Abstract

Measuring nanoscale displacement is crucial for optical nanometrology and optical calibration. Here, we present a comprehensive analysis of the far-field scattering of dielectric nano-dimer antennas excited precisely by a Gaussian beam. We demonstrated that the interaction of a Gaussian beam with a dielectric nanoantenna will lead to remarkable sensitivity of the far-field scattering to the displacement at a scale much smaller than the wavelength. The electric/magnetic dipole-dipole interaction model is drawn to analyze the far-field scattering and the results are in good agreement with numerical simulations. This study will pave a simple way to a novel position detection and displacement sensing based on the interaction of general Gaussian beam with nanoantennas.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (3)

A. I. Barreda, H. Saleh, A. Litman, F. González, J.-M. Geffrin, and F. Moreno, “Electromagnetic polarization-controlled perfect switching effect with high-refractive-index dimers and the beam-splitter configuration,” Nature Commun. 8, 13910 (2017).
[Crossref] [PubMed]

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, P. Albella, and S. A. Maier, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4, 489–494 (2017).
[Crossref]

2016 (3)

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nature Commun. 7, 11286 (2016).
[Crossref] [PubMed]

Z. Xi, L. Wei, A. Adam, H. Urbach, and L. Du, “Accurate feeding of nanoantenna by singular optics for nanoscale translational and rotational displacement sensing,” Phys. Rev. Lett. 117, 113903 (2016).
[Crossref] [PubMed]

T. Shibanuma, P. Albella, and S. A. Maier, “Unidirectional light scattering with high efficiency at optical frequencies based on low-loss dielectric nanoantennas,” Nanoscale 8, 14184–14192 (2016).
[Crossref] [PubMed]

2015 (3)

P. Albella, T. Shibanuma, and S. A. Maier, “Switchable directional scattering of electromagnetic radiation with subwavelength asymmetric silicon dimers,” Sci. Rep. 5, 18322 (2015).
[PubMed]

U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photonics 2, 913–920 (2015).
[Crossref]

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]

2014 (3)

V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, and S. A. Tretyakov, “Determining polarizability tensors for an arbitrary small electromagnetic scatterer,” Photonics and Nanostructures-Fundamentals and Applications 12, 298–304 (2014).

G. Boudarham, R. Abdeddaim, and N. Bonod, “Enhancing the magnetic field intensity with a dielectric gap antenna,” Applied Physics Letters 104, 021117 (2014).
[Crossref]

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nature Photon. 8, 889–898 (2014).
[Crossref]

2013 (3)

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano letters 13, 1806–1809 (2013).
[Crossref] [PubMed]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[Crossref] [PubMed]

2012 (5)

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

J. B. Khurgin and A. Boltasseva, “Reflecting upon the losses in plasmonics and metamaterials,” MRS Bulletin 37, 768–779 (2012).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
[Crossref] [PubMed]

B. Rolly, B. Stout, and N. Bonod, “Boosting the directivity of optical antennas with magnetic and electric dipolar resonant particles,” Opt. Express 20, 20376–20386 (2012).
[Crossref] [PubMed]

M. Agio, “Optical antennas as nanoscale resonators,” Nanoscale 4, 692–706 (2012).
[Crossref]

2011 (3)

A. Kuznetsov, A. Miroshnichenko, Y. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2, 492 (2011).
[Crossref]

L. Novotny and N. Van Hulst, “Antennas for light,” Nature Photon. 5, 83–90 (2011).
[Crossref]

M. Nieto-Vesperinas, R. Gomez-Medina, and J. Saenz, “Angle-suppressed scattering and optical forces on submicrometer dielectric particles,” JOSA A 28, 54–60 (2011).
[Crossref] [PubMed]

2006 (1)

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref] [PubMed]

2005 (1)

P. Mühlschlegel, H.-J. Eisler, O. Martin, B. Hecht, and D. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[Crossref] [PubMed]

1998 (1)

F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Optics letters 23, 7–9 (1998).
[Crossref]

1983 (1)

M. Kerker, D.-S. Wang, and C. Giles, “Electromagnetic scattering by magnetic spheres,” JOSA 73, 765–767 (1983).
[Crossref]

Abdeddaim, R.

