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Faraday rotation for 17 nm diameter gold NPs, from experiment, and according to the Drude model for the bound electrons, using the Drude fitting parameters of figure 1. The experimental results have been scaled by 1/100 to allow them to be plotted together with the Drude theory. The theory result was obtained with the MG effective medium approach. Faraday rotation angle φ and ellipticity angle 𝒳 have been scaled by B, z, fs, to give Ψ = ϒ + iZ.
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The Faraday rotation in metallic nanoparticles is considered based on a quantum model for the dielectric function ϵ(ω) in the presence of a DC magnetic field B. We focus on effects in ϵ(ω) due to interband transitions (IBTs), which are important in the blue and ultraviolet for noble metals used in plasmonics. The dielectric function is found using...
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Citations
... In other words, to the level of approximation discussed above, the effective particle contributions to the susceptibility are associated with interband transitions of an (effective) and potentially highly doped semiconductor. Wysin et al. [24] have adopted this viewpoint in order to determine the contribution of these interband transitions to the Faraday rotation in metallic nanostructures. The corresponding contribution of the hydrodynamic part has been developed in Ref. [16]. ...
... the matrix element of the electric dipole operator ⃗ d between two Bloch states. For the details of the calculations leading to (4), we refer to the work of Wysin et al. [24]. ...
... Irrespective of this choice, due to the treatment of the EPs as effective two-band semiconductor, we have that the effective Fermi energy represents a fitting parameter that lies between the top of the lower and the bottom of the upper band. Assuming a step function for the occupation of the effective two-band model and further assuming that the corresponding dipole matrix elements and damping constants do not depend on wave vector, Eq. (4) evaluates to (for details of the calculation using the same notation, see Ref. [24]) ...
Efficient modeling of dispersive materials via time-domain simulations of the Maxwell equations relies on the technique of auxiliary differential equations. In this approach, a material’s frequency-dependent permittivity is represented via a sum of rational functions, e.g., Lorentz poles, and the associated free parameters are determined by fitting to experimental data. In the present work, we present a modified approach for plasmonic materials that requires considerably fewer fit parameters than traditional approaches. Specifically, we consider the underlying microscopic theory and, in the frequency domain, separate the hydrodynamic contributions of the quasi-free electrons in partially filled bands from the interband transitions. As an illustration, we apply our approach to gold and demonstrate how to treat the interband transitions within the effective model via connecting to the underlying electronic band structure, thereby assigning physical meaning to the remaining fit parameters. Finally, we show how to utilize this approach within the technique of auxiliary differential equations. Our approach can be extended to other plasmonic materials and leads to efficient time-domain simulations of plasmonic structures for frequency ranges where interband transitions have to be considered.
... Direct FR studies of noble metals are very rare. To best of our knowledge, only two experimental papers are devoted to FR measurements of AuNPs suspension [10,11] and none is devoted to AgNPs suspension. Very recently, invers FR (IFR) of AuNPs suspension was investigated theoretically [12] and experimentally [11,13]. ...
... As one may notice for AuNP with size 40 nm MORD associated with the plasmon band is much better resolved and shaped in comparison to smaller AuNP studied. Our results for size 40 nm are in agreement with data provided, for AuNPs with dimension of D = 17 nm as stabilized aqueous suspension in sodium citrate, by Wysin et al. [10] (note that opposite convention is used by this authors). So, we used AuNPs with size 40 nm to prepare a mixture with AgNPs, although SPR is shifted 10 nm to red side of spectrum, and in discussion of K-K transformation (see below). ...
... Accordingly, in [87], ...
... Hence, the standard momentum operator for the electrons is expressed asp = −i ∇. The kinetic momentum operator for the physical momentum can be put in this form [87]: ...
... , ω g , s, and ∆m represent gap frequency, scaled wave-vector, and orbital angular momentum quantum number, accordingly and are represented as [87]: ...
The study of Plasmonics has been evolutionary and fascinating over the last few decades. This area of research has attracted extensive interest predominantly as a result of the possibility to direct and confine light at the nano-scale level using metallic materials as fundamental building blocks. This provides an explanation of the interaction of light and nano-sized metallic devices. The optical properties of nano-structured systems depend on the collective resonance of conducting electrons which are determined by the geometrical features as well the polarization characteristics of the incident light and frequency. For large systems with size in the order of tens of the size of nano-scale materials, the response has been extensively studied and is now well understood. The response of these large systems can be described using classical Maxwell’s equations with reasonable accuracy. On the other hand, the application of this classical solution to Plasmonic-based nano-particles is severely limited by quantum phenomena such as tunnelling and non-local screening. These quantum effects can neither be described nor explained by the classical method. There is, therefore, the need to understand how the theory of the quantum method can be utilized to describe the
properties of nano-materials. This forms the main focus of this thesis.
