Abstract

We propose a near-field imaging concept for obtaining a complete experimental description of the structure of light in three dimensions around nanodevices. Our approach is based on a near-field microscope able to simultaneously and independently map the phase and amplitude distributions of two orthogonal electric-field components at the sample surface. From a single 2D acquisition of these two components, the complementary electric and magnetic field lines and Poynting vector distributions are reconstructed in a volume above the sample using rigorous numerical methods. This experimental analysis of localized electric and magnetic optical effects as well as energy flows at the subwavelength scale enables the development of a complete electromagnetic diagnostic of nano-optical devices and metamaterials.

© 2010 Optical Society of America

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  56. T. Grosjean, A. Sabac, and D. Courjon, "A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations," Opt. Commun. 252, 12-21 (2005).
    [CrossRef]
  57. V. Niziev and A. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D: Appl. Phys. 32, 1455-1561 (1999).
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  58. T. Grosjean, D. Courjon, and D. V. Labeke, "Bessel beams as virtual tips for near-field optics," J. Microsc. 210, 319-323 (2003).
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    [CrossRef] [PubMed]

2009 (2)

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, "Probing the Magnetic Field of Light at Optical Frequencies," Science 326, 550-553 (2009).
[CrossRef] [PubMed]

W. Chen and Q. Zhan, "Realization of an evanescent Bessel beam via surface plasmon interference excited by a radially polarized beam," Opt. Lett. 34(6), 722-724 (2009).
[CrossRef] [PubMed]

2008 (2)

T. Grosjean, A. Fahys, M. Suarez, D. Charraut, R. Salut, and D. Courjon, "Annular nanoantenna on fibre microaxicon," J. Microscopy 229, 354-364 (2008).
[CrossRef]

N. Fabre, L. Lalouat, B. Cluzel, X. Melique, D. Lippens, F. de Fornel, and O. Vanbesien, "Optical Near-Field Microscopy of Light Focusing through a Photonic Crystal Flat Lens," Phys. Rev. Lett. 101(7), 073901 (2008).
[CrossRef] [PubMed]

2007 (6)

J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic and electric excitations in split ring resonators," Opt. Express 15(26), 17,881-17,890 (2007).
[CrossRef]

M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, "Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors," Opt. Express 15(19), 11,781-11,789 (2007).
[CrossRef]

K. Lee, H. Kihm, J. Kihm, W. Choi, H. Kim, C. Ropers, D. Park, Y. Yoon, S. Choi, D. Woo, J. Kim, B. Lee, Q. Parka, C. Lienau, and D. Kim, "Vector field microscopic imaging of light," Nat. Photonics 1, 53-56 (2007).
[CrossRef]

T. Grosjean, F. Baida, and D. Courjon, "Conical optics: the solution to confine light," Appl. Opt. 46(11), 1994-2000 (2007).
[CrossRef] [PubMed]

Y. Poujet, J. Salvi, and F. Baida, "90% Extraordinary optical transmission in the visible range through annular aperture metallic arrays," Opt. Lett. 32(20), 2942-2944 (2007).
[CrossRef] [PubMed]

T. Grosjean, S. S. Saleh, M. A. Suarez, I. A. Ibrahim, V. Piquerey, D. Charraut, and P. Sandoz, "Fiber microaxicons fabricated by a polishing technique for the generation of Bessel-like beams," Appl. Opt. 46(33), 8061-8067 (2007).
[CrossRef] [PubMed]

2006 (2)

N. Gregersen, B. Tromborg, V. S. Volkov, S. I. Bozhevolnyi, and J. Holm, "Topography characterization of a deep grating using near-field imaging," Appl. Opt. 45(1), 117-121 (2006).
[CrossRef] [PubMed]

S. Bozhevolnyi, V. Volkov, E. Devaux, J. Laluet, and T. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

2005 (8)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87(22), 221101 (2005).
[CrossRef]

L. Yin, V. Vlasko-Vlasov, J. Pearson, J. Hiller, J. Hua, U. Welp, D. Brown, and C. Kimball, "Subwavelength Focusing and Guiding of Surface Plasmons," Nano Lett. 5(7), 1399-1402 (2005).
[CrossRef] [PubMed]

J. Farahani, D. Pohl, H.-J. Eisler, and B. Hecht, "Single quantum dot coupled to a scanning optical antenna : A tunable superemitter," Phys. Rev. Lett. 95(1), 017402 (2005).
[CrossRef] [PubMed]

P. Schuck, D. Fromm, A. Sundaramurthy, G. Kino, andW. Moerner, "Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas," Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

