Abstract

Aperture based scanning near field optical microscopes are important instruments to study light at the nanoscale and to understand the optical functionality of photonic nanostructures. In general, a detected image is affected by both the transverse electric and magnetic field components of light. The discrimination of the individual field components is challenging as these four field components are contained within two signals in the case of a polarization resolved measurement. Here, we develop a methodology to solve the inverse imaging problem and to retrieve the vectorial field components from polarization and phase resolved measurements. Our methodology relies on the discussion of the image formation process in aperture based scanning near field optical microscopes. On this basis, we are also able to explain how the relative contributions of the electric and magnetic field components within detected images depend on the chosen probe. We can therefore also describe the influence of geometrical and material parameters of individual probes within the image formation process. This allows probes to be designed that are primarily sensitive either to the electric or magnetic field components of light.

© 2016 Optical Society of America

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2015 (4)

R. M. Bakker, D. Permyakov, Y. F. Yu, D. Markovich, R. Paniagua-Domínguez, L. Gonzaga, A. Samusev, Y. Kivshar, B. Luk’yanchuk, and A. I. Kuznetsov, “Magnetic and electric hotspots with silicon nanodimers,” Nano Lett. 15, 2137–2142 (2015).
[Crossref] [PubMed]

I. S. Sinev, P. M. Voroshilov, I. S. Mukhin, A. I. Denisyuk, M. E. Guzhva, A. K. Samusev, P. A. Belov, and C. R. Simovski, “Demonstration of unusual nanoantenna array modes through direct reconstruction of the near-field signal,” Nanoscale 7, 765–770 (2015).
[Crossref]

N. Caselli, F. La China, W. Bao, F. Riboli, A. Gerardino, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, P. J. Schuck, S. Cabrini, A. Weber-Bargioni, M. Gurioli, and F. Intonti, “Deep-subwavelength imaging of both electric and magnetic localized optical fields by plasmonic campanile nanoantenna,” Sci. Rep. 5, 9606 (2015).
[Crossref] [PubMed]

D. K. Singh, J. S. Ahn, S. Koo, T. Kang, J. Kim, S. Lee, N. Park, and D.-S. Kim, “Selective electric and magnetic sensitivity of aperture probes,” Opt. Express 23, 20820–20828 (2015).
[Crossref] [PubMed]

2014 (3)

B. le Feber, N. Rotenberg, D. van Oosten, and L. Kuipers, “Modal symmetries at the nanoscale: a route toward a complete vectorial near-field mapping,” Opt. Lett. 39, 2802–2805 (2014).
[Crossref] [PubMed]

N. Rotenberg and L. Kuipers, “Mapping nanoscale light fields,” Nature Photon. 8, 919–926 (2014).
[Crossref]

A. E. Klein, N. Janunts, M. Steinert, A. Tünnermann, and T. Pertsch, “Polarization-resolved near-field mapping of plasmonic aperture emission by a dual-snom system,” Nano Lett. 14, 5010–5015 (2014). PMID: .
[Crossref] [PubMed]

2013 (3)

B. le Feber, N. Rotenberg, D. M. Beggs, and L. Kuipers, “Simultaneous measurement of nanoscale electric and magnetic optical fields,” Nature Photon. 8, 43–46 (2013).
[Crossref]

D. Denkova, N. Verellen, A. V. Silhanek, V. K. Valev, P. V. Dorpe, and V. V. Moshchalkov, “Mapping magnetic near-field distributions of plasmonic nanoantennas,” ACS Nano 7, 3168–3176 (2013).
[Crossref] [PubMed]

H. W. Kihm, J. Kim, S. Koo, J. Ahn, K. Ahn, K. Lee, and N. Park, “Optical magnetic field mapping using a subwavelength aperture,” Opt. Express 21, 5625–5633 (2013).
[Crossref] [PubMed]

2012 (5)

A. E. Klein, A. Minovich, M. Steinert, N. Janunts, A. Tünnermann, and T. Pertsch, “Controlling plasmonic hot spots by interfering airy beams,” Opt. Lett. 37, 3402–3404 (2012).
[Crossref]

D. C. Kohlgraf-Owens, S. Sukhov, and A. Dogariu, “Discrimination of field components in optical probe microscopy,” Opt. Lett. 37, 3606–3608 (2012).
[Crossref] [PubMed]

P. Uebel, M. A. Schmidt, H. W. Lee, and P. S. Russell, “Polarisation-resolved near-field mapping of a coupled gold nanowire array,” Opt. Express 20, 28409–28417 (2012).
[Crossref] [PubMed]

