Abstract

We analyze the far-field resolution of apertures that are illuminated by a point dipole located at subwavelength distances. It is well known that radiation emitted by a localized source can be considered a combination of traveling and evanescent waves, when represented by the angular spectrum method. The evanescent wave part of the source can be converted to propagating waves by diffraction at the aperture; thereby it contributes to the far-field detection. Therefore one can expect an increase in the resolution of objects. We present explicit calculations showing that the resolution at the far zone is improved by decreasing the source-aperture distance. We also utilize the resolution enhancement by the near field of a dipole to resolve two closely located apertures. The results show that without the near field (evanescent field) the apertures are not resolved, whereas with the near field of the dipole the far zone intensity distribution shows improved resolution. This method eliminates the requirements of near-field techniques such as controlling and scanning closely located tip detectors.

© 2012 Optical Society of America

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2011 (3)

L. Novotny, Phys. Today 64(7), 47 (2011).
[CrossRef]

I. Aharonovich, S. Castelletto, D. A. Simpson, C-H. Su, A. D. Greentree, and S. Prawer, Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

X. Chen, S. Götzinger, and V. Sandoghdar, Opt. Lett. 36, 3545 (2011).
[CrossRef]

2009 (1)

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

2007 (2)

Y. Oshikan, T. Kataoka, M. Okuda, S. Hara, H. Inoue, and M. Nakano, Sci. Tech. Adv. Mater. 8, 181 (2007).
[CrossRef]

L. Rogobete, F. Kaminski, M. Agio, and V. Sandoghdar, Opt. Lett. 32, 1623 (2007).
[CrossRef]

2005 (1)

N. Fang, H. S. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

1998 (1)

G. S. Agarwal, Pure Appl. Opt. 7, 1143 (1998).
[CrossRef]

1992 (1)

1991 (1)

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251 (5000), 1468 (1991).
[CrossRef]

1990 (1)

1970 (1)

E. Wolf, J. Opt. Soc. Am 60, 18 (1970).
[CrossRef]

1919 (1)

H. Weyl, Ann. Phys. 365, 481 (1919).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, Pure Appl. Opt. 7, 1143 (1998).
[CrossRef]

Agio, M.

Aharonovich, I.

I. Aharonovich, S. Castelletto, D. A. Simpson, C-H. Su, A. D. Greentree, and S. Prawer, Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

Almendros, M.

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Betzig, E.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251 (5000), 1468 (1991).
[CrossRef]

Blatt, R.

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Castelletto, S.

I. Aharonovich, S. Castelletto, D. A. Simpson, C-H. Su, A. D. Greentree, and S. Prawer, Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

Chen, X.

Depasse, F.

Dubin, F.

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Eschner, J.

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Fang, N.

N. Fang, H. S. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Gehr, R.

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Gerber, S.

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Girard, C.

Götzinger, S.

Greentree, A. D.

I. Aharonovich, S. Castelletto, D. A. Simpson, C-H. Su, A. D. Greentree, and S. Prawer, Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

Guerra, J. M.

J. M. Guerra, Appl. Opt. 29, 3741 (1990).
[CrossRef]

J. M. Guerra and W. T. Plummer, “Optical proximity imaging method and apparatus,” U.S. patent 4,681,451(July21, 1987).

Hara, S.

Y. Oshikan, T. Kataoka, M. Okuda, S. Hara, H. Inoue, and M. Nakano, Sci. Tech. Adv. Mater. 8, 181 (2007).
[CrossRef]

Harris, T. D.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251 (5000), 1468 (1991).
[CrossRef]

Hennrich, M.

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Inoue, H.

Y. Oshikan, T. Kataoka, M. Okuda, S. Hara, H. Inoue, and M. Nakano, Sci. Tech. Adv. Mater. 8, 181 (2007).
[CrossRef]

Kaminski, F.

Kataoka, T.

Y. Oshikan, T. Kataoka, M. Okuda, S. Hara, H. Inoue, and M. Nakano, Sci. Tech. Adv. Mater. 8, 181 (2007).
[CrossRef]

Kostelak, R. L.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251 (5000), 1468 (1991).
[CrossRef]

Lee, H. S.

N. Fang, H. S. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Moyer, P. J.

M. A. Paesler and P. J. Moyer, Near Field Optics (Wiley, 1996).

Nakano, M.

Y. Oshikan, T. Kataoka, M. Okuda, S. Hara, H. Inoue, and M. Nakano, Sci. Tech. Adv. Mater. 8, 181 (2007).
[CrossRef]

Novotny, L.

L. Novotny, Phys. Today 64(7), 47 (2011).
[CrossRef]

Okuda, M.

Y. Oshikan, T. Kataoka, M. Okuda, S. Hara, H. Inoue, and M. Nakano, Sci. Tech. Adv. Mater. 8, 181 (2007).
[CrossRef]

Oshikan, Y.