G. Boudarham, R. Abdeddaim, and N. Bonod, “Enhancing the magnetic field intensity with a dielectric gap antenna,” Applied Physics Letters 104, 021117 (2014).
[Crossref]

Adam, A.

Z. Xi, L. Wei, A. Adam, H. Urbach, and L. Du, “Accurate feeding of nanoantenna by singular optics for nanoscale translational and rotational displacement sensing,” Phys. Rev. Lett. 117, 113903 (2016).
[Crossref] [PubMed]

Agio, M.

M. Agio, “Optical antennas as nanoscale resonators,” Nanoscale 4, 692–706 (2012).
[Crossref]

Aizpurua, J.

U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photonics 2, 913–920 (2015).
[Crossref]

Albella, P.

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, P. Albella, and S. A. Maier, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4, 489–494 (2017).
[Crossref]

T. Shibanuma, P. Albella, and S. A. Maier, “Unidirectional light scattering with high efficiency at optical frequencies based on low-loss dielectric nanoantennas,” Nanoscale 8, 14184–14192 (2016).
[Crossref] [PubMed]

P. Albella, T. Shibanuma, and S. A. Maier, “Switchable directional scattering of electromagnetic radiation with subwavelength asymmetric silicon dimers,” Sci. Rep. 5, 18322 (2015).
[PubMed]

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

Asadchy, V. S.

V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, and S. A. Tretyakov, “Determining polarizability tensors for an arbitrary small electromagnetic scatterer,” Photonics and Nanostructures-Fundamentals and Applications 12, 298–304 (2014).

Bag, A.

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nature Commun. 7, 11286 (2016).
[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]

Banzer, P.

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nature Commun. 7, 11286 (2016).
[Crossref] [PubMed]

Barnes, W. L.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nature Photon. 8, 889–898 (2014).
[Crossref]

Barreda, A. I.

A. I. Barreda, H. Saleh, A. Litman, F. González, J.-M. Geffrin, and F. Moreno, “Electromagnetic polarization-controlled perfect switching effect with high-refractive-index dimers and the beam-splitter configuration,” Nature Commun. 8, 13910 (2017).
[Crossref] [PubMed]

Boltasseva, A.

J. B. Khurgin and A. Boltasseva, “Reflecting upon the losses in plasmonics and metamaterials,” MRS Bulletin 37, 768–779 (2012).
[Crossref]

Bonod, N.

G. Boudarham, R. Abdeddaim, and N. Bonod, “Enhancing the magnetic field intensity with a dielectric gap antenna,” Applied Physics Letters 104, 021117 (2014).
[Crossref]

B. Rolly, B. Stout, and N. Bonod, “Boosting the directivity of optical antennas with magnetic and electric dipolar resonant particles,” Opt. Express 20, 20376–20386 (2012).
[Crossref] [PubMed]

Boudarham, G.

G. Boudarham, R. Abdeddaim, and N. Bonod, “Enhancing the magnetic field intensity with a dielectric gap antenna,” Applied Physics Letters 104, 021117 (2014).
[Crossref]

Bozhevolnyi, S. I.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
[Crossref] [PubMed]

Brener, I.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

Chichkov, B. N.

U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photonics 2, 913–920 (2015).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
[Crossref] [PubMed]

Decker, M.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

Dominguez, J.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

Du, L.

Z. Xi, L. Wei, A. Adam, H. Urbach, and L. Du, “Accurate feeding of nanoantenna by singular optics for nanoscale translational and rotational displacement sensing,” Phys. Rev. Lett. 117, 113903 (2016).
[Crossref] [PubMed]

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. Martin, B. Hecht, and D. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[Crossref] [PubMed]

Eriksen, R. L.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
[Crossref] [PubMed]

Evlyukhin, A. B.

U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photonics 2, 913–920 (2015).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
[Crossref] [PubMed]

Eyraud, C.

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

Faniayeu, I. A.

V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, and S. A. Tretyakov, “Determining polarizability tensors for an arbitrary small electromagnetic scatterer,” Photonics and Nanostructures-Fundamentals and Applications 12, 298–304 (2014).

