Abstract

This paper presents and compares two basis systems, spherical harmonics and plane waves, for studying diverging and converging beams in an optical system. We show a similarity between a converging field and the time reversed field of a radiation field. We present and analyze the differences between the Debye-Wolf diffraction integral and the multipole theory for focusing of polarized light. The Debye-Wolf diffraction integral gives a well-known anomalous behavior on the optical axis and at the edge of the focused beam that can be avoided by using the multipole theory.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  49. A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, N. F. van Hulst, “Multipolar radiation of quantum emitters with nanowire optical antennas,” Nat. Commun. 4, 1750 (2013).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2013 (7)

H. Noh, S. M. Popoff, H. Cao, “Broadband subwavelength focusing of light using a passive sink,” Opt. Express 21, 17435–17446 (2013).
[CrossRef] [PubMed]

A. Sentenac, P. C. Chaumet, G. Leuchs, “Total absorption of light by a nanoparticle: an electromagnetic sink in the optical regime,” Opt. Lett. 38, 818–820 (2013).
[CrossRef] [PubMed]

Y. Urzhumov, C. Ciracì, D. R. Smith, “Optical time reversal with graphene,” Nat. Phys. 9, 393–394 (2013).
[CrossRef]

G. Leuchs, M. Sondermann, “Light-matter interaction in free space,” J. Mod. Opt. 60, 36–42 (2013).
[CrossRef] [PubMed]

T. X. Hoang, X. Chen, C. J. R. Sheppard, “Rigorous analytical modeling of high-aperture focusing through a spherical interface,” J. Opt. Soc. Am. A 30, 1426–1440 (2013).
[CrossRef]

C. J. R. Sheppard, “Intermediate field behind a nanostructure,” Phys. Rev. A 88, 033839 (2013).
[CrossRef]

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, N. F. van Hulst, “Multipolar radiation of quantum emitters with nanowire optical antennas,” Nat. Commun. 4, 1750 (2013).
[CrossRef] [PubMed]

2012 (3)

T. X. Hoang, X. Chen, C. J. R. Sheppard, “Interpretation of the scattering mechanism for particles in a focused beam,” Phys. Rev. A 86, 033817 (2012).
[CrossRef]

T. X. Hoang, X. Chen, C. J. R. Sheppard, “Multipole theory for tight focusing of polarized light, including radially polarized and other special cases,” J. Opt. Soc. Am. A 29, 32–43 (2012).
[CrossRef]

G. Leuchs, M. Sondermann, “Time reversal symmetry in optics,” Phys. Scr. 85, 058101 (2012).
[CrossRef]

2011 (4)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[CrossRef] [PubMed]

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, U. Leonhardt, ”Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[CrossRef]

R. Merlin, “Maxwell’s fish-eye lens and the mirage of perfect imaging,” J. Opt. 13, 024017 (2011).
[CrossRef]

X. Zhang, “Perfect lenses in focus: No drain, no gain,” Nature 480, 42–43 (2011).
[CrossRef]

2010 (7)

U. Leonhardt, T. G. Philbin, “Perfect imaging with positive refraction in three dimensions,” Phys. Rev. A 81, 011804 (2010).
[CrossRef]

R. J. Blaikie, “Comment on ‘Perfect imaging without negative refraction’,” New J. Phys. 12, 058001 (2010).
[CrossRef]

R. Merlin, “Comment on “Perfect imaging with positive refraction in three dimensions”,” Phys. Rev. A 82, 057801 (2010).
[CrossRef]

U. Leonhardt, “Reply to “Comment on ‘Perfect imaging with positive refraction in three dimensions’”,” Phys. Rev. A 82, 057802 (2010).
[CrossRef]

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Y. D. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef] [PubMed]

S. Heugel, A. S. Villar, M. Sondermann, U. Peschel, G. Leuchs, “On the analogy between a single atom and an optical resonator,” Laser Phys. 20, 100–106 (2010).
[CrossRef]

2009 (1)

U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys. 11, 093040 (2009).
[CrossRef]

2008 (2)

2007 (2)

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef] [PubMed]

M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, G. Leuchs, “Design of a mode converter for efficient light-atom coupling in free space,” Appl. Phys. B 89, 489–492 (2007).
[CrossRef]

2003 (1)

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

2002 (2)