T. Kalkbrenner, U. Hakanson, A. Schädle, S. Burger, C. Henkel, and V. Sandoghdar, "Optical microscopy via spectral modifications of a nano-antenna," Phys. Rev. Lett. 95(20), 200801 (2005).
[CrossRef] [PubMed]

N. Louvion, D. Gerard, J. Mouette, F. de Fornel, C. Seassal, X. Letartre, A. Rahmani, and S. Callard, "Local observation and spectroscopy of optical modes in an active photonic-crystal microcavity," Phys. Rev. Lett. 94, 113907 (2005).
[CrossRef] [PubMed]

T. Grosjean, A. Sabac, and D. Courjon, "A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations," Opt. Commun. 252, 12-21 (2005).
[CrossRef]

2004 (1)

E. Descrovi, L. Vaccaro,W. Nakagawa, L. Aeschimann, U. Staufer, and H. Herzig, "Collection of transverse and longitudinal fields by means of apertureless nanoprobes with different metal coating characteristics," Appl. Phys. Lett. 85(22), 5340-5342 (2004).
[CrossRef]

2003 (4)

A. Bouhelier, J. Renger, M. Beversluis, and L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy," J. Microscopy 210, 220-224 (2003).
[CrossRef]

T. Grosjean and D. Courjon, "Polarization filtering induced by imaging systems: Effect on image structure," Phys. Rev. E 67, 46611 (2003).
[CrossRef]

S. McNab, N. Moll, and Y. Vlasov, "Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides," Opt. Express 11(22), 2927-2939 (2003).
[CrossRef] [PubMed]

T. Grosjean, D. Courjon, and D. V. Labeke, "Bessel beams as virtual tips for near-field optics," J. Microsc. 210, 319-323 (2003).
[CrossRef] [PubMed]

2002 (1)

"Measuring amplitude and phase distribution of fields generated by gratings with sub-wavelength resolution," Opt. Commun. 205(4-6), 229-238 (2002).

2001 (2)

U. Schröter and A. Dereux., "Surface plasmon polaritons on metal cylinders with dielectric core." Phys. Rev. B. 64, 125420 (2001).
[CrossRef]

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86(23), 5251 (2001).
[CrossRef] [PubMed]

2000 (4)

E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, and C. Girard, "Local detection of the optical magnetic field in the near zone of dielectric samples," Phys. Rev. B 62(15), 10,504-10,514 (2000).
[CrossRef]

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 107, 608-610 (2000).
[CrossRef]

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85(18), 3966-3969 (2000).
[CrossRef] [PubMed]

M. Balistreri, J. Korterik, L. Kuipers, and N. van Hulst, "Local Observations of Phase Singularities in Optical Fields in Waveguide Structures," Phys. Rev. Lett. 85(2), 294-297 (2000).
[CrossRef] [PubMed]

1999 (4)

C. Adelmann, J. Hetzler, G. Scheiber, T. Schimmel, M. Wegener, H. B. Weber, and H. v. Lohneysen, "Experiments on the depolarization near-field scanning optical microscope," Appl. Phys. Lett. 74(2), 179-181 (1999).
[CrossRef]

V. Niziev and A. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D: Appl. Phys. 32, 1455-1561 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74(10), 1370-1372 (1999).
[CrossRef]

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. Aussenegg, and C. Girard, "Squeezing the Optical Near-Field Zone by Plasmon Coupling of Metallic Nanoparticles," Phys. Rev. Lett. 82(12), 2590-2593 (1999).
[CrossRef]

1998 (3)

T. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

T. Lacoste, T. Huser, R. Prioli, and H. Heinzelmann, "Contrast enhancement using polarization-modulation scanning near-field optical microscopy (PM-SNOM)," Ultramicroscopy 71, 333-340 (1998).
[CrossRef]

S. Ruschin and A. Leizer, "Evanescent Bessel beams," J. Opt. Soc. Am. A 15(5), 1139-1143 (1998).
[CrossRef]

1997 (1)

J.-J. Greffet and R. Carminati, "Image formation in near-field optics," Prog. Surf. Sci. 56(3), 133-237 (1997).
[CrossRef]

1996 (1)

J. Weeber, F. de Fornel, and J. Goudonnet, "Numerical study of the tip-sample interaction in the photon scanning tunneling microscope," Opt. Commun. 126, 285-292 (1996).
[CrossRef]

1995 (2)

1994 (1)

1993 (1)

1992 (1)

1991 (2)