Fofang, N. T.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

Froufe-Pérez, L.

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

Fu, Y.

A. Kuznetsov, A. Miroshnichenko, Y. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2, 492 (2011).
[Crossref]

Fu, Y. H.

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[Crossref] [PubMed]

García-Cámara, B.

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

Geffrin, J.-M.

A. I. Barreda, H. Saleh, A. Litman, F. González, J.-M. Geffrin, and F. Moreno, “Electromagnetic polarization-controlled perfect switching effect with high-refractive-index dimers and the beam-splitter configuration,” Nature Commun. 8, 13910 (2017).
[Crossref] [PubMed]

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

Giles, C.

M. Kerker, D.-S. Wang, and C. Giles, “Electromagnetic scattering by magnetic spheres,” JOSA 73, 765–767 (1983).
[Crossref]

Gittes, F.

F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Optics letters 23, 7–9 (1998).
[Crossref]

Gomez-Medina, R.

M. Nieto-Vesperinas, R. Gomez-Medina, and J. Saenz, “Angle-suppressed scattering and optical forces on submicrometer dielectric particles,” JOSA A 28, 54–60 (2011).
[Crossref] [PubMed]

Gómez-Medina, R.

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

Gonzaga, L.

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]

Gonzales, E.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

González, F.

A. I. Barreda, H. Saleh, A. Litman, F. González, J.-M. Geffrin, and F. Moreno, “Electromagnetic polarization-controlled perfect switching effect with high-refractive-index dimers and the beam-splitter configuration,” Nature Commun. 8, 13910 (2017).
[Crossref] [PubMed]

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

Håkanson, U.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref] [PubMed]

Hao, H.

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. Martin, B. Hecht, and D. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[Crossref] [PubMed]

L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University, 2012).
[Crossref]

Hooper, I. R.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nature Photon. 8, 889–898 (2014).
[Crossref]

Jain, M.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano letters 13, 1806–1809 (2013).
[Crossref] [PubMed]

Kerker, M.

M. Kerker, D.-S. Wang, and C. Giles, “Electromagnetic scattering by magnetic spheres,” JOSA 73, 765–767 (1983).
[Crossref]

Khaidarov, E.

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

Khurgin, J. B.

J. B. Khurgin and A. Boltasseva, “Reflecting upon the losses in plasmonics and metamaterials,” MRS Bulletin 37, 768–779 (2012).
[Crossref]

Kivshar, Y.

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]

Kühn, S.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref] [PubMed]

Kuznetsov, A.

A. Kuznetsov, A. Miroshnichenko, Y. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2, 492 (2011).
[Crossref]

Kuznetsov, A. I.

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

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]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[Crossref] [PubMed]

Lapin, Z.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano letters 13, 1806–1809 (2013).
[Crossref] [PubMed]

Leuchs, G.

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nature Commun. 7, 11286 (2016).
[Crossref] [PubMed]

Litman, A.

A. I. Barreda, H. Saleh, A. Litman, F. González, J.-M. Geffrin, and F. Moreno, “Electromagnetic polarization-controlled perfect switching effect with high-refractive-index dimers and the beam-splitter configuration,” Nature Commun. 8, 13910 (2017).
[Crossref] [PubMed]

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

Liu, S.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

Luk, T. S.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

Luk’yanchuk, B.

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]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[Crossref] [PubMed]

A. Kuznetsov, A. Miroshnichenko, Y. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2, 492 (2011).
[Crossref]

Maier, S. A.

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, P. Albella, and S. A. Maier, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4, 489–494 (2017).
[Crossref]

T. Shibanuma, P. Albella, and S. A. Maier, “Unidirectional light scattering with high efficiency at optical frequencies based on low-loss dielectric nanoantennas,” Nanoscale 8, 14184–14192 (2016).
[Crossref] [PubMed]

P. Albella, T. Shibanuma, and S. A. Maier, “Switchable directional scattering of electromagnetic radiation with subwavelength asymmetric silicon dimers,” Sci. Rep. 5, 18322 (2015).
[PubMed]

Markovich, D.

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]

Martin, O.

