Abstract

The knife-edge method is an established technique for profiling light beams. It was shown, that this technique even works for tightly focused beams, if the material and geometry of the probing knife-edges are chosen carefully. Furthermore, it was also reported recently that this method fails, when the knife-edges are made from pure materials. The artifacts introduced in the reconstructed beam shape and position depend strongly on the edge and input beam parameters, because the knife-edge is excited by the incoming beam. Here we show, that the actual beam shape and spot size of tightly focused beams can still be derived from knife-edge measurements for pure edge materials and different edge thicknesses by adapting the analysis method of the experimental data taking into account the interaction of the beam with the edge.

© 2013 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc.229, 337–343 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express18, 10905–10923 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2011

2010

2009

2008

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc.229, 337–343 (2008).
[CrossRef] [PubMed]

2007

B. Sturman, E. Podivilov, and M. Gorkunov, “Eigenmodes for metal-dielectric light-transmitting nanostructures”, Phys. Rev. B76, 125104 (2007).
[CrossRef]

J. Kindler, P. Banzer, S. Quabis, U. Peschel, and G. Leuchs, “Waveguide properties of single subwavelength holes demonstrated with radially and azimuthally polarized light,” Appl. Phys. B89, 517–520 (2007).
[CrossRef]

2003

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt.50, 1917–1926 (2003).

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

2000

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

1985

1984

1983

1981

1977

A. H. Firester, M. E. Heller, and P. Sheng, “Knife-edge scanning measurements of subwavelength focussed light beams,” Appl. Opt.16, 197-1–1974 (1977).
[CrossRef]

1959

B. Richards and E. Wolf, “Electromagnetic diffraction in optical Systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A253, 358–379 (1959).
[CrossRef]

Abtahi, A.

Banzer, P.

Brost, G.

de Araujo, M. A.

de Lima, E.

de Oliveira, P. C.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt.50, 1917–1926 (2003).

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. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun.179, 1–7 (2000).
[CrossRef]

Eberler, M.

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

Failla, A. V.

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc.229, 337–343 (2008).
[CrossRef] [PubMed]

Fan, S.

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal wavequides”, Phys. Rev. B79, 035120 (2009).
[CrossRef]

Firester, A. H.

A. H. Firester, M. E. Heller, and P. Sheng, “Knife-edge scanning measurements of subwavelength focussed light beams,” Appl. Opt.16, 197-1–1974 (1977).
[CrossRef]

Garetz, B. A.

Glöckl, O.

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

Gorkunov, M.

B. Sturman, E. Podivilov, and M. Gorkunov, “Eigenmodes for metal-dielectric light-transmitting nanostructures”, Phys. Rev. B76, 125104 (2007).
[CrossRef]

Hartschuh, A.

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc.229, 337–343 (2008).
[CrossRef] [PubMed]

Heller, M. E.

A. H. Firester, M. E. Heller, and P. Sheng, “Knife-edge scanning measurements of subwavelength focussed light beams,” Appl. Opt.16, 197-1–1974 (1977).
[CrossRef]

Horn, P. D.

Huber, C.

Khosrofian, J. M.

Kindler, J.

P. Banzer, J. Kindler, S. Quabis, U. Peschel, and G. Leuchs, “Extraordinary transmission through a single coaxial aperture in a thin metal film,” Opt. Express18, 10896–10904 (2010).
[CrossRef] [PubMed]

J. Kindler, P. Banzer, S. Quabis, U. Peschel, and G. Leuchs, “Waveguide properties of single subwavelength holes demonstrated with radially and azimuthally polarized light,” Appl. Phys. B89, 517–520 (2007).
[CrossRef]

Kocabas, S. E.

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal wavequides”, Phys. Rev. B79, 035120 (2009).
[CrossRef]

Leuchs, G.

P. Marchenko, S. Orlov, C. Huber, P. Banzer, S. Quabis, U. Peschel, and G. Leuchs, “Interaction of highly focused vector beams with a metal knife-edge,” Opt. Express197244–7261 (2011).
[CrossRef] [PubMed]

P. Banzer, J. Kindler, S. Quabis, U. Peschel, and G. Leuchs, “Extraordinary transmission through a single coaxial aperture in a thin metal film,” Opt. Express18, 10896–10904 (2010).
[CrossRef] [PubMed]

P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express18, 10905–10923 (2010).
[CrossRef] [PubMed]

J. Kindler, P. Banzer, S. Quabis, U. Peschel, and G. Leuchs, “Waveguide properties of single subwavelength holes demonstrated with radially and azimuthally polarized light,” Appl. Phys. B89, 517–520 (2007).
[CrossRef]

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

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt.50, 1917–1926 (2003).

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

Marchenko, P.

McCally, R. L.

Meixner, A. J.

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc.229, 337–343 (2008).
[CrossRef] [PubMed]

Miller, D. A. B.

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal wavequides”, Phys. Rev. B79, 035120 (2009).
[CrossRef]

Orlov, S.

