. Opt. 47, 905–916 (2000).

J. Opt. A, Pure Appl. Opt. (1)

S. N. Khonina, S. A. Balalayev, R. V. Skidanov, V. V. Kotlyar, B. Paivanranta, and J. Turunen, “Encoded binary diffractive element to form hyper-geometric laser beams,” J. Opt. A, Pure Appl. Opt. 11, 065702 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Phys. A (1)

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).
[CrossRef]

Jpn. J. Appl. Phys., Part 1 (1)

K. Yonezawa, Y. Kozawa, and S. Sato, “Compact laser with radial polarization using birefringent laser medium,” Jpn. J. Appl. Phys., Part 1 46, 5160–5163 (2007).
[CrossRef]

Nano Lett. (1)

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9, 1249–1254 (2009).
[CrossRef] [PubMed]

Nat. Photonics (2)

K. A. Serrels, E. Ramsay, R. J. Warburton, and D. T. Reid, “Nanoscale optical microscopy in the vectorial focusing regime,” Nat. Photonics 2, 311–314 (2008).
[CrossRef]

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[CrossRef]

Opt. Commun. (5)

S. F. Pereira and A. S. van de Nes, “Superresolution by means of polarisation, phase and amplitude pupil masks,” Opt. Commun. 234, 119–124 (2004).
[CrossRef]

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265, 411–417 (2006).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[CrossRef]

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
[CrossRef]

L. E. Helseth, “Optical vortices in focal regions,” Opt. Commun. 229, 85–91 (2004).
[CrossRef]

Opt. Express (4)

Opt. Lett. (9)

V. P. Kalosha and I. Golub, “Toward the subdiffraction focusing limit of optical superresolution,” Opt. Lett. 32, 3540–3542 (2007).
[CrossRef] [PubMed]

C.-C. Sun and C.-K. Liu, “Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation,” Opt. Lett. 28, 99–101 (2003).
[CrossRef] [PubMed]

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21, 1948–1950 (1996).
[CrossRef] [PubMed]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002).
[CrossRef]

N. Davidson and N. Bokor, “High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens,” Opt. Lett. 29, 1318–1320 (2004).
[CrossRef] [PubMed]

K. Huang, P. Shi, X.-L. Kang, X. Zhang, and Y.-P. Li, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35, 965–967 (2010).
[CrossRef] [PubMed]

J. Stadler, C. Stanciu, C. Stupperich, and A. J. Meixner, “Tighter focusing with a parabolic mirror,” Opt. Lett. 33, 681–683 (2008).
[CrossRef] [PubMed]

Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30, 3063–3065 (2005).
[CrossRef] [PubMed]

Z. Zhou, Q. Tan, Q. Li, and G. Jin, “Achromatic generation of radially polarized beams in visible range using segmented subwavelength metal wire gratings,” Opt. Lett. 34, 3361–3363 (2009).
[CrossRef] [PubMed]

Optik (1)

X. Gao, J. Wang, H. Gu, and W. Xu, “Focusing properties of concentric piecewise cylindrical vector beam,” Optik 118, 257–265 (2007).
[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]

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

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

Rev. Sci. Instrum. (1)

B. R. Boruah and M. A. A. Neil, “Laser scanning confocal microscope with programmable amplitude, phase, and polarization of the illumination beam,” Rev. Sci. Instrum. 80, 013705 (2009).
[CrossRef] [PubMed]

Science (1)

X. S. Xie and R. C. Dunn, “Probing single molecule dynamics,” Science 265, 361–364 (1994).
[CrossRef] [PubMed]

Other (2)

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Courier Dover, 1972), p. 1046.

G. S. Landsberg, Optics (Fizmatlit, 2003) (in Russian), p. 848.

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Figures (8)

Fig. 1
Fig. 1

The effect of the binary phase transmission function of a high-aperture lens for the linearly polarized light.

Fig. 2
Fig. 2

Simulation results for the aplanatic objective with NA = 0.99 for the linear x-polarization, R ( θ ) = 1 .

Fig. 3
Fig. 3

Simulation results for the diffractive lens with NA = 0.9987 for the linear x-polarization, B ( θ , ϕ ) = arg ( cos   ϕ ) : (a) longitudinal josaa-27-10-2188-i001and (b) transverse josaa-27-10-2188-i002, distributions | E | 2 , and (c) the distribution profile in the focal plane along the x-axis.

Fig. 4
Fig. 4

A change in the ray tilt in the central lens part due to the annular phase structure.

Fig. 5
Fig. 5

Simulation results for the aplanatic objective with ring diaphragm ( NA = 0.99 ) for the linear x-polarization z [ 20 λ , 20 λ ] , x , y [ 1.5 λ , 1.5 λ ] .

Fig. 6
Fig. 6

Simulation results for the aplanatic objective with NA = 0.99 complemented with a semi-annular phase structure for the linear x-polarization z [ 3 λ , 3 λ ] , x , y [ 1.5 λ , 1.5 λ ] .