P. Mühlschlegel, H.-J. Eisler, O. Martin, B. Hecht, and D. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[Crossref] [PubMed]

Mascher, P.

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, P. Albella, and S. A. Maier, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4, 489–494 (2017).
[Crossref]

Matsui, T.

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, P. Albella, and S. A. Maier, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4, 489–494 (2017).
[Crossref]

Meinzer, N.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nature Photon. 8, 889–898 (2014).
[Crossref]

Miroshnichenko, A.

A. Kuznetsov, A. Miroshnichenko, Y. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2, 492 (2011).
[Crossref]

Miroshnichenko, A. E.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
[Crossref] [PubMed]

Moreno, F.

A. I. Barreda, H. Saleh, A. Litman, F. González, J.-M. Geffrin, and F. Moreno, “Electromagnetic polarization-controlled perfect switching effect with high-refractive-index dimers and the beam-splitter configuration,” Nature Commun. 8, 13910 (2017).
[Crossref] [PubMed]

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. Martin, B. Hecht, and D. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[Crossref] [PubMed]

Neshev, D. N.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

Neugebauer, M.

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nature Commun. 7, 11286 (2016).
[Crossref] [PubMed]

Ng, J. S. K.

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

Nieto-Vesperinas, M.

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

M. Nieto-Vesperinas, R. Gomez-Medina, and J. Saenz, “Angle-suppressed scattering and optical forces on submicrometer dielectric particles,” JOSA A 28, 54–60 (2011).
[Crossref] [PubMed]

Novikov, S. M.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
[Crossref] [PubMed]

Novotny, L.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano letters 13, 1806–1809 (2013).
[Crossref] [PubMed]

L. Novotny and N. Van Hulst, “Antennas for light,” Nature Photon. 5, 83–90 (2011).
[Crossref]

L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University, 2012).
[Crossref]

Palik, E. D.

E. D. Palik, Handbook of optical constants of solids, vol. 3 (Academic, 1998).

Paniagua-Domínguez, R.

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

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]

Permyakov, D.

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]

Person, S.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano letters 13, 1806–1809 (2013).
[Crossref] [PubMed]

Pohl, D.

P. Mühlschlegel, H.-J. Eisler, O. Martin, B. Hecht, and D. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[Crossref] [PubMed]

Ra’di, Y.

V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, and S. A. Tretyakov, “Determining polarizability tensors for an arbitrary small electromagnetic scatterer,” Photonics and Nanostructures-Fundamentals and Applications 12, 298–304 (2014).

Reinhardt, C.

U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photonics 2, 913–920 (2015).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
[Crossref] [PubMed]

Rogobete, L.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref] [PubMed]

Rolly, B.

Roschuk, T.

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, P. Albella, and S. A. Maier, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4, 489–494 (2017).
[Crossref]

Saenz, J.

M. Nieto-Vesperinas, R. Gomez-Medina, and J. Saenz, “Angle-suppressed scattering and optical forces on submicrometer dielectric particles,” JOSA A 28, 54–60 (2011).
[Crossref] [PubMed]

Sáenz, J. J.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano letters 13, 1806–1809 (2013).
[Crossref] [PubMed]

Saleh, H.

A. I. Barreda, H. Saleh, A. Litman, F. González, J.-M. Geffrin, and F. Moreno, “Electromagnetic polarization-controlled perfect switching effect with high-refractive-index dimers and the beam-splitter configuration,” Nature Commun. 8, 13910 (2017).
[Crossref] [PubMed]

Samusev, A.

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]

Sandoghdar, V.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref] [PubMed]

Schmidt, C. F.

F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Optics letters 23, 7–9 (1998).
[Crossref]

Schmidt, M. K.

U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photonics 2, 913–920 (2015).
[Crossref]

Shibanuma, T.

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, P. Albella, and S. A. Maier, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4, 489–494 (2017).
[Crossref]

T. Shibanuma, P. Albella, and S. A. Maier, “Unidirectional light scattering with high efficiency at optical frequencies based on low-loss dielectric nanoantennas,” Nanoscale 8, 14184–14192 (2016).
[Crossref] [PubMed]

P. Albella, T. Shibanuma, and S. A. Maier, “Switchable directional scattering of electromagnetic radiation with subwavelength asymmetric silicon dimers,” Sci. Rep. 5, 18322 (2015).
[PubMed]

Staude, I.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and et al., “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref] [PubMed]

Stout, B.