J. de Rosny, M. Fink, “Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink,” Phys. Rev. Lett. 89, 124301 (2002).
[CrossRef] [PubMed]

S. K. Rhodes, K. A. Nugent, A. Roberts, “Precision measurement of the electromagnetic fields in the focal region of a high-numerical-aperture lens using a tapered fiber probe,” J. Opt. Soc. Am. A 19, 1689–1693 (2002).
[CrossRef]

2001 (1)

2000 (2)

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

J. B. Pendry, “Negative refraction makes perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1999 (1)

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100nm axial resolution,” J. Microsc. 195, 10–16 (1999).
[CrossRef] [PubMed]

1992 (1)

1981 (1)

1977 (1)

1975 (1)

1974 (1)

A. J. Devaney, E. Wolf, “Multipole expansions and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974).
[CrossRef]

1970 (2)

W. H. Carter, “Bandlimited angular spectrum approximation to a scalar dipole field,” Opt. Commun. 2, 142–148 (1970).
[CrossRef]

J. D. Lawson, “Some attributes of real and virtual photons,” Contemp. Phys. 11, 575–580 (1970).
[CrossRef]

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

B. Richards, 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]

1949 (1)

N. G. Van Kampen, “An asymptotic treatment of diffraction problems,” Physica XIV, 575–589 (1949).
[CrossRef]

1937 (1)

A. Erdélyi, “Zur theorie der kugelwellen von Artur Erdélyi,” Physica IV, 107–120 (1937).
[CrossRef]

1858 (1)

J. C. Maxwell, “On the general laws of optical instruments,” Q. J. Pure Appl. Math. 2, 271 (1858).

Agard, D. A.

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100nm axial resolution,” J. Microsc. 195, 10–16 (1999).
[CrossRef] [PubMed]

Blaikie, R. J.

R. J. Blaikie, “Comment on ‘Perfect imaging without negative refraction’,” New J. Phys. 12, 058001 (2010).
[CrossRef]

Born, M.

M. Born, W. Wolf, Principles of Optics, 7 (Cambridge University, 2005).

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (John Wiley, 1998).

Cao, H.

H. Noh, S. M. Popoff, H. Cao, “Broadband subwavelength focusing of light using a passive sink,” Opt. Express 21, 17435–17446 (2013).
[CrossRef] [PubMed]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef] [PubMed]

Carter, W. H.

W. H. Carter, “Bandlimited angular spectrum approximation to a spherical scalar wave field,” J. Opt. Soc. Am. 65, 1054–1058 (1975).
[CrossRef]

W. H. Carter, “Bandlimited angular spectrum approximation to a scalar dipole field,” Opt. Commun. 2, 142–148 (1970).
[CrossRef]

Chaumet, P. C.

A. Sentenac, P. C. Chaumet, G. Leuchs, “Total absorption of light by a nanoparticle: an electromagnetic sink in the optical regime,” Opt. Lett. 38, 818–820 (2013).
[CrossRef] [PubMed]

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Chen, X.

Chew, W. C.

Chong, Y.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[CrossRef] [PubMed]

Chong, Y. D.

Y. D. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef] [PubMed]

Ciracì, C.

Y. Urzhumov, C. Ciracì, D. R. Smith, “Optical time reversal with graphene,” Nat. Phys. 9, 393–394 (2013).
[CrossRef]

Cogswell, C. J.

C. J. R. Sheppard, C. J. Cogswell, “Reflection and transmission confocal microscopy,” presented at the Optics in Medicine, Biology and Environmental Research: Proceedings of the International Conference on Optics Within Life Sciences, Garmisch-Partenkirchen, Germany, 1993, 1990.

Curto, A. G.

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, N. F. van Hulst, “Multipolar radiation of quantum emitters with nanowire optical antennas,” Nat. Commun. 4, 1750 (2013).
[CrossRef] [PubMed]

de Rosny, J.

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef] [PubMed]

J. de Rosny, M. Fink, “Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink,” Phys. Rev. Lett. 89, 124301 (2002).
[CrossRef] [PubMed]

Devaney, A. J.

A. J. Devaney, E. Wolf, “Multipole expansions and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974).
[CrossRef]

Dorn, R.

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

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

Eberler, M.

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

Erdélyi, A.

