Strongly Directional Scattering from Dielectric Nanowires Peter Wiecha, Aurelien Cuche, Arnaud Arbouet, Christian Girard, Gérard Colas Des Francs, Aurélie Lecestre, Guilhem Larrieu, Frank Fournel, Vincent Larrey, Thierry Baron, et al. To cite this version: Peter Wiecha, Aurelien Cuche, Arnaud Arbouet, Christian Girard, Gérard Colas Des Francs, et al.. Strongly Directional Scattering from Dielectric Nanowires. ACS photonics, American Chemical Soci- ety„ 2017, 4 (8), pp.2036 - 2046. 10.1021/acsphotonics.7b00423. hal-01730478 HAL Id: hal-01730478 https://hal.archives-ouvertes.fr/hal-01730478 Submitted on 13 Mar 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Strongly directional scattering from dielectric nanowires 1, 1 1 1 2 Peter R. Wiecha, ∗ Aurélien Cuche, Arnaud Arbouet, Christian Girard, Gérard Colas des Francs, Aurélie 3 3 4 4 5 1, Lecestre, Guilhem Larrieu, Frank Fournel, Vincent Larrey, Thierry Baron, and Vincent Paillard y 1CEMES-CNRS, Université de Toulouse, CNRS, UPS, Toulouse, France 2ICB, UMR 6303 CNRS - Université Bourgogne-Franche Comté, Dijon, France 3LAAS-CNRS, Université de Toulouse, CNRS, INP, Toulouse, France 4CEA-LETI/MINATEC, CEA, Grenoble, France 5CNRS, LTM, Université Grenoble Alpes, Grenoble, France It has been experimentally demonstrated only recently that a simultaneous excitation of interfer- ing electric and magnetic resonances can lead to uni-directional scattering of visible light in zero- dimensional dielectric nanoparticles. We show both theoretically and experimentally, that strongly anisotropic scattering also occurs in individual dielectric nanowires. The effect occurs even under either pure transverse electric or pure transverse magnetic polarized normal illumination. This al- lows for instance to toggle the scattering direction by a simple rotation of the incident polarization. Finally, we demonstrate that directional scattering is not limited to cylindrical cross-sections, but can be further tailored by varying the shape of the nanowires. The search for ways to control light at subwavelength ized in the visible spectral range using dielectric nanopar- dimensions has increasingly attracted the interest of re- ticles. Kerker et al. described two possible configura- searchers for about the last two decades. Due to their tions, called the Kerker conditions. At the first Kerker strong polarizability and tunable plasmon resonances, condition zero backward scattering occurs for equal elec- metallic nanostructures are particularly suitable for the tric permittivity and magnetic permeability (r = µr). nanoscale manipulation of light – especially at visible The second Kerker condition predicts zero forward scat- frequencies.1 However, such plasmonic structures suffer tering in small spherical particles when the first order from certain drawbacks like strong dissipation associated magnetic and electric Mie coefficients are of equal abso- to the large imaginary part of the dielectric function in lute value and with opposite sign (a1 = −b1). In con- metals. trast to particularly designed metamaterials,24 the mag- Recently, dielectric nanostructures from high-index netic permeability µr is unitary in dielectric nanoparti- materials have proven to offer a promising alternative cles. Nevertheless, simultaneously occurring electric and platform with far lower losses.2 Like in plasmonics, it is magnetic resonances can de-facto fulfill the first Kerker possible to tune optical resonances from the near ultra- condition.25,26 While the Kerker conditions were origi- violet to the near infrared, yet with almost no dissipative nally derived for spherical particles, it has been shown losses. At these resonances, which can be of both elec- that the conditions are a result of a cylindrical symme- tric or magnetic nature, strong local field enhancements3 try and therefore can be generalized accordingly.27 and intense scattering4 occur, tunable via the mate- Recent publications have confirmed the possibility rial and the geometry of the nanostructure. Promi- to obtain optimum FW scattering also from elon- nent dielectric materials are, among others, silicon, ger- gated structures such as nanopillars,21 spheroids28 or manium or III-V compound semiconductors with indi- even from cuboidal dielectric particles8. Other dielec- rect band-gap.5,6 Conventional geometries include spher- tric particles on which directional scattering was in- ical nanoparticles4 or nanowires (NWs),7,8 but also more vestigated include nanodiscs for FW/BW directional complex dielectric