R. Herman and T. Wiggins, "Production and Uses of Diffractionless Beams," J. Opt. Soc. Am. A 8(6), 932-942 (1991).
[CrossRef]

A. Dereux, J.-P. Vigneron, P. Lambin, and A. Lucas, "Theory of near-field optics with applications to SNOM and optical binding," Physica B 175, 65-67 (1991).
[CrossRef]

1987 (2)

E. Betzig, M. Isaacson, and A. Lewis, "Collection mode near-field scanning optical microscopy," Appl. Phys. Lett. 51(25), 2088-2090 (1987).
[CrossRef]

J. Durnin, "Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A 4(4), 651-654 (1987).
[CrossRef]

1954 (1)

C. Bouwkamp, "Diffraction theory," Rep. Phys. 27, 35-100 (1954).
[CrossRef]

1944 (1)

H. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
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M. Balistreri, J. Korterik, L. Kuipers, and N. van Hulst, "Local Observations of Phase Singularities in Optical Fields in Waveguide Structures," Phys. Rev. Lett. 85(2), 294-297 (2000).
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C. Adelmann, J. Hetzler, G. Scheiber, T. Schimmel, M. Wegener, H. B. Weber, and H. v. Lohneysen, "Experiments on the depolarization near-field scanning optical microscope," Appl. Phys. Lett. 74(2), 179-181 (1999).
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L. Yin, V. Vlasko-Vlasov, J. Pearson, J. Hiller, J. Hua, U. Welp, D. Brown, and C. Kimball, "Subwavelength Focusing and Guiding of Surface Plasmons," Nano Lett. 5(7), 1399-1402 (2005).
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O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, "Two-Dimensional Photonic Band-Gap Defect Mode Laser," Science 284(5421), 1819-1821.
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L. Yin, V. Vlasko-Vlasov, J. Pearson, J. Hiller, J. Hua, U. Welp, D. Brown, and C. Kimball, "Subwavelength Focusing and Guiding of Surface Plasmons," Nano Lett. 5(7), 1399-1402 (2005).
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J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87(22), 221101 (2005).
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C. Adelmann, J. Hetzler, G. Scheiber, T. Schimmel, M. Wegener, H. B. Weber, and H. v. Lohneysen, "Experiments on the depolarization near-field scanning optical microscope," Appl. Phys. Lett. 74(2), 179-181 (1999).
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L. Yin, V. Vlasko-Vlasov, J. Pearson, J. Hiller, J. Hua, U. Welp, D. Brown, and C. Kimball, "Subwavelength Focusing and Guiding of Surface Plasmons," Nano Lett. 5(7), 1399-1402 (2005).
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Nat. Photonics (1)

K. Lee, H. Kihm, J. Kihm, W. Choi, H. Kim, C. Ropers, D. Park, Y. Yoon, S. Choi, D. Woo, J. Kim, B. Lee, Q. Parka, C. Lienau, and D. Kim, "Vector field microscopic imaging of light," Nat. Photonics 1, 53-56 (2007).
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N. Fabre, L. Lalouat, B. Cluzel, X. Melique, D. Lippens, F. de Fornel, and O. Vanbesien, "Optical Near-Field Microscopy of Light Focusing through a Photonic Crystal Flat Lens," Phys. Rev. Lett. 101(7), 073901 (2008).
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N. Louvion, D. Gerard, J. Mouette, F. de Fornel, C. Seassal, X. Letartre, A. Rahmani, and S. Callard, "Local observation and spectroscopy of optical modes in an active photonic-crystal microcavity," Phys. Rev. Lett. 94, 113907 (2005).
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[CrossRef] [PubMed]

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. Aussenegg, and C. Girard, "Squeezing the Optical Near-Field Zone by Plasmon Coupling of Metallic Nanoparticles," Phys. Rev. Lett. 82(12), 2590-2593 (1999).
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Physica B (1)

A. Dereux, J.-P. Vigneron, P. Lambin, and A. Lucas, "Theory of near-field optics with applications to SNOM and optical binding," Physica B 175, 65-67 (1991).
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O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, "Two-Dimensional Photonic Band-Gap Defect Mode Laser," Science 284(5421), 1819-1821.
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T. Grosjean, M. Mivelle, and G. Burr, "Polarization-dependent extraction properties of bare fiber probes," Accepted.

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L. Novotny and B. Hecht, Principle of nano-optics (Cambridge University Press, 2006).

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Supplementary Material (3)

» Media 1: MOV (6004 KB)     
» Media 2: MOV (4316 KB)     
» Media 3: MOV (3925 KB)     

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Figures (11)

Fig. 1.
Fig. 1.