Fig. 7
Fig. 7

Simulation results for the aplanatic objective with NA = 0.99 for the radial polarization.

Fig. 8
Fig. 8

Simulation results for the aplanatic objective with NA = 0.99 for the azimuthal polarization.

Equations (23)

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E ( ρ , φ , z ) = i f λ 0 α 0 2 π B ( θ , ϕ ) T ( θ ) P ( θ , ϕ ) exp [ i k ( ρ   sin   θ   cos ( ϕ φ ) + z   cos   θ ) ] sin   θ d θ d ϕ ,
P ( θ , ϕ ) = [ 1 + cos 2 ϕ ( cos   θ 1 ) sin   ϕ   cos   ϕ ( cos   θ 1 ) cos   ϕ   sin   θ sin   ϕ   cos   ϕ ( cos   θ 1 ) 1 + sin 2 ϕ ( cos   θ 1 ) sin   ϕ   sin   θ sin   θ   cos   ϕ sin   θ   sin   ϕ cos   θ ] [ a ( θ , ϕ ) b ( θ , ϕ ) c ( θ , ϕ ) ] ,
B ( θ , ϕ ) = R ( θ ) Ω B ( ϕ ) ,
Ω B ( ϕ ) = m = M 1 M 2 d m   exp ( i m ϕ ) ,
0 2 π exp ( i k ρ   sin   θ   cos ( ϕ φ ) ) Ω p ( ϕ ) Ω B ( ϕ ) d ϕ = 0 2 π exp ( i k ρ   sin   θ   cos ( ϕ φ ) ) l , m p l d m   exp [ i ( l + m ) ϕ ] d ϕ = 2 π l , m p l d m i l + m   exp [ i ( l + m ) φ ] J l + m ( t ) ,     t = k ρ   sin   θ ,
E ( ρ , φ , z ) = i k f 0 α Q ( ρ , φ , θ ) q ( θ ) d θ ,
P ( θ , ϕ ) = [ 1 + cos 2 ϕ ( cos   θ 1 ) sin   ϕ   cos   ϕ ( cos   θ 1 ) cos   ϕ   sin   θ ] .
Q ( ρ , φ , θ ) = [ J 0 ( t ) + C 2 ( t ) ( cos   θ 1 ) S C ( t ) ( cos   θ 1 ) C ( t ) sin   θ ] ,
E x ( 0 , 0 , z ) = i k f 2 0 α R ( θ ) T ( θ ) sin   θ ( cos   θ + 1 ) exp ( i k z   cos   θ ) d θ .
E z ( 0 , 0 , z ) = i k f 2 0 α R ( θ ) T ( θ ) sin 2 θ   exp ( i k z   cos   θ ) d θ ,
E y ( 0 , 0 , z ) = i k f 2 0 α R ( θ ) T ( θ ) sin   θ ( 1 cos   θ ) exp ( i k z   cos   θ ) d θ .
B δ ( θ , ϕ ) = δ ( θ π / 2 ) ,
B δ c ( θ , ϕ ) = δ ( θ π / 2 ) cos   ϕ .
B 1 ( θ , ϕ ) = arg [ R 1 ( θ ) cos   ϕ ] = arg [ cos ( β k f   sin   θ ) cos   ϕ ] ,
B 2 ( θ , ϕ ) = arg [ R 2 ( θ ) cos   ϕ ] = arg [ L G 3 , 0 ( ( γ k f   sin   θ ) 2 ) cos   ϕ ] ,
P ( θ , ϕ ) = 1 2 [ [ 1 + cos 2 ϕ ( cos   θ 1 ) ] ± i [ sin   ϕ   cos   ϕ ( cos   θ 1 ) ] [ sin   ϕ   cos   ϕ ( cos   θ 1 ) ] ± i [ 1 + sin 2 ϕ ( cos   θ 1 ) ] sin   θ [ cos   ϕ ± i   sin   ϕ ] ] .
Q m ( ρ , φ , θ ) = 1 2 exp ( i m φ ) [ J m ( t ) + 1 2 [ J m ( t ) + E 2 m ( t ) ] ( cos   θ 1 ) sgn ( p ) i { J m ( t ) + 1 2 ( J m ( t ) E 2 m ( t ) ) ( cos   θ 1 ) } E 1 m ( t ) sin   θ ] ,
Q 0 ( 0 , 0 , θ ) = ( 1 + cos   θ ) 2 [ 1 sgn ( p ) i 0 ] ,
Q cos   ϕ ( 0 , 0 , θ ) = 1 2 [ 0 0 sin   θ ] ,
Q sin   2 ϕ ( 0 , 0 , θ ) = ( cos   θ 1 ) 8 2 [ sgn ( p ) i 1 0 ] ,
P ( θ , ϕ ) = [ cos   ϕ   cos   θ sin   ϕ   cos   θ sin   θ ] .
Q ( ρ , φ , θ ) = [ C ( t ) cos   θ S ( t ) cos   θ J 0 ( t ) sin   θ ] ,
P ( θ , ϕ ) = [ sin   ϕ cos   ϕ 0 ] ,

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