nanostructures9. Dielectric optical an- metasurfaces,29,30 patch antennas,31 V-shaped structures tennas are promising candidates for applications in field- for multi-directional color routing,32 or asymmetric hol- enhanced spectroscopy,10–13 imaging,14 to enhance and low nanodiscs for bi-anisotropic scattering33, all of them control nonlinear effects15–17 or to increase the efficiency based on the interplay between electric and magnetic in photovoltaics18. modes. Control over the directional scattering can A peculiarity of dielectric particles is the possibil- also be obtained using arrangements of nanoparticles ity to simultaneously obtain a strong electric and mag- like dimers34–36 or via hybrid metal/dielectric nano- netic response using very simple geometries.3,4,19,20 Re- structures37. Even directional shaping of nonlinear emis- cently, it has been independently shown by two research sion has been demonstrated: The radiation pattern of groups,21,22 that exclusive forward (FW) or backward the third harmonic generation from silicon dimers can (BW) scattering, predicted by Kerker et al. in 1983 for be controlled via the geometry of the structure.38 In hypothetical magneto-dielectric particles,23 can be real- a plasmonic-dielectric hybrid structure, the interplay of electric and magnetic resonances in dielectric TiO2 spheres was used to impose an uni-directional radiation pattern on the second harmonic generation from a plas- 39 ∗ e-mail : [email protected] monic driver element. y e-mail : [email protected] Compared to zero-dimensional (0D) particles of deeply 2 a) TE b) TM leading to the occurrence of directional scattering. We 40 FW/BW scat. ratio 1 FW/BW 10 then compare experimental results from individual, sin- 30 FW/BW=1 gle crystal silicon nanowires (SiNWs) of cylindrical and 20 100 rectangular cross-sections. In both cases spectral zones E 2 10 10 | | × of strongly anisotropic FW/BW scattering ratios can be H 2 1 | | 10− 0 identified and we find that asymmetric wire geometries 400 500 600 700 800 900 400 500 600 700 800 900 1000 avg. field enhancement allow even further tailoring of directional scattering and wavelength (nm) wavelength (nm) offer the incident angle of the illumination as a supple- mentary free parameter. We confront our experimental c) TE, λ = 550 nm d) TM, λ = 550 nm results with simulations using the Green dyadic method (GDM), yielding a very good agreement. I. DIRECTIONAL SCATTERING FROM 0.0 0.5 1.0 1.5 0 25 50 75 0.0 2.5 5.0 7.5 0 25 50 75 CYLINDRICAL NANOWIRES E 2/ E 2 H 2/ H 2 E 2/ E 2 H 2/ H 2 | | | 0| | | | 0| | | | 0| | | | 0| Mie theory can be applied to infinitely long cylinders FIG. 1. Average electric (red lines) and magnetic (blue lines) by expanding the fields in vector cylindrical harmonics. field intensity enhancement inside a silicon nanowire of diam- The Mie scattering coefficients ai and bi of the expansion eter D = 100 nm as function of wavelength for a) a TE and can be regarded as weights for corresponding electric and b) a TM polarized incident plane wave, calculated using Mie magnetic multipole moments, representing the response theory. Normalized to the illumination field intensity. For of the wire to an external illumination. Under normal comparison, the FW/BW scattering ratio in the far-field is incidence, the Mie S-matrix, connecting the incident (Ei) shown as dashed green line (right axis ticks). c) and d) show 49 the internal field intensity distributions at λ = 550 nm for and the asymptotic, scattered field (Es) writes TE and TM polarization, respectively (left subplot: electric, r right: magnetic field). D = 100 nm, plane wave incident from E 2 T 0 E s;TM = ei3π=4 eikR 1 i;TM (1) the top. Es;TE πkR 0 T2 Ei;TE with the wavenumber k = 2π/λ, the distance R to the sub-wavelength size in all directions (like nano-spheres), cylinder axis and one-dimensional (1D) nanowires have a strongly polar- X1 ization dependent optical response, which offers an addi- T = b + 2 b cos(n') tional degree of freedom, supplementary to the choice 1 0 n n=1 of material and modifications of the nano-structure’s (2) geometry. Despite this opportunity, research on di- X1 T2 = a0 + 2 an cos(n'): rectional scattering from dielectric nanowires is still n=1 scarce. As for scattering, it has been shown theoretically 40 that multi-layer dielectric or plasmonic-dielectric core- ' is the scattering angle with respect to the incident wave 41 shell nanowires can be rendered invisible by tailoring vector and ' = 0 corresponds to the forward scattering destructive