Pereira, D. P.

Peschel, U.

Podivilov, E.

B. Sturman, E. Podivilov, and M. Gorkunov, “Eigenmodes for metal-dielectric light-transmitting nanostructures”, Phys. Rev. B76, 125104 (2007).
[CrossRef]

Quabis, S.

P. Marchenko, S. Orlov, C. Huber, P. Banzer, S. Quabis, U. Peschel, and G. Leuchs, “Interaction of highly focused vector beams with a metal knife-edge,” Opt. Express197244–7261 (2011).
[CrossRef] [PubMed]

P. Banzer, J. Kindler, S. Quabis, U. Peschel, and G. Leuchs, “Extraordinary transmission through a single coaxial aperture in a thin metal film,” Opt. Express18, 10896–10904 (2010).
[CrossRef] [PubMed]

P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express18, 10905–10923 (2010).
[CrossRef] [PubMed]

J. Kindler, P. Banzer, S. Quabis, U. Peschel, and G. Leuchs, “Waveguide properties of single subwavelength holes demonstrated with radially and azimuthally polarized light,” Appl. Phys. B89, 517–520 (2007).
[CrossRef]

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

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt.50, 1917–1926 (2003).

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun.179, 1–7 (2000).
[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. A253, 358–379 (1959).
[CrossRef]

Schneider, M. B.

Sheng, P.

A. H. Firester, M. E. Heller, and P. Sheng, “Knife-edge scanning measurements of subwavelength focussed light beams,” Appl. Opt.16, 197-1–1974 (1977).
[CrossRef]

Silva, R.

Sturman, B.

B. Sturman, E. Podivilov, and M. Gorkunov, “Eigenmodes for metal-dielectric light-transmitting nanostructures”, Phys. Rev. B76, 125104 (2007).
[CrossRef]

Veronis, G.

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal wavequides”, Phys. Rev. B79, 035120 (2009).
[CrossRef]

Webb, W. W.

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. A253, 358–379 (1959).
[CrossRef]

Züchner, T.

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc.229, 337–343 (2008).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. B

J. Kindler, P. Banzer, S. Quabis, U. Peschel, and G. Leuchs, “Waveguide properties of single subwavelength holes demonstrated with radially and azimuthally polarized light,” Appl. Phys. B89, 517–520 (2007).
[CrossRef]

J. Microsc.

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc.229, 337–343 (2008).
[CrossRef] [PubMed]

J. Mod. Opt.

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light-linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt.50, 1917–1926 (2003).

Opt. Commun.

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

Opt. Express

Phys. Rev. B

B. Sturman, E. Podivilov, and M. Gorkunov, “Eigenmodes for metal-dielectric light-transmitting nanostructures”, Phys. Rev. B76, 125104 (2007).
[CrossRef]

Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal wavequides”, Phys. Rev. B79, 035120 (2009).
[CrossRef]

Phys. Rev. Lett.

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. A

B. Richards and E. Wolf, “Electromagnetic diffraction in optical Systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A253, 358–379 (1959).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic depiction of the knife-edge method for a two-dimensional beam (a). Typical beam profiling data (photocurrent curves) (b) and their derivatives (beam-projections) (c). The state of polarization always refers to the orientation of the electric field of the input beam relative to the knife-edge in the xy-plane.

Fig. 2
Fig. 2

Dependence of the conventionally determined beamwidths wp, ws on the wavelength λ for various edge material of thickness h = 130 nm. The dashed lines represent the FWHM of the squared modulus of the electric field calculated with vectorial diffraction theory.

Fig. 3
Fig. 3

Depiction of the adapted knife-edge method for a tightly focused and linearly polarized beam. The derivatives of the experimentally measured photocurrents (gray circles) and the fitted curve (black) with the beam profile (red) and its first four derivatives (moments) are shown for λ = 700 nm and a knife-edge made from gold with a thickness of h = 130 nm. The corresponding states of polarization are shown in the graphs. The position of the knife-edge is schematically depicted by the gray bar.

Fig. 4
Fig. 4

Dependence of the beamwidths wp, ws on the wavelength λ reconstructed with the adapted method for Au, Ti and Ge samples of thickness h = 130 nm. The dashed lines represent the FWHM of the squared electric field estimated from the Debye integrals [3].

Equations (5)

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P = P 0 d y 0 I ( x x 0 , y , z = 0 ) d x ,
P = P 0 0 d x d k x U ^ E ( k x , x 0 ) T ^ ( k x ) e i k x x
T ^ ( k x ) = 1 + n = 1 k x n n ! n T ^ ( k x ) k x n | k x = 0 .
P = P 0 0 d x [ U E ( x ± x 0 ) + n = 1 A n n U E ( x ± x 0 ) x n ] ,
P P 0 x 0 = U E , 0 ( ± x 0 ) + n = 1 A n n U E , 0 ( ± x 0 ) x 0 n .

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