M. Esslinger, J. Dorfmüller, W. Khunsin, R. Vogelgesang, and K. Kern, “Background-free imaging of plasmonic structures with cross-polarized apertureless scanning near-field optical microscopy,” Rev. Sci. Instrum. 83, 033704 (2012).
[Crossref] [PubMed]

M. Esslinger and R. Vogelgesang, “Reciprocity theory of apertureless scanning near-field optical microscopy with point-dipole probes,” ACS Nano 6, 8173–8182 (2012).
[Crossref] [PubMed]

2011 (3)

W. Smigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98, 111107 (2011).
[Crossref]

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. Halas, N. Park, and D.-S. Kim, “Bethe-hole polarization analyser for the magnetic vector of light,” Nat. Commun. 2, 451 (2011).
[Crossref] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, and T. Pertsch, “Generation and near-field imaging of airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[Crossref] [PubMed]

2010 (4)

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
[Crossref] [PubMed]

M. Schnell, A. Garcia-Etxarri, A. J. Huber, K. B. Crozier, A. Borisov, J. Aizpurua, and R. Hillenbrand, “Amplitude- and phase-resolved near-field mapping of infrared antenna modes by transmission-mode scattering-type near-field microscopy,” J. Phys. Chem. C 114, 7341–7345 (2010).
[Crossref]

M. Burresi, D. Diessel, D. van Oosten, S. Linden, M. Wegener, and L. Kuipers, “Negative-index metamaterials: Looking into the unit cell,” Nano Lett. 10, 2480–2483 (2010).
[Crossref] [PubMed]

T. Grosjean, I. Ibrahim, M. Suarez, G. Burr, M. Mivelle, and D. Charraut, “Full vectorial imaging of electromagnetic light at subwavelength scale,” Opt. express 18, 5809–5824 (2010).
[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]

M. Burresi, A. Engelen, R. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 2480–2483 (2009).
[Crossref]

2008 (2)

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8, 3155–3159 (2008).
[Crossref] [PubMed]

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (1)

S. Diziain, D. Barchiesi, T. Grosges, and P.-M. Adam, “Recovering of the apertureless scanning near-field optical microscopy signal through a lock-in detection,” Appl. Phys. B 84, 233–238 (2006).
[Crossref]

2003 (1)

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

2002 (2)

2001 (3)

A. Nesci, R. Dändliker, and H. P. Herzig, “Quantitative amplitude and phase measurement by use of a heterodyne scanning near-field optical microscope,” Opt. Lett. 26, 208–210 (2001).
[Crossref]

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

A. Dereux, E. Devaux, J. C. Weeber, J. P. Goudonnet, and C. Girard, “Direct interpretation of near-field optical images,” J. Microsc. 202, 320–331 (2001).
[Crossref] [PubMed]

2000 (3)

J. A. Porto, R. Carminati, and J.-J. Greffet, “Theory of electromagnetic field imaging and spectroscopy in scanning near-field optical microscopy,” J. Appl. Phys. 88, 4845 (2000).
[Crossref]

E. Devaux, A. Dereux, E. Bourillot, Y. Weeber, J. C. Lacroute, J. Goudonnet, and C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504 (2000).
[Crossref]

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys 112, 7761 (2000).
[Crossref]

1998 (1)

1997 (1)

J. J. Greffet and R. Carminati, “Image formation in near-field optics,” Progr. Surf. Sci. 56, 133–237 (1997).
[Crossref]

1994 (1)

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50, 4094–4106 (1994).
[Crossref]

1993 (1)

1992 (1)

S. Roose, B. Brichau, and E. Stijns, “An efficient interpolation algorithm for Fourier and diffractive optics,” Opt. Commun. 97, 312–318 (1992).
[Crossref]

1969 (1)

L. Rabiner, R. Schafer, and C. Rader, “The chirp z-transform algorithm,” IEEE Trans Sig. Process. 17, 86–92 (1969).

Adam, P.-M.

S. Diziain, D. Barchiesi, T. Grosges, and P.-M. Adam, “Recovering of the apertureless scanning near-field optical microscopy signal through a lock-in detection,” Appl. Phys. B 84, 233–238 (2006).
[Crossref]

Ahn, J.

Ahn, J. S.

Ahn, K.

Aizpurua, J.

M. Schnell, A. Garcia-Etxarri, A. J. Huber, K. B. Crozier, A. Borisov, J. Aizpurua, and R. Hillenbrand, “Amplitude- and phase-resolved near-field mapping of infrared antenna modes by transmission-mode scattering-type near-field microscopy,” J. Phys. Chem. C 114, 7341–7345 (2010).
[Crossref]

Baba, T.