(a) SNOM architecture for the simultaneous collection of Ex and Ey (amplitude and phase) at the sample surface. (b): polarization diagram of a pulled dielectric fiber tip.

Fig. 2.
Fig. 2.

(a): Scheme of the experimental set-up for the generation and full vectorial characterization of an azimuthally-polarized propagative Bessel beam. (b,c): Image of the orthogonal transverse electric field components Ex = Ax cosϕx and Ey = Ay cosϕy, respectively. Ax, Ay are the amplitude and ϕx, ϕy the phase distributions of the two field components, respectively (scale bar: 2 μm).

Fig. 3.
Fig. 3.

Intensity distributions, reconstructed from empirical data measured across the plane z=0 by our phase- and polarization-sensitive SNOM probe, of (a,b) the electric field and (c,d) the magnetic field of an azimuthally-polarized propagative Bessel beam, in (a,c) the longitudinal plane (y=0) and (b,d) the transverse plane (z=0). The fields are expressed in Gaussian units.

Fig. 4.
Fig. 4.

(Media 1) Full vectorial description of the reconstructed electromagnetic optical field for our empirical azimuthally-polarized propagative Bessel beam. (a): longitudinal cross-section (y=0): out-of-plane transverse electric field component Ex (background colored image) and in-plane magnetic field lines (black arrows). (b): electric field in the transverse plane (z=0): in-plane transverse electric-field lines (black arrows) and out-of-plane longitudinal electric field component Ez (background colored image). (c): magnetic field in the transverse plane (z=0): in-plane transverse magnetic-field lines (black arrows) and out-of-plane longitudinal magnetic field component Hz (background colored image).

Fig. 5.
Fig. 5.

Spatial distribution of the time-averaged Poynting vector in the longitudinal plane (x=0). (a): reconstructed from experimental SNOM data and (b) ideal Bessel beam

Fig. 6.
Fig. 6.

Interplay between the optical displacement current density (ODCD) and magnetic field over half a beam wavefront. (a):transverse plane: out-of-plane longitudinal magnetic-field component Hz (background colored image) and in-plane ODCD lines (black arrows). (b): longitudinal plane (x=0): out-of-plane x-component of the ODCD (background colored image) and in-plane magnetic-field lines (black arrows).

Fig. 7.
Fig. 7.

(a): Scheme of the experimental set-up for the generation and full vectorial characterization of a radially-polarized evanescent Bessel beam. (b,c): Image of the orthogonal transverse electric field components Ex = Ax cos ϕx and Ey = Ay cosϕy, respectively. Ax, Ay are the amplitude and ϕx, ϕy the phase distributions of the two field components, respectively (scale bar: 0.9 μm).

Fig. 8.
Fig. 8.

Intensity distributions, reconstructed from empirical data measured across the plane z=0 by our phase- and polarization-sensitive SNOM probe, of (a,b) the electric field and (c,d) the magnetic field of a radially-polarized evanescent Bessel beam, in (a,c) the longitudinal plane (y=0) and (b,d) the transverse plane (z=0). The fields are expressed in gaussian units. The π-line shown in (b) and (d) refers to the direction along which the visibility of the Bessel beam fringes vanish.

Fig. 9.
Fig. 9.

Plane wave spectrum of the transverse field amplitude E x ( x , y ) 2 + E y ( x , y ) 2 in (a) and (b) the ideal and experimental cases, respectively. (c): (a) modulated by a cosine function of the azimuthal angle: simulation of an unbalanced Bessel beam that approximate the experimental one.

Fig. 10.
Fig. 10.

(Media 2 and Media 3) (a,b,c): 3D electromagnetic distribution of the experimental radially-polarized evanescent Bessel beam. (d,e,f): 3D field distribution of the unbalanced theoretical Bessel beam. (a,d): longitudinal plane (y=0): out-of-plane transverse magnetic field component Hy (background colored image) and in-plane electric-field lines (black arrows). (b,e): transverse electric-field lines. (c,f): transverse magnetic-field lines.

Fig. 11.
Fig. 11.

Time-averaged Poynting vector of the evanescent field distribution in (a) the transverse plane (z=0) and (b) the longitudinal plane (y=0).

Equations (2)

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

E ( x , y , z , t ) = 1 4 π 2 exp [ iωt ] e ( u , v ) exp [ i ( ux + vy + wz ) ] dudv ,
e ( u , v ) = E ( x , y , z = 0 ) exp [ i ( ux + vy ) ] dxdy ,

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