... Our calculations predict pronounced macroscopic drift currents that circulate around the exterior of nanoparticles normal to the incident beam, in addition to the coherent solenoid-like motion of all electrons at optical frequency 18 . Moreover, these associated phenomena of the IFE are enhanced in nanoparticles compared with bulk films, due to resonant optical concentration at plasmonic hot spots and, separately, an enhanced Verdet constant resulting from the electronic behaviour of the confined geometry 10,12,14,19 . Indeed, a recent theoretical study using a quantum hydrodynamic model predicted the generation of magnetic moments exceeding 1 μ B per gold atom in 2-nm-diameter Au nanoparticles 13 . ...
Strategies for the ultrafast optical control of magnetism have been a topic of intense research for several decades because of the potential impact in technologies such as magnetic memory1, spintronics2 and quantum computation, as well as the opportunities for nonlinear optical control and modulation3 in applications such as optical isolation and non-reciprocity4. Here we report experimental quantification of optically induced magnetization in plasmonic gold nanoparticles due to the inverse Faraday effect. The induced magnetic moment is large under typical ultrafast pulse excitation (<1014 W m−2 peak intensity), with magnetization and demagnetization kinetics that are instantaneous within the subpicosecond time resolution of our study. Our results support a mechanism of coherent transfer of angular momentum from the optical field to the electron gas, and open the door to all-optical subwavelength strategies for optical isolation that do not require externally applied magnetic fields. Optically induced magnetization is experimentally demonstrated using gold nanoparticles. The inverse-Faraday-effect-enabled magnetization may lead to new types of compact optical isolator.
... It also agrees with that there is transverse spin ( ⊥ = × ) [47] for surface waves which is represented by the elliptical trace of the field vector at local points. Following this, here we define [48] ̂, =̂, ...
Quantum theory of surface plasmons is very important for studying the interactions between light and different metal nanostructures in nanoplasmonics. In this work, using the canonical quantization method, the SPPs on nanowires and their orbital and spin angular momentums are investigated. The results show that the SPPs on nanowire carry both orbital and spin momentums during propagation. Later, the result is applied to the plasmonic nanowire waveguide to show the agreement of the theory. The study is helpful for the nano wire based plasmonic interactions and the quantum information based optical circuit in the future.
... By ignoring the on-site Coulomb interaction between electrons, we aim to see only the effect of confinement to the formation of unconventional plasmons. We can see from dielectric function curve that it has the characteristic of multi-oscillator model [4] and interband transition due to bound charges [5,6,7] as at 0.75 and 1 eV. Intense peak arises from loss function curve shows the characteristic of conventional plasmons due to its correspondence to the point where ε 1 = 0. Other conventional plasmons can also be found at low frequency (0.1 eV and 0.8 eV) as shown in Figure 3. Setting U = 0.5 and 1 eV, resulting in lowering the magnitude of the peaks and slightly shifting the loss function. ...
Recent experimental study on Strontium Niobate Oxide system has revealed unconventional plasmons generated due to confinement by oxygen planes. A phenomenological model accompanied the experimental data on that report has suggested that the confined electrons behave as harmonic oscillators. These motivate us to further study the effect of space confinement to the electrons on the formation of unconventional plasmons theoretically. For this purpose, we propose a method of modeling the generation of the unconventional plasmons in a finite system. The dynamics of correlated electrons in this confined system is described using finite-size 3D Hubbard model that is solved within mean field approximation. We study a hypothetical cubic system that consists of 5x5x5 single-orbital atoms. The calculation is done with and without incorporating the on-site Coulomb repulsion. We also consider both restricted and unrestricted mean field treatments to the calculation. Our dielectric function results show that for restricted mean field with U = 0 eV and unrestricted mean field with U ≤ 2 eV, the system is metal and only two and four unconventional plasmons found respectively. While, for U > 2 eV, it becomes insulator and shows more emergence of unconventional plasmons.
... Faraday rotation is theoretically expected in gold nanoparticles or aggregates [24,25]. A negative peak is predicted and observed, its origin being strongly correlated with the plasmon resonance [26,27]. ...
Gold nanoparticles have been discovered to possess peculiar properties not found in the bulk metal, such as optical, catalytic, or magnetic properties. Whereas some of the properties are well understood, such as the optical ones, the magnetic properties are much more mysterious. This chapter is devoted to the magnetic characterization of nanoparticulate gold samples, using a variety of techniques.
... The Drude model has been used to reveal the essence of plasmon-induced magneto-optical activity of noble metal NPs [11,24]. However, the Drude model does not reproduce the measured dielectric function of bulk noble metals. ...
... In Eqs. (23), (24), and (28), the terms of the second bracket can be obtained from the first one upon η; ξ; μ → −η; −ξ; −μ. The orientational average of σ mag CD is zero, i.e., ...
... The LD and CD spectra depend on the dielectric constant of the host medium [see