M. Burresi, A. Engelen, R. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 2480–2483 (2009).
[Crossref]

Bak, W. S.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. Halas, N. Park, and D.-S. Kim, “Bethe-hole polarization analyser for the magnetic vector of light,” Nat. Commun. 2, 451 (2011).
[Crossref] [PubMed]

Bakker, R. M.

R. M. Bakker, D. Permyakov, Y. F. Yu, D. Markovich, R. Paniagua-Domínguez, L. Gonzaga, A. Samusev, Y. Kivshar, B. Luk’yanchuk, and A. I. Kuznetsov, “Magnetic and electric hotspots with silicon nanodimers,” Nano Lett. 15, 2137–2142 (2015).
[Crossref] [PubMed]

Bakx, J.

Bao, K.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. Halas, N. Park, and D.-S. Kim, “Bethe-hole polarization analyser for the magnetic vector of light,” Nat. Commun. 2, 451 (2011).
[Crossref] [PubMed]

Bao, W.

N. Caselli, F. La China, W. Bao, F. Riboli, A. Gerardino, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, P. J. Schuck, S. Cabrini, A. Weber-Bargioni, M. Gurioli, and F. Intonti, “Deep-subwavelength imaging of both electric and magnetic localized optical fields by plasmonic campanile nanoantenna,” Sci. Rep. 5, 9606 (2015).
[Crossref] [PubMed]

Barchiesi, D.

S. Diziain, D. Barchiesi, T. Grosges, and P.-M. Adam, “Recovering of the apertureless scanning near-field optical microscopy signal through a lock-in detection,” Appl. Phys. B 84, 233–238 (2006).
[Crossref]

D. Van Labeke and D. Barchiesi, “Probes for scanning tunneling optical microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993).
[Crossref]

Beggs, D. M.

B. le Feber, N. Rotenberg, D. M. Beggs, and L. Kuipers, “Simultaneous measurement of nanoscale electric and magnetic optical fields,” Nature Photon. 8, 43–46 (2013).
[Crossref]

Belov, P. A.

I. S. Sinev, P. M. Voroshilov, I. S. Mukhin, A. I. Denisyuk, M. E. Guzhva, A. K. Samusev, P. A. Belov, and C. R. Simovski, “Demonstration of unusual nanoantenna array modes through direct reconstruction of the near-field signal,” Nanoscale 7, 765–770 (2015).
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Figures (3)

Fig. 1
Fig. 1

Sketch of a typical probe used for aperture SNOM measurements in the visible wavelength range. The investigated field incident on the probe excites the modes supported by the aperture. The aperture should be understood as a metal coated fiber with the dimensions of the apex of the tip. The complete coupling process of the externally investigated field into the probe takes place only via the aperture, since the 200 nm thick metal coating prohibits any side coupling of light into the probe.

Fig. 2
Fig. 2

Real part of the mainly x-polarized mode accessible in an aperture at a wavelength of 663 nm. The magnetic field components were multiplied by the free-space impedance |Z0|, for better comparability of the field magnitudes. The aperture is made of fused-silica glass with a refractive index of n = 1.5 surrounded by a 200 nm thick gold coating. The ex and hy fields have a mirror-symmetry with respect to both coordinate axes x and y, whereas the ey and hx fields have an odd symmetry. The second accessible mode in the aperture is the mainly y-polarized one, in which the symmetries are reversed compared to the mainly x-polarized mode.

Fig. 3
Fig. 3

Spectrally resolved mode-impedance factor | Z M ( λ ) Z 0 | for 2 commercially available probes normalized by the free-space impedance Z0 = 376Ω. Both tips share the same geometrical parameters, i.e. the aperture diameter is D = 150 nm, the core is made from fused silica with n = 1.5, and the core is covered with a 200 nm thick metal coating. The tips differ only by their coating material. Both probes show resonances of the mode-impedance in the visible wavelength range which are slightly shifted relative to each other. The resonance of the gold coated tip lies in the range of commonly used wavelengths for near field measurements with such aperture diameters. In this regime, around λ = 650 nm, gold coated probes tend to be much more sensitive to magnetic field components in a detected image when compared to aluminum coated tips.