A. Erdélyi, “Zur theorie der kugelwellen von Artur Erdélyi,” Physica IV, 107–120 (1937).
[CrossRef]

Ferrand, P.

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Feynman, R. P.

R. P. Feynman, R. P. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 2006), Vol. II.

Fink, M.

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef] [PubMed]

J. de Rosny, M. Fink, “Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink,” Phys. Rev. Lett. 89, 124301 (2002).
[CrossRef] [PubMed]

Foreman, M. R.

Ge, L.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef] [PubMed]

Gustafsson, M. G. L.

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100nm axial resolution,” J. Microsc. 195, 10–16 (1999).
[CrossRef] [PubMed]

Hell, S. W.

Hellwarth, R. W.

Heugel, S.

S. Heugel, A. S. Villar, M. Sondermann, U. Peschel, G. Leuchs, “On the analogy between a single atom and an optical resonator,” Laser Phys. 20, 100–106 (2010).
[CrossRef]

Hoang, T. X.

Keller, O.

O. Keller, Quantum Theory of Near-Field Electrodynamics (Springer, 2011).

Konermann, H.

M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, G. Leuchs, “Design of a mode converter for efficient light-atom coupling in free space,” Appl. Phys. B 89, 489–492 (2007).
[CrossRef]

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2008).

Kreuzer, M. P.

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, N. F. van Hulst, “Multipolar radiation of quantum emitters with nanowire optical antennas,” Nat. Commun. 4, 1750 (2013).
[CrossRef] [PubMed]

Lawson, J. D.

J. D. Lawson, “Some attributes of real and virtual photons,” Contemp. Phys. 11, 575–580 (1970).
[CrossRef]

Le Moal, E.

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Leighton, R. P.

R. P. Feynman, R. P. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 2006), Vol. II.

Leonhardt, U.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, U. Leonhardt, ”Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[CrossRef]

U. Leonhardt, T. G. Philbin, “Perfect imaging with positive refraction in three dimensions,” Phys. Rev. A 81, 011804 (2010).
[CrossRef]

U. Leonhardt, “Reply to “Comment on ‘Perfect imaging with positive refraction in three dimensions’”,” Phys. Rev. A 82, 057802 (2010).
[CrossRef]

U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys. 11, 093040 (2009).
[CrossRef]

Lerosey, G.

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef] [PubMed]

Leuchs, G.

A. Sentenac, P. C. Chaumet, G. Leuchs, “Total absorption of light by a nanoparticle: an electromagnetic sink in the optical regime,” Opt. Lett. 38, 818–820 (2013).
[CrossRef] [PubMed]

G. Leuchs, M. Sondermann, “Light-matter interaction in free space,” J. Mod. Opt. 60, 36–42 (2013).
[CrossRef] [PubMed]

G. Leuchs, M. Sondermann, “Time reversal symmetry in optics,” Phys. Scr. 85, 058101 (2012).
[CrossRef]

S. Heugel, A. S. Villar, M. Sondermann, U. Peschel, G. Leuchs, “On the analogy between a single atom and an optical resonator,” Laser Phys. 20, 100–106 (2010).
[CrossRef]

M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, G. Leuchs, “Design of a mode converter for efficient light-atom coupling in free space,” Appl. Phys. B 89, 489–492 (2007).
[CrossRef]

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

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

Lindlein, N.

M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, G. Leuchs, “Design of a mode converter for efficient light-atom coupling in free space,” Appl. Phys. B 89, 489–492 (2007).
[CrossRef]

Lueg, P.

P. Lueg, “Process of silencing sound oscillations,” US Patent No.2043416 (1936).

Ma, Y. G.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, U. Leonhardt, ”Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[CrossRef]

Maiwald, R.

M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, G. Leuchs, “Design of a mode converter for efficient light-atom coupling in free space,” Appl. Phys. B 89, 489–492 (2007).
[CrossRef]

Maxwell, J. C.

J. C. Maxwell, “On the general laws of optical instruments,” Q. J. Pure Appl. Math. 2, 271 (1858).

Merlin, R.

R. Merlin, “Maxwell’s fish-eye lens and the mirage of perfect imaging,” J. Opt. 13, 024017 (2011).
[CrossRef]

R. Merlin, “Comment on “Perfect imaging with positive refraction in three dimensions”,” Phys. Rev. A 82, 057801 (2010).
[CrossRef]

Mudry, E.