Toh, Y. T.

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

Tretyakov, S. A.

V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, and S. A. Tretyakov, “Determining polarizability tensors for an arbitrary small electromagnetic scatterer,” Photonics and Nanostructures-Fundamentals and Applications 12, 298–304 (2014).

Urbach, H.

Z. Xi, L. Wei, A. Adam, H. Urbach, and L. Du, “Accurate feeding of nanoantenna by singular optics for nanoscale translational and rotational displacement sensing,” Phys. Rev. Lett. 117, 113903 (2016).
[Crossref] [PubMed]

Vaillon, R.

J.-M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, and et al., “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nature Commun. 3, 1171 (2012).
[Crossref]

Valuckas, V.

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

Van Hulst, N.

L. Novotny and N. Van Hulst, “Antennas for light,” Nature Photon. 5, 83–90 (2011).
[Crossref]

Wang, D.-S.

M. Kerker, D.-S. Wang, and C. Giles, “Electromagnetic scattering by magnetic spheres,” JOSA 73, 765–767 (1983).
[Crossref]

Wei, L.

Z. Xi, L. Wei, A. Adam, H. Urbach, and L. Du, “Accurate feeding of nanoantenna by singular optics for nanoscale translational and rotational displacement sensing,” Phys. Rev. Lett. 117, 113903 (2016).
[Crossref] [PubMed]

Wicks, G.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano letters 13, 1806–1809 (2013).
[Crossref] [PubMed]

Wojcik, J.

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, P. Albella, and S. A. Maier, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4, 489–494 (2017).
[Crossref]

Wozniak, P.

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nature Commun. 7, 11286 (2016).
[Crossref] [PubMed]

Xi, Z.

Z. Xi, L. Wei, A. Adam, H. Urbach, and L. Du, “Accurate feeding of nanoantenna by singular optics for nanoscale translational and rotational displacement sensing,” Phys. Rev. Lett. 117, 113903 (2016).
[Crossref] [PubMed]

Yap, S. L. K.

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

Yu, Y. F.

E. Khaidarov, H. Hao, R. Paniagua-Domínguez, Y. F. Yu, Y. H. Fu, V. Valuckas, S. L. K. Yap, Y. T. Toh, J. S. K. Ng, and A. I. Kuznetsov, “Asymmetric nanoantennas for ultrahigh angle broadband visible light bending,” Nano letters 17, 6267–6272 (2017).
[Crossref] [PubMed]

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]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nature Commun. 4, 1527 (2013).
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Zhang, J.

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Figures (8)

Fig. 1
Fig. 1 (a) Schematic of the structure. The origin of the coordinate system is chosen at the center of the gap of the dimer and the x-axis is chosen to be aligned with the dimer axis. The dimer consists of two coupled silicon nano-cubes. The distance between the two cube centers is d = 200nm. The side length of the nano-cube is a = 100nm. (b) Electric (blue solid/dashed line for amplitude/phase part) and magnetic (green solid/dashed line for amplitude/phase part) polarizability of an individual cube as a function of the wavelength.
Fig. 2
Fig. 2 (a) Schematic representation of the induced dipoles of the silicon dimer antenna when the electric polarization of the incident wave is perpendicular to the dimer axis. (b) Lateral scattering intensity contrast ratio V as ρ varies from 0 to +1 when φ = 0. (c) Contrast ratio V as φ varies from −π to +π when ρ = 1. (d) Contrast ratio V at λ = 528nm.
Fig. 3
Fig. 3 (a) Schematic representation of the induced dipoles of the silicon dimer antenna when the electric polarization of the incident wave is parallel to the dimer axis. (b) Lateral scattering intensity contrast ratio V as ρ varies from 0 to +1 when φ = 0. (c) Contrast ratio V as φ varies from −π to +π when ρ = 1. (d) Contrast ratio V at λ = 482nm.
Fig. 4
Fig. 4 (a) Schematic illustration of the configuration, the Gaussian beam is initially focusing on the center of the dimer, then moves towards +x direction with a displacement Δx. Contrast ration as a function of Δx for (b) x-polarized incident Gaussian beam at 482 nm and (c) y-polarized incident Gaussian beam at 528 nm, respectively.
Fig. 5
Fig. 5 (a) Amplitude ratio as a function of lateral displacement Δx. (b) Contrast ratio as a function of ρ for x-polarized incident Gaussian beam at 482 nm (blue solid line) and y-polarized incident Gaussian beam at 528 nm (green solid line), respectively.
Fig. 6
Fig. 6 FDTD simulation results. Far-field scattering pattern under x-polarized excitation (a) and y-polarized excitation (b) for different lateral displacement when the beam waist is fixed at 400 nm. Far-field scattering pattern under x-polarized excitation (c) and y-polarized excitation (d) in xy-plane for different beam waist when the lateral displacement is fixed at 100 nm. Contrast ratio under x-polarized excitation (e) and y-polarized excitation (f) as a function of lateral displacement for different beam waist.
Fig. 7
Fig. 7 Contrast ratio as a function of the gap for (a) x-polarized incident Gaussian beam at 482 nm and (b) y-polarized incident Gaussian beam at 528 nm
Fig. 8
Fig. 8 Contrast ratio as a function of Δx for x-polarized incident HG10 mode at 482 nm.