Equations (16)

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t 1 ( x , y ) = 2 [ e 1 ( x ˜ x , y ˜ y ) × H ( x ˜ , y ˜ ) E ( x ˜ , y ˜ ) × h 1 ( x ˜ x , y ˜ y ) ] n z d x ˜ d y ˜ , t 2 ( x , y ) = 2 [ e 2 ( x ˜ x , y ˜ y ) × H ( x ˜ , y ˜ ) E ( x ˜ , y ˜ ) × h 2 ( x ˜ x , y ˜ y ) ] n z d x ˜ d y ˜ .
( x , y ) = | t 1 ( x , y ) | 2 + | t 2 ( x , y ) | 2 = | 2 [ e 1 ( x ˜ x , y ˜ y ) × H ( x ˜ , y ˜ ) E ( x ˜ , y ˜ ) × h 1 ( x ˜ x , y ˜ y ) ] n z d x ˜ d y ˜ | 2 + | 2 [ e 2 ( x ˜ x , y ˜ y ) × H ( x ˜ , y ˜ ) E ( x ˜ , y ˜ ) × h 2 ( x ˜ x , y ˜ y ) ] n z d x ˜ d y ˜ | 2 .
t 1 ( x , y ) = [ e 1 × H E × h 1 ] n z d x ˜ d y ˜ , = H y e 1 x d x ˜ d y ˜ H x e 1 y d x ˜ d y ˜ = 0 E x h 1 y d x ˜ d y ˜ + E y h 1 x d x ˜ d y ˜ = 0 ,
= H y e 1 x d x ˜ d y ˜ e 1 x ¯ E x h 1 y d x ˜ d y ˜ h 1 y ¯ , = H y e 1 x ¯ E x h 1 y ¯ .
h 1 y ¯ = Z M 1 e 1 x ¯ , Z M = e 1 x ¯ h 1 y ¯ .
( x , y ) = | t 1 ( x , y ) | 2 + | t 2 ( x , y ) | 2 = | H ( x , y ) | 2 + | Z M | 2 | E ( x , y ) | 2 2 | Z M | 1 | E x ( x , y ) | | H y ( x , y ) | cos ( ϕ H y ( x , y ) ϕ E x ( x , y ) ϕ Z M ) 2 | Z M | 1 | H x ( x , y ) | | E y ( x , y ) | cos ( ϕ H x ( x , y ) ϕ E y ( x , y ) ϕ Z M ) .
Γ = | Z | 2 | Z M | 2 .
h ˜ ( k ) = { h ( r ) } = 1 2 π 2 h ( r ) e i ( k x x + k y y ) d r
h ( r ) = 1 { h ˜ ( k ) } = 1 2 π 2 h ˜ ( k ) e i ( k x x + k y y ) d k ,
t ˜ 1 ( k ) = [ e ˜ 1 ( k ) × H ˜ ( k ) E ˜ ( k ) × h ˜ 1 ( k ) ] n z , t ˜ 2 ( k ) = [ e ˜ 2 ( k ) × H ˜ ( k ) E ˜ ( k ) × h 2 ( k ) ] n z .
t ˜ 1 = ( γ 3 e ˜ 1 x γ 1 e ˜ 1 y h ˜ 1 y ) M 11 E ˜ x + ( γ 4 e ˜ 1 x γ 2 e ˜ 1 y + h ˜ 1 x ) M 12 E ˜ y , t ˜ 2 = ( γ 3 e ˜ 2 x γ 1 e ˜ 2 y h ˜ 2 y ) M 21 E ˜ x + ( γ 4 e ˜ 2 x γ 2 e ˜ 2 y + h ˜ 2 x ) M 22 E ˜ y , γ 1 = 1 k 0 Z 0 k y k x k z , γ 2 = 1 k 0 Z 0 ( k y 2 k z + k z ) , γ 3 = 1 k 0 Z 0 ( k x 2 k z + k z ) , γ 4 = 1 k 0 Z 0 k y k x k z , k z = ( 2 π λ ) 2 k x 2 k y 2 .
( x , y ) = | t 1 ( x , y ) | 2 + | t 2 ( x , y ) | 2 .
2 i k | P k + incident field + 2 r k | P k reflected field = t m | T m + excited aperture modes ,
ψ m | ψ n = 2 [ e m × h n e n × h m ] n z d x d y ,
ψ m + | ψ n = α m 2 δ m n , ψ m + | ψ n + = 0 , ψ m | ψ n + = α m 2 δ m n , ψ m | ψ n = 0 ,
( x , y ) = | 2 [ e 1 ( x ˜ , x , y ˜ y ) × H ( x ˜ , y ˜ ) E ( x ˜ , y ˜ ) × h 1 ( x ˜ , x , y ˜ y ) ] n z d x ˜ d y ˜ | 2 + | 2 [ e 2 ( x ˜ , x , y ˜ y ) × H ( x ˜ , y ˜ ) E ( x ˜ , y ˜ ) × h 2 ( x ˜ , x , y ˜ y ) ] n z d x ˜ d y ˜ | 2 ,

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