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Munro, P. R. T.

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, 2 (World Scientific, 2006).
[CrossRef]

Noh, H.

H. Noh, S. M. Popoff, H. Cao, “Broadband subwavelength focusing of light using a passive sink,” Opt. Express 21, 17435–17446 (2013).
[CrossRef] [PubMed]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[CrossRef] [PubMed]

Nugent, K. A.

Ong, C. K.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, U. Leonhardt, ”Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[CrossRef]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Peschel, U.

S. Heugel, A. S. Villar, M. Sondermann, U. Peschel, G. Leuchs, “On the analogy between a single atom and an optical resonator,” Laser Phys. 20, 100–106 (2010).
[CrossRef]

M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, G. Leuchs, “Design of a mode converter for efficient light-atom coupling in free space,” Appl. Phys. B 89, 489–492 (2007).
[CrossRef]

Philbin, T. G.

U. Leonhardt, T. G. Philbin, “Perfect imaging with positive refraction in three dimensions,” Phys. Rev. A 81, 011804 (2010).
[CrossRef]

Popoff, S. M.

Quabis, S.

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

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

Quidant, R.

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, N. F. van Hulst, “Multipolar radiation of quantum emitters with nanowire optical antennas,” Nat. Commun. 4, 1750 (2013).
[CrossRef] [PubMed]

Rhodes, S. K.

Richards, B.

B. Richards, 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]

B. Richards, “Diffraction in systems of high relative aperture,” in Astronomical Optics and Related Subjects, Z. Kopal, ed. (North Holland, 1955).

Roberts, A.

Sahebdivan, S.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, U. Leonhardt, ”Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[CrossRef]

Sands, M.

R. P. Feynman, R. P. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 2006), Vol. II.

Sedat, J. W.

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100nm axial resolution,” J. Microsc. 195, 10–16 (1999).
[CrossRef] [PubMed]

Sentenac, A.

A. Sentenac, P. C. Chaumet, G. Leuchs, “Total absorption of light by a nanoparticle: an electromagnetic sink in the optical regime,” Opt. Lett. 38, 818–820 (2013).
[CrossRef] [PubMed]

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Sheppard, C. J. R.

T. X. Hoang, X. Chen, C. J. R. Sheppard, “Rigorous analytical modeling of high-aperture focusing through a spherical interface,” J. Opt. Soc. Am. A 30, 1426–1440 (2013).
[CrossRef]

C. J. R. Sheppard, “Intermediate field behind a nanostructure,” Phys. Rev. A 88, 033839 (2013).
[CrossRef]

T. X. Hoang, X. Chen, C. J. R. Sheppard, “Interpretation of the scattering mechanism for particles in a focused beam,” Phys. Rev. A 86, 033817 (2012).
[CrossRef]

T. X. Hoang, X. Chen, C. J. R. Sheppard, “Multipole theory for tight focusing of polarized light, including radially polarized and other special cases,” J. Opt. Soc. Am. A 29, 32–43 (2012).
[CrossRef]

C. J. R. Sheppard, “High-aperture beams,” J. Opt. Soc. Am. A 18, 1579–1587 (2001).
[CrossRef]

C. J. R. Sheppard, C. J. Cogswell, “Reflection and transmission confocal microscopy,” presented at the Optics in Medicine, Biology and Environmental Research: Proceedings of the International Conference on Optics Within Life Sciences, Garmisch-Partenkirchen, Germany, 1993, 1990.

Sherif, S. S.

Sherman, G. C.

Smith, D. R.

Y. Urzhumov, C. Ciracì, D. R. Smith, “Optical time reversal with graphene,” Nat. Phys. 9, 393–394 (2013).
[CrossRef]

Sondermann, M.

G. Leuchs, M. Sondermann, “Light-matter interaction in free space,” J. Mod. Opt. 60, 36–42 (2013).
[CrossRef] [PubMed]

G. Leuchs, M. Sondermann, “Time reversal symmetry in optics,” Phys. Scr. 85, 058101 (2012).
[CrossRef]

S. Heugel, A. S. Villar, M. Sondermann, U. Peschel, G. Leuchs, “On the analogy between a single atom and an optical resonator,” Laser Phys. 20, 100–106 (2010).
[CrossRef]

M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, G. Leuchs, “Design of a mode converter for efficient light-atom coupling in free space,” Appl. Phys. B 89, 489–492 (2007).
[CrossRef]

Stelzer, E. H. K.