Equations (11)

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p i = α ¯ ¯ e e E l o c ( r i ) + α ¯ ¯ e m H l o c ( r i ) , m i = α ¯ ¯ m e E l o c ( r i ) + α ¯ ¯ m m H l o c ( r i ) ,
E l o c ( r i ) = E i n c ( r i ) + G ¯ ¯ e e ( r i r j ) p j + G ¯ ¯ e m ( r i r j ) m j , H l o c ( r i ) = H i n c ( r i ) + G ¯ ¯ m e ( r i r j ) p j + G ¯ ¯ m m ( r i r j ) m j ,
G ¯ ¯ e e ( r i r j ) p j = 1 4 π ϵ 0 { k 2 ( n i j × p j ) × n i j e i k r i j r i j + [ 3 n i j ( n i j p j ) p j ] ( 1 r i j 3 i k r i j 2 ) e i k r i j } , G ¯ ¯ e m ( r i r j ) m j = η 0 k 2 4 π ( n i j × m j ) e i k r i j r i j ( 1 1 i k r i j ) , G ¯ ¯ m e ( r i r j ) p j = c k 2 4 π ( n i j × p j ) e i k r i j r i j ( 1 1 i k r i j ) , G ¯ ¯ m m ( r i r j ) m j = 1 4 π { k 2 ( n i j × m j ) × n i j e i k r i j r i j + [ 3 n i j ( n i j m j ) m j ] ( 1 r i j 3 i k r i j 2 ) e i k r i j } ,
E f a r = i = 1 , 2 1 4 π ϵ 0 k 2 ( n o i × p i ) × n o i e i k r o i r o i η 0 k 2 4 π ( n o i × m i ) e i k r o i r o i ,
m 1 x = α m m ( H i n c 1 x + 2 g 1 m 2 x ) , m 2 x = α m m ( H i n c 2 x + 2 g 1 m 1 x ) , p 1 y = α e e ( E i n c 1 y + 1 ϵ 0 g 2 p 2 y η 0 g 3 m 2 z ) , p 2 y = α e e ( E i n c 2 y + 1 ϵ 0 g 2 p 1 y + η 0 g 3 m 1 z ) , m 1 z = α m m ( c g 3 p 2 y + g 2 m 2 z + H i n c 1 z ) , m 2 z = α m m ( c g 3 p 1 y + g 2 m 1 z + H i n c 2 z ) ,
m 1 x = α m m H i n c 1 x + 2 g 1 α m m 2 H i n c 2 x [ 1 4 ( g 1 α m m ) 2 ] , m 2 x = α m m H i n c 2 x + 2 g 1 α m m 2 H i n c 1 x [ 1 4 ( g 1 α m m ) 2 ] , p 1 y = Δ 1 E i n c 1 y + Δ 2 E i n c 2 y + Δ 3 H i n c 1 z + Δ 4 H i n c 2 z Δ , p 2 y = Δ 1 E i n c 2 y + Δ 2 E i n c 1 y Δ 3 H i n c 2 z Δ 4 H i n c 1 z Δ , m 1 z = Δ 5 E i n c 1 y + Δ 6 E i n c 2 y + Δ 7 H i n c 1 z + Δ 8 H i n c 2 z Δ , m 2 z = Δ 5 E i n c 2 y Δ 6 E i n c 1 y + Δ 7 H i n c 2 z + Δ 8 H i n c 1 z Δ ,