Y. Oshikan, T. Kataoka, M. Okuda, S. Hara, H. Inoue, and M. Nakano, Sci. Tech. Adv. Mater. 8, 181 (2007).
[CrossRef]

Paesler, M. A.

M. A. Paesler and P. J. Moyer, Near Field Optics (Wiley, 1996).

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Plummer, W. T.

J. M. Guerra and W. T. Plummer, “Optical proximity imaging method and apparatus,” U.S. patent 4,681,451(July21, 1987).

Prawer, S.

I. Aharonovich, S. Castelletto, D. A. Simpson, C-H. Su, A. D. Greentree, and S. Prawer, Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

Rogobete, L.

Rohde, F.

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Rotter, D.

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Sandoghdar, V.

Schuck, C.

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Simpson, D. A.

I. Aharonovich, S. Castelletto, D. A. Simpson, C-H. Su, A. D. Greentree, and S. Prawer, Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

Su, C-H.

I. Aharonovich, S. Castelletto, D. A. Simpson, C-H. Su, A. D. Greentree, and S. Prawer, Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

Sun, C.

N. Fang, H. S. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Trautman, J. K.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251 (5000), 1468 (1991).
[CrossRef]

Vigoureux, J. M.

Weiner, J. S.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251 (5000), 1468 (1991).
[CrossRef]

Weyl, H.

H. Weyl, Ann. Phys. 365, 481 (1919).
[CrossRef]

Wolf, E.

E. Wolf, J. Opt. Soc. Am 60, 18 (1970).
[CrossRef]

Zhang, X.

N. Fang, H. S. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Ann. Phys. (1)

H. Weyl, Ann. Phys. 365, 481 (1919).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am (1)

E. Wolf, J. Opt. Soc. Am 60, 18 (1970).
[CrossRef]

New J. Phys. (1)

S. Gerber, D. Rotter, M. Hennrich, R. Blatt, F. Rohde, C. Schuck, M. Almendros, R. Gehr, F. Dubin, and J. Eschner, New J. Phys. 11, 013032 (2009).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Phys. Today (1)

L. Novotny, Phys. Today 64(7), 47 (2011).
[CrossRef]

Pure Appl. Opt. (1)

G. S. Agarwal, Pure Appl. Opt. 7, 1143 (1998).
[CrossRef]

Rep. Prog. Phys. (1)

I. Aharonovich, S. Castelletto, D. A. Simpson, C-H. Su, A. D. Greentree, and S. Prawer, Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

Sci. Tech. Adv. Mater. (1)

Y. Oshikan, T. Kataoka, M. Okuda, S. Hara, H. Inoue, and M. Nakano, Sci. Tech. Adv. Mater. 8, 181 (2007).
[CrossRef]

Science (2)

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251 (5000), 1468 (1991).
[CrossRef]

N. Fang, H. S. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Other (2)

J. M. Guerra and W. T. Plummer, “Optical proximity imaging method and apparatus,” U.S. patent 4,681,451(July21, 1987).

M. A. Paesler and P. J. Moyer, Near Field Optics (Wiley, 1996).

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Figures (3)

Fig. 1.
Fig. 1.

Coordinates for diffraction of a dipole field by a circular aperture.

Fig. 2.
Fig. 2.

Far-field image of a circular aperture of radius a=2λ. (a) The dipole is located in the far zone, and the intensity pattern is an Airy disk (solid line). To check the validity of Fraunhofer approximations, we also show the result (dashed line) of the Kirchoff integral given in Eq. (2). (b)–(d) show intensities with decreasing dipole-aperture distance, ϵ. rz is 100λ in all figures.

Fig. 3.
Fig. 3.

Computed far-field images of two separated circular apertures. rz is 500λ in all figures. The insets in (d), (e), and (f) show the intensities in two dimensions.

Equations (7)

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

(2+k2)U(r⃗)=0.
U(r⃗,R⃗)=14πSdS{Un[eik|r⃗ρ⃗||r⃗ρ⃗|]Un[eik|r⃗ρ⃗||r⃗ρ⃗|]},
U(r⃗,R⃗)=iAkaeik(rz+Rz)eik2r2rzRzrzJ1(2πξa)2πξ,
U(r⃗,R⃗)=ΦrzλSdρxdρyeikrz(ρxrx+ρyry)eik|R⃗ρ⃗||R⃗ρ⃗|Rz|R⃗ρ⃗|(11ik|R⃗ρ⃗|),
eik|R⃗ρ⃗||R⃗ρ⃗|=i2π+dkxdkykzei[kx(Rxρx)+ky(Ryρy)+kzRz],
kz={k2k2fork2k2,ik2k2fork2>k2,
k⃗=kr⃗rz+k⃗.

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