Stone, A. D.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef] [PubMed]

Taminiau, T. H.

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, N. F. van Hulst, “Multipolar radiation of quantum emitters with nanowire optical antennas,” Nat. Commun. 4, 1750 (2013).
[CrossRef] [PubMed]

Török, P.

Tourin, A.

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef] [PubMed]

Tyc, T.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, U. Leonhardt, ”Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[CrossRef]

Urzhumov, Y.

Y. Urzhumov, C. Ciracì, D. R. Smith, “Optical time reversal with graphene,” Nat. Phys. 9, 393–394 (2013).
[CrossRef]

van Hulst, N. F.

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, N. F. van Hulst, “Multipolar radiation of quantum emitters with nanowire optical antennas,” Nat. Commun. 4, 1750 (2013).
[CrossRef] [PubMed]

Van Kampen, N. G.

N. G. Van Kampen, “An asymptotic treatment of diffraction problems,” Physica XIV, 575–589 (1949).
[CrossRef]

Villar, A. S.

S. Heugel, A. S. Villar, M. Sondermann, U. Peschel, G. Leuchs, “On the analogy between a single atom and an optical resonator,” Laser Phys. 20, 100–106 (2010).
[CrossRef]

Volpe, G.

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, N. F. van Hulst, “Multipolar radiation of quantum emitters with nanowire optical antennas,” Nat. Commun. 4, 1750 (2013).
[CrossRef] [PubMed]

Wan, W.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[CrossRef] [PubMed]

Wolf, E.

A. J. Devaney, E. Wolf, “Multipole expansions and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974).
[CrossRef]

B. Richards, 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]

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

Wolf, W.

M. Born, W. Wolf, Principles of Optics, 7 (Cambridge University, 2005).

Zhang, X.

X. Zhang, “Perfect lenses in focus: No drain, no gain,” Nature 480, 42–43 (2011).
[CrossRef]

Zheludev, N. I.

N. I. Zheludev, “What diffraction limit?,” Nat. Mater. 7, 420–422 (2008).
[CrossRef] [PubMed]

Appl. Phys. B (1)

M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, G. Leuchs, “Design of a mode converter for efficient light-atom coupling in free space,” Appl. Phys. B 89, 489–492 (2007).
[CrossRef]

Contemp. Phys. (1)

J. D. Lawson, “Some attributes of real and virtual photons,” Contemp. Phys. 11, 575–580 (1970).
[CrossRef]

J. Math. Phys. (1)

A. J. Devaney, E. Wolf, “Multipole expansions and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974).
[CrossRef]

J. Microsc. (1)

M. G. L. Gustafsson, D. A. Agard, J. W. Sedat, “I5M: 3D widefield light microscopy with better than 100nm axial resolution,” J. Microsc. 195, 10–16 (1999).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

G. Leuchs, M. Sondermann, “Light-matter interaction in free space,” J. Mod. Opt. 60, 36–42 (2013).
[CrossRef] [PubMed]

J. Opt. (1)

R. Merlin, “Maxwell’s fish-eye lens and the mirage of perfect imaging,” J. Opt. 13, 024017 (2011).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (5)

Laser Phys. (1)

S. Heugel, A. S. Villar, M. Sondermann, U. Peschel, G. Leuchs, “On the analogy between a single atom and an optical resonator,” Laser Phys. 20, 100–106 (2010).
[CrossRef]

Nat. Commun. (1)

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, N. F. van Hulst, “Multipolar radiation of quantum emitters with nanowire optical antennas,” Nat. Commun. 4, 1750 (2013).
[CrossRef] [PubMed]

Nat. Mater. (1)

N. I. Zheludev, “What diffraction limit?,” Nat. Mater. 7, 420–422 (2008).
[CrossRef] [PubMed]

Nat. Phys. (1)

Y. Urzhumov, C. Ciracì, D. R. Smith, “Optical time reversal with graphene,” Nat. Phys. 9, 393–394 (2013).
[CrossRef]

Nature (1)

