Electromagnetic multipole theory for optical nanomaterials

Grahn, Patrick; Shevchenko, Andriy; Kaivola, Matti

doi:10.1088/1367-2630/14/9/093033

Cited by 340 publications

(359 citation statements)

References 10 publications

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“…2 of Ref. [40]). Furthermore, the excitable electric-current configurations representing the elements of our expansion are connected to the geometry of the nanoscatterer, which helps tremendously in designing the metamaterial constituents.…”

Section: General Considerationmentioning

confidence: 88%

“…If the structural units of a metasurface are small compared to the excitation wavelength, one can truncate the multipole expansion after the electric-current quadrupoles, which are the multipoles combining the classical electric quadrupoles and magnetic dipoles [29,40]. In this case, the normal-incidence reflection and transmission coefficients ρ 0 and τ 0 of the metasurface can, for a linearly polarized optical wave, be written as [19] …”

Section: General Considerationmentioning

confidence: 99%

“…The expansion in the electric-current multipoles we use is described in detail in Ref. [40]. Briefly, we expand the electric-current density distribution JðrÞ in a scatterer (a metamolecule in our case) in a series of elementary current excitations, as shown schematically in Fig.…”

Section: General Considerationmentioning

confidence: 99%

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Bifacial Metasurface with Quadrupole Optical Response

et al. 2015

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We design, fabricate, and characterize a metasurface, whose multipole optical response depends significantly on the illumination direction. The metasurface is composed of gold-nanodisc dimers embedded in glass. In spite of their nanoscale size, the dimers exhibit a dominating electric-currentquadrupole response in a wide range of wavelengths around 700 nm when illuminated from one side, and a primarily electric-dipole response when illuminated from the opposite side. This leads to two consequences. First, the reflection coefficient of the metasurface considerably differs for the two sides of illumination. Second, quadrupole excitation results in a significant local enhancement of both electric and magnetic fields around the dimers. Our experimental spectroscopic data are in good agreement with simulations obtained using a multipole expansion model.

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Section: General Considerationmentioning

confidence: 88%

Section: General Considerationmentioning

confidence: 99%

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Bifacial Metasurface with Quadrupole Optical Response

et al. 2015

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“…Dynamic toroidal dipoles, in contrast to their static counterparts, interact with oscillating electromagnetic fields, and thus contribute to the optical properties of materials across the entire electromagnetic spectrum 3 . However, the inclusion or omission of the dynamic toroidal multipoles from the multipole expansion has been the subject of an on going discussion [46][47][48] , in particular with respect to equivalent descriptions, such as Mie theory 49,50 . We address this in detail in a dedicated section (see tutorial inset II), where we demonstrate that although both the vector spherical harmonic Mie expansion and the (full, including toroidal contributions) charge-current multipole expansion are complete, the toroidal multipoles appear as distinct entities only in the latter.…”

Section: Dynamic Toroidal Multipolesmentioning

confidence: 99%

Electromagnetic toroidal excitations in matter and free space

et al. 2016

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The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion, and optical activity. Toroidal excitations also exist in free-space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal response can have important implications for the fields of photonics, sensing, energy and information. IntroductionThe interactions of electromagnetic radiation with matter underpin some of the most important technologies today -from telecommunications to information processing and data storage; from spectroscopy and imaging to light-assisted manufacturing. Our understanding and description of the electromagnetic properties of matter traditionally involves the concept of electric and magnetic dipoles, as well as their more complex combinations, known as multipoles. Introduced by Maxwell and Lorentz and later refined by Jackson and Landau, this framework, termed the multipole expansion, is central in physics and is being routinely applied in the study of optical, condensed matter, atomic, nuclear phenomena and beyond 1 . Within this framework, electromagnetic media can be represented by a set of point-like multipole sources [2][3][4][5] . The commonly used set of multipoles comprises the electric and magnetic families, which can be represented by oscillating charges and loop currents respectively. Dynamic toroidal multipoles constitute a third independent family of elementary electromagnetic sources, rather than an alternative multipole expansion or higher-order corrections to the conventional electric and magnetic multipoles (see tutorial inset I).Introduced in 1958 by Y. B. Zeldovich, toroidal moments have been considered in systems of toroidal topology (see Fig. 1) and studied in the context of nuclear 6 , atomic 7 , and molecular physics 8 , classical electrodynamics 9,10 , and solid state physics 3 . In the field of electromagnetism, in particular, a number of works have led to the development of a complete theoretical framework for toroidal electrodynamics [11][12][13][14][15] and the prediction of exotic effects, including dynamic non-radiating charge current configurations 10 and non-reciprocal interactions 9 . Following recent experimental observations of toroidal contributions in the response of materials across the electromagnetic spectrum, dyn...

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“…1(a). The multipole expansion of Q sca , calculated by applying the method in [19], is also shown in Fig. 1(a).…”

Section: Design Of Algaas Nanoantennasmentioning

confidence: 99%

Enhanced second-harmonic generation from magnetic resonance in AlGaAs nanoantennas

et al. 2015

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Abstract:We designed AlGaAs-on-aluminium-oxide all-dielectric nanoantennas with magnetic dipole resonance at near-infrared wavelengths. These devices, shaped as cylinders of 400nm height and different radii, offer a few crucial advantages with respect to the silicon-on-insulator platform for operation around 1.55μm wavelength: absence of two-photon absorption, high χ (2) nonlinearity, and the perspective of a monolithic integration with a laser. We analyzed volume χ (2) nonlinear effects associated to a magnetic dipole resonance in these nanoantennas, and we predict second-harmonic generation exceeding 10 −3 efficiency with 1GW/cm 2 of pump intensity.

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Electromagnetic multipole theory for optical nanomaterials

Cited by 340 publications

References 10 publications

Bifacial Metasurface with Quadrupole Optical Response

Bifacial Metasurface with Quadrupole Optical Response

Electromagnetic toroidal excitations in matter and free space

Enhanced second-harmonic generation from magnetic resonance in AlGaAs nanoantennas

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