Polarizability and magnetoplasmonic properties of magnetic general nanoellipsoids

Abstract

An approach to compute the polarizability tensor of magnetic nanoparticles having general ellipsoidal shape is presented. We find a surprisingly excellent quantitative agreement between calculated and experimental magneto-optical spectra measured in the polar Kerr configuration from nickel nanodisks of large size (exceeding 100 nm) with circular and elliptical shape. In spite of its approximations and simplicity, the formalism presented here captures the essential physics of the interplay between magneto-optical activity and the plasmonic resonance of the individual particle. The results highlight the key role of the dynamic depolarization effects to account for the magneto-optical properties of plasmonic nanostructures. ©2013 Optical Society of AmericaOCIS codes: (290.5850) Scattering, particles; (160.1190) Anisotropic optical materials; (160.3820) Magneto-optical materials. References and links1. M. Sandtke and L. Kuipers, "Slow guided surface plasmons at telecom frequencies," Nat. Photonics 1(10), 573-576 (2007). 2. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, "Plasmonic nanostructure design for efficient light coupling into solar cells," Nano Lett. 8(12), 4391-4397 (2008). 3. S. Lal, S. Link, and N. J. Halas, "Nano-optics from sensing to waveguiding," Nat. Photonics 1(11), 641-648 (2007 5333-5338 (2011). 12. J. Chen, P. Albella, Z. Pirzadeh, P. Alonso-González, F. Huth, S. Bonetti, V. Bonanni, J. Åkerman, J. Nogués, P.Vavassori, A. Dmitriev, J. Aizpurua, and R. Hillenbrand, "Plasmonic nickel nanoantennas," Small 7 ( Ration. Mech. Anal. 188(1), 93-116 (2008). 47. W. L. Bragg and A. B. Pippard, "The form birefringence of macromolecules," Acta Crystallogr. 6(11), 865-867 (1953). 48. One should consider also the phase difference due to the incoming light hitting a finite size body. There are several ways to account for this phase difference reported in literature [30,32, 49]. Although, we verified that inclusion of these corrections have negligible effects, and therefore for sake of clarity we neglect them. We point out, in addition, that for the particular geometry used in our experiments, namely perpendicular incidence over flat disks, this phase difference effects are rigorously zero. 385-420 (1904). 60. A. Lakhtakia, "General theory of Maxwell-Garnett model for particulate composites with bi-isotropic host materials," Int. J. Electron. 73(6), 1355-1362 (1992). 61. M. Abe, "Derivation of non-diagonal effective dielectric-permeability tensors for magnetized granular composites," Phys. Rev. B 53(11), 7065-7075 (1996). 62. M. Abe and T. Suwa, "Surface plasma resonance and magneto-optical enhancement in composites containing multicore-shell structured nanoparticles," Phys. 50(15), 950-952 (1987). 64. T. K. Xia, P. M. Hui, and D. Stroud, "Theory of Faraday rotation in granular magnetic materials," J.

Magnetoplasmonic Design Rules for Active Magneto-Optics

“…Comparison of the measured spectra with theoretical calculations show an outstanding agreement (see Figures 2c and 2d). The calculated spectra are obtained by computing the polarizability of an individual nickel nanoparticle (material parameters from reference [43]), taking into account the dynamic depolarization fields, as described in detail in references [38,44]. The nanostructures layer is modelled using a Maxwell-Garnett effective medium approximation (EMA) where the polarizability of the layer is calculated based on the response of the individual nanoparticles and taking into account their density.…”

Effects of a non‐absorbing substrate on the magneto‐optical Kerr response of plasmonic ferromagnetic nanodisks

“…. We calculated the diagonal polarizability tensor elements α ii = [ ϵ m ( ϵ − ϵ m )]/[ ϵ m + N ii ( ϵ − ϵ m )], where ϵ is the electric permittivity of the material of the disk, ϵ m the dielectric constant of the embedding medium and N ii is the depolarizing factor along the i ‐direction, which accounts for the finite size and shape of the disk . To reproduce the experimental extinction efficiency we considered, first, an isolated disk embedded in a medium with an index of refraction n = 1.15, to account for the disks–substrate interface.…”

“…Since now we are dealing with the field reflected by the surface of the effective medium film, the relevant phases to be considered are those of the Fresnel reflectivity coefficients r ss and r ps calculated using the TMM. These coefficients take into account the boundary conditions that the total electric and magnetic fields must fulfill at the air/film and film/air interfaces, besides including the relevant nanodisks polar-izabilities [43]. As a result, the wavelength dependences of f ss and f ps have substantially the same shape of those of f y and f z in the L-MOKE case, and of f y and f x in the P-MOKE case, as they are mainly determined by the corresponding polarizability tensor elements (compare dotted and dashed lines in Fig.…”

“…Purely ferromagnetic nanostructures have received less attention, although they provide an ideal playground for studying effects arising from the excitation of LPRs and the simultaneous presence of MO activity. Indeed, recent experimental and theoretical investigations of the MO Kerr effect in systems made of Ni nanostructures, have shown how the excitation of a LPR can act upon the phase of the reflected light and, thereby, be used to tune the light polarization through the manufacturing of the nanostructures dimension and shape .…”

Coupling phenomena and collective effects in resonant meta-atoms supporting both plasmonic and (opto-)magnetic functionalities: an overview on properties and applications [Invited]

“…In this framework, and thank to the development of simple fabrication routes for the metal nanoparticles (e.g., by colloidal chemistry based on reduction of metal salts [51]) and nanoparticle arrays (e.g., by nanosphere colloidal lithography [52][53][54][55][56]), LSPs have been found to be suitable for a wide range of applications, including subwavelength imaging and superlensing [57 -61], nanolasing [62][63][64], light trapping and concentrators [65][66][67], plasmon-enhanced optical tweezers [68][69][70] supersensitive plasmonic metamaterials sensors [71][72][73][74], improved photovoltaic devices [75] active optical elements [76,77] etc. In this framework, magnetism have emerged as a valuable route to add an extra degree of freedom to plasmonics, since it allows to actively induce significant changes in the optical response of meta-atoms either entirely [78][79][80][81][82][83][84][85]or partially [86][87][88][89][90][91] made of magnetic materials and supporting LSPs (for a detailed overview we refer the reader to the reviews by Maksymov [ 92], and Pineider and Sangregorio [ 93]). More in detail, magnetic materials possess what is called a magneto-optical (MO) activity, arising from spin-orbit coupling of electrons, resulting in a weak magnetic-field i...…”