X. Zhang, “Perfect lenses in focus: No drain, no gain,” Nature 480, 42–43 (2011).
[CrossRef]

New J. Phys. (3)

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, U. Leonhardt, ”Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[CrossRef]

U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys. 11, 093040 (2009).
[CrossRef]

R. J. Blaikie, “Comment on ‘Perfect imaging without negative refraction’,” New J. Phys. 12, 058001 (2010).
[CrossRef]

Opt. Commun. (2)

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

W. H. Carter, “Bandlimited angular spectrum approximation to a scalar dipole field,” Opt. Commun. 2, 142–148 (1970).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (5)

R. Merlin, “Comment on “Perfect imaging with positive refraction in three dimensions”,” Phys. Rev. A 82, 057801 (2010).
[CrossRef]

U. Leonhardt, “Reply to “Comment on ‘Perfect imaging with positive refraction in three dimensions’”,” Phys. Rev. A 82, 057802 (2010).
[CrossRef]

U. Leonhardt, T. G. Philbin, “Perfect imaging with positive refraction in three dimensions,” Phys. Rev. A 81, 011804 (2010).
[CrossRef]

T. X. Hoang, X. Chen, C. J. R. Sheppard, “Interpretation of the scattering mechanism for particles in a focused beam,” Phys. Rev. A 86, 033817 (2012).
[CrossRef]

C. J. R. Sheppard, “Intermediate field behind a nanostructure,” Phys. Rev. A 88, 033839 (2013).
[CrossRef]

Phys. Rev. Lett. (5)

J. B. Pendry, “Negative refraction makes perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef] [PubMed]

J. de Rosny, M. Fink, “Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink,” Phys. Rev. Lett. 89, 124301 (2002).
[CrossRef] [PubMed]

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

E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Phys. Scr. (1)

G. Leuchs, M. Sondermann, “Time reversal symmetry in optics,” Phys. Scr. 85, 058101 (2012).
[CrossRef]

Physica (2)

A. Erdélyi, “Zur theorie der kugelwellen von Artur Erdélyi,” Physica IV, 107–120 (1937).
[CrossRef]

N. G. Van Kampen, “An asymptotic treatment of diffraction problems,” Physica XIV, 575–589 (1949).
[CrossRef]

Proc. R. Soc. London Ser. A (2)

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

B. Richards, 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]

Q. J. Pure Appl. Math. (1)

J. C. Maxwell, “On the general laws of optical instruments,” Q. J. Pure Appl. Math. 2, 271 (1858).

Science (2)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[CrossRef] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120–1122 (2007).
[CrossRef] [PubMed]

Other (9)

O. Keller, Quantum Theory of Near-Field Electrodynamics (Springer, 2011).

M. Born, W. Wolf, Principles of Optics, 7 (Cambridge University, 2005).

P. Lueg, “Process of silencing sound oscillations,” US Patent No.2043416 (1936).

R. P. Feynman, R. P. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 2006), Vol. II.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, 2 (World Scientific, 2006).
[CrossRef]

B. Richards, “Diffraction in systems of high relative aperture,” in Astronomical Optics and Related Subjects, Z. Kopal, ed. (North Holland, 1955).

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (John Wiley, 1998).

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2008).

C. J. R. Sheppard, C. J. Cogswell, “Reflection and transmission confocal microscopy,” presented at the Optics in Medicine, Biology and Environmental Research: Proceedings of the International Conference on Optics Within Life Sciences, Garmisch-Partenkirchen, Germany, 1993, 1990.

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Figures (9)

Fig. 1
Fig. 1

Source radiates a wave propagating towards infinity.

Fig. 2
Fig. 2

A sink absorbs a wave converging from infinity.

Fig. 3
Fig. 3

Gaussian reference sphere represents an aplanatic focusing system.

Fig. 4
Fig. 4

Integration contours.

Fig. 5
Fig. 5

Contour plot of electric energy density due to the time reversed field in absence of the sink.

Fig. 6
Fig. 6

Electric intensity distributions on the GRS with a low numerical aperture beam (upper) and a high numerical aperture beam (lower) with L = 400.

Fig. 7
Fig. 7

Electric intensity distributions on spheres of different radius R = 0.2cm (top) and R = 0.1cm (bottom) with L = 400.

Fig. 8
Fig. 8

Electric intensity distributions on the GRS (top) with L = 100 and on a sphere (bottom) R = 10μm with L=50.

Fig. 9
Fig. 9

Electric intensity distribution on a sphere R = 5μm with L=30.

Equations (23)

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

N l m ( r ¯ ) = × × [ r ¯ Λ l m ( r ¯ ) ] , M l m ( r ¯ ) = i k × [ r ¯ Λ l m ( r ¯ ) ] ,
l m ( r ¯ ) = j l ( k r ) Y l m ( θ , ϕ ) = C l m { [ 1 i k ( x + i y ) ] m P l ( m ) ( 1 i k z ) } sin ( k r ) k r ,
Π l m ( 1 ) ( r ¯ ) = h l ( 1 ) ( k r ) Y l m ( θ , ϕ ) = C l m { [ 1 i k ( x + i y ) ] m P l ( m ) ( 1 i k z ) } e i k r i k r ,
Π l m ( 2 ) ( r ¯ ) = h l ( 2 ) ( k r ) Y l m ( θ , ϕ ) = C l m { [ 1 i k ( x + i y ) ] m P l ( m ) ( 1 i k z ) } e i k r i k r .
ρ 1 ( r ¯ , t ) = Re { ρ 1 ( r ¯ ) e i ω t } , J ¯ 1 ( r ¯ , t ) = Re { J ¯ 1 ( r ¯ ) e i ω t } .
E ¯ 1 ( r ¯ ) = i k 1 2 π 0 2 π d β 1 C ± d α 1 sin α 1 E ^ 1 ( s ^ 1 ) e i k ¯ 1 r ¯ ,
E ^ 1 ( s ^ 1 ) = | r ¯ | R [ i k 1 c J ¯ 1 ( r ¯ ) ρ 1 ( r ¯ ) ] e i k ¯ 1 r ¯ d 3 r ¯ .
E ¯ 1 ( r ¯ ) = l = 1 m = l l [ g E l m N l m ( 1 ) ( r ¯ ) + g M l m M l m ( 1 ) ( r ¯ ) ] ,
g E l m = i l + 1 l ( l + 1 ) 0 2 π 0 π ( E ^ 1 ( s ^ 1 ) × s ^ 1 ) Y l m * ( α 1 , β 1 ) sin α 1 d α 1 d β 1 ,
g M l m = i l + 1 l ( l + 1 ) 0 2 π 0 π E ^ 1 ( s ^ 1 ) Y l m * ( α 1 , β 1 ) sin α 1 d α 1 d β 1 .
E ¯ 1 t r ( r ¯ ) = l = 1 m = l l [ g E l m * N l m ( 2 ) ( r ¯ ) g M l m * M l m ( 2 ) ( r ¯ ) ] .
E ¯ 2 ( r ¯ ) = i k 2 2 π 0 2 π d β 2 D ± d α 2 sin α 2 E ^ 2 ( s ^ 2 ) e i k ¯ 2 r ¯ .
E ¯ 2 ( r ¯ ) = l = 1 m = l l [ q E l m N l m ( 2 ) ( r ¯ ) + q M l m M l m ( 2 ) ( r ¯ ) ] ,
E ¯ ( r ¯ ) = E ¯ 1 ( r ¯ ) + E ¯ 2 ( r ¯ ) = 2 l = 1 m = l l [ p E l m N l m ( r ¯ ) + p M l m M l m ( r ¯ ) ] .
E ¯ ( r ¯ ) = i k 2 π 0 2 π d β 0 π d α sin α E ^ ( s ^ ) e i k ¯ . r ¯ .
E ^ 1 ( s ^ 1 ) = i ω μ I l 4 π sin ( α 1 ) α ^ 1 ,
E ¯ 1 ( r ¯ ) = g E 1 0 N 10 ( 1 ) ,
E ¯ 1 t r ( r ¯ ) = g E 1 0 N 10 ( 2 ) .
E ¯ ( r ¯ ) = 2 g E 1 0 N 10 .
E ¯ 2 f = a ( α ) α ^ ,
a ( α ) = sin α for α α m ; and a ( α ) = 0 for α > α m .
E ^ 2 = f e i k f E ¯ 2 f .
E ¯ 2 R = e i k ( f R ) f R E ¯ 2 f = e i k ( f R ) f R a ( α ) α ^ .

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