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The interplay between optical bianisotropy and magnetism in plasmonic metamolecules Liuyang Sun, Tzuhsuan Ma, Seung-Cheol Yang, Dong-Kwan Kim, Gaehang Lee, Jinwei Shi, Irving Martinez, Gi-Ra Yi, Gennady Shvets, and Xiaoqin Li Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b01380 • Publication Date (Web): 22 Jun 2016 Downloaded from http://pubs.acs.org on June 23, 2016
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The Interplay Between Optical Bianisotropy and Magnetism in Plasmonic Metamolecules Liuyang Sun1, Tzuhsuan Ma1, Seung-Cheol Yang1, Dong-Kwan Kim2, Gaehang Lee3, Jinwei Shi4, Irving Martinez5, Gi-Ra Yi2, Gennady Shvets1,6*, and Xiaoqin Li1,6* 1 Department of Physics and the Center for Complex Quantum Systems, The University of Texas at Austin, Austin, Texas 78712, USA 2 School of Chemical Engineering, Sungkyunkwan University, Suwon 16419, Republic of Korea 3 Korea Basic Science Institute and University of Science and Technology, Daejeon 34113, Republic of Korea 4 Department of Physics and Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China 5 Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA 6 Materials Science and Engineering Program, Texas Materials Institute, The University of Texas at Austin, Austin, Texas 78712, USA
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Abstract: The smallness of natural molecules and atoms with respect to the wavelength of light imposes severe limits on the nature of their optical response. For example, the well-known argument of Landau and Lifshitz and its recent extensions that include chiral molecules show that the electric dipole response dominates over the magneto-electric (bianisotropic) and an even smaller magnetic dipole optical response for all natural materials. Here, we experimentally demonstrate that both these responses can be greatly enhanced in plasmonic nanoclusters. Using AFM nano-manipulation technique, we assemble a plasmonic metamolecule that is designed for strong and simultaneous optical magnetic and magneto-electric excitation. Angle-dependent scattering spectroscopy is used to disentangle the two responses and to demonstrate that their constructive/destructive interplay causes strong directional scattering asymmetry. This asymmetry is used to extract both magneto-electric and magnetic dipole responses, and to demonstrate their enhancement in comparison to ordinary atomistic materials.
KEYWORDS: Plasmonics, Nanoparticle, Bi-anisotropy, Optical magnetism, Meta-molecular
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, play Due to the symmetry of Maxwell’s equations, the electric and magnetic fields, and equivalent roles in light waves propagating in a vacuum. However, their equivalence no longer holds after light enters a medium comprised of atoms or molecules. In fact, the most important part of the medium response can be described in the dipole approximation that assumes that the electric field induces an electric dipole moment = , where is a polarizability. The accuracy of the dipole approximation rests on the textbook argument1 by Landau and Lifshitz induced by the magnetic field is negligible because that the magnetic dipole moment =
/ ∼ /2, where is the typical size of a molecule and is the wavelength of light. Somewhat less familiar, but crucial for understanding such fundamental phenomena as optical
activity of chiral media, is the magneto-electric coupling which describes the excitation of
and the electric dipole moment by the magnetic field, and vice versa: = + ⋅
∗ +
= ⋅ 3-7. The extension8, 9 of the Landau-Lifshitz argument to chiral molecular
media indicates that| | ≪ | | ≪ | | in the low-frequency regime, i.e. when the light is detuned far from any atomic transitions. Note that the diagonal and off-diagonal components of the magneto-electric coupling tensor are usually referred to as chiral and bianisotropic, respectively3. For a fully-symmetric molecule possessing all three mirror symmetry planes ≡ 0, and breaking of at least one reflection symmetry is required for at least some components of to be non-vanishing10-14.
Recent advances in plasmonics and metamaterials demonstrated that these restrictive scalings can be lifted for plasmonic nanoclusters2,
15
. While recent experiments demonstrated the
excitation of magnetic resonances by observing characteristic Fano interference features in the scattering spectrum16-23, distinguishing between magneto-electric (ME) and magnetic-moment (MM) coupling has not been feasible. This difficulty mainly arises from the complicated
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tensorial nature of the former, and the fact that the simplest manifestations of the two coupling mechanisms, such as Fano–resonance in the scattering cross section, are essentially the same. In this Letter, we use a precise nano-manipulation technique to assemble four nearly identical spherical nanoparticles (NPs) into an isosceles trapezoid geometry. The resulting metamolecule possesses a very simple ME coupling tensor with a single dominant component ≡ . We show experimentally and theoretically that the combination of the ME and MM coupling mechanisms has an unambiguous experimental manifestation: highly asymmetric scattering that strongly depends on the polarization and incidence direction of light19, 24, 25. Finally, we use angle-resolved scattering spectroscopy to disentangle these two contributions to the magnetic resonance, and to demonstrate that the Landau-Lifshitz inequality | | ≪ | | is broken in the metamolecule. The experiment schematically illustrated in Figure 1a utilizes an asymmetric nanocluster comprised of identical nanospheres assembled into an isosceles trapezoid geometry and illuminated by a broadband light source either in normal or oblique incident direction. The resulting metamolecule supports three plasmonic resonances schematically shown in Figure 1b: two electric dipole resonances pointing in x and y-directions (black arrows in Figure 1b) excited by the electric field components and , respectively, and a magnetic dipole resonance pointing in the z-direction (black circulating arrows). It has been previously demonstrated that the magnetic dipole resonance arising from the circulating displacement current can be tuned in wavelength by simply changing the gap size between the NPs17, 26. When the magnetic and electric dipole resonances spectrally overlap, Fano resonance features at the magnetic resonance frequency are observed in the scattering spectra for either the normal or oblique incident light as illustrated in Figure 1. However, the
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details of the Fano feature strongly depend on the incident light’s polarization state and incidence angle. We exploit the angle and polarization dependent scattering spectra to disentangle the ME and MM excitation mechanisms. The role of the ME excitation of the magnetic resonance is particularly transparent for normally incident light (Figure 1b) because it does not contain the z-component of the magnetic field. The symmetry of the metamolecule prohibits the coupling between the xoriented electric dipole and the magnetic dipole moment, and no magnetic dipole excitation takes place. Thus, no spectral Fano features are observed in the scattering spectra shown in Figure 1b (case I, dashed line) for -polarized light. For all other polarizations, the !-oriented electric dipole resonance of the two unequal dipole pairs of NPs (left and right) is excited. The near field ME coupling of the above electric dipole (with the amplitude "# ) to the $-polarized magnetic dipole (with the amplitude "% ) is enabled by the broken mirror symmetry of the metamolecule. The corresponding characteristic Fano feature, which is maximized for the y-polarized light (Figure 1b, case II, solid line), can be used for extracting | | (see Methods for details). However, to separately quantify the MM-coupling schematically illustrated in Figure 1c (i.e. to extract the coefficient) it is imperative to measure and characterize the scattering spectra of the obliquely incident light. The simplest analytic description of the scattering of the s-polarized light obliquely incident at an angle & in the
− $ plane with the field amplitude (&) = * and (&) = * sin & is based
on the coupled-mode theory (CMT) that describes the excitation of the electric and magnetic dipole resonances27, 28: ". # = /0 1# "# + 2"% + 3 (&)
". % = /0 1% "% − 2"# + 3 (&)
(1) (2)
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where 0 1#(%) = 0#(%) + /4#(%) are the complex-valued eigenfrequencies of the electric (magnetic) dipole resonances, whose imaginary parts are divided into the radiative and Ohmic decay rates according to 4#(%) = 4#(%),6 + 4#(%),7 . The near-field coupling rate between the two resonances given by the bianisotropy coefficient 2 is proportional to the asymmetry of the gaps’ sizes, and is related to the magneto-electric coefficient (see Methods for details). The farfield coupling strength of the cluster to the incident field is proportional to the external coupling coefficients 3 ( ) which determine the radiative lifetimes of the resonances according . Within the CMT framework, the electric and magnetic dipole moments and to 4#(%),6 = 3 ( )
are given by = 3 "# and = 3 "% , respectively. If the full set of coupling coefficients (2, 3 , and 3 ) can be extracted from the scattering spectra, then the set of low-frequency
polarizabilities ( , , ) are expressed (see Methods for details) as follows:
3 = , 0 1#
23 3 = −/ , 0 1# 0 18
3 = (3) 0 18
Their relative magnitudes can then be compared with the Landau-Lifshitz scalings which are valid for atomic systems in the optical (low frequency) regime. When the upward-scattered light is collected by a small numerical aperture (NA) lens as illustrated in Figure 1a, the amplitude of the signal collected in the direction normal to the plane of the metamolecules is proportional to the square of the in-plane dipole moment: :(&, 0) ≡
|| ∝