E + x y = k 2 4 π ( 1 ϵ 0 p 2 y e i k ( r o d / 2 ) r o d / 2 + 1 ϵ 0 p 1 y e i k ( r o + d / 2 ) r o + d / 2 + η 0 m 2 z e i k ( r o d / 2 ) r o d / 2 + η 0 m 1 z e i k ( r o + d / 2 ) r o + d / 2 ) , E x y = k 2 4 π ( 1 ϵ 0 p 1 y e i k ( r o d / 2 ) r o d / 2 + 1 ϵ 0 p 2 y e i k ( r o + d / 2 ) r o + d / 2 η 0 m 1 z e i k ( r o d / 2 ) r o d / 2 η 0 m 2 z e i k ( r o + d / 2 ) r o + d / 2 ) ,
V = | I + x | | I x | | I + x | + | I x | = | E + x | 2 | E x | 2 | I + x | 2 + | E x | 2 .
p 1 x = α e e ( E i n c 1 x + 2 1 ϵ 0 g 1 p 2 x ) , p 2 x = α e e ( E i n c 2 x + 2 1 ϵ 0 g 1 p 1 x ) , m 1 y = α m m ( H i n c 1 y + c g 3 p 2 z + g 2 m 2 y ) , m 2 y = α m m ( H i n c 2 y c g 3 p 1 z + g 2 m 1 y ) , p 1 z = α e e ( E i n c 1 z + 1 ϵ 0 g 2 p 2 z + η 0 g 3 m 2 y ) , p 2 z = α e e ( E i n c 2 z + 1 ϵ 0 g 2 p 1 z η 0 g 3 m 1 y ) .
p 1 x = α e e ( E i n c 1 x + 2 1 ϵ 0 g 1 α e e E i n c 2 x ) 1 ( 2 1 ϵ 0 g 1 α e e ) 2 , p 2 x = α e e ( E i n c 2 x + 2 1 ϵ 0 g 1 α e e E i n c 1 x ) 1 ( 2 1 ϵ 0 g 1 α e e ) 2 , m 1 y = Δ 9 H i n c 1 y + Δ 10 H i n c 2 y + Δ 11 E i n c 1 z + Δ 12 E i n c 2 z Δ , m 2 y = Δ 9 H i n c 2 y + Δ 10 H i n c 1 y Δ 11 E i n c 2 z Δ 12 E i n c 1 z Δ , p 1 z = Δ 13 H i n c 1 y + Δ 14 H i n c 2 y + Δ 15 E i n c 1 z + Δ 16 E i n c 2 z Δ , p 2 z = Δ 13 H i n c 2 y Δ 14 H i n c 1 y + Δ 15 E i n c 2 z + Δ 16 E i n c 1 z Δ ,
E + x z = k 2 4 π ( 1 ϵ 0 p 1 z e i k ( r o + d / 2 ) r o + d / 2 + 1 ϵ 0 p 2 z e i k ( r o d / 2 ) r o d / 2 η 0 m 1 y e i k ( r o + d / 2 ) r o + d / 2 η 0 m 2 y e i k ( r o d / 2 ) r o d / 2 ) , E x z = k 2 4 π ( 1 ϵ 0 p 1 z e i k ( r o d / 2 ) r o d / 2 + 1 ϵ 0 p 2 z e i k ( r o + d / 2 ) r o + d / 2 + η 0 m 1 y e i k ( r o d / 2 ) r o d / 2 + η 0 m 2 y e i k ( r o + d / 2 ) r o + d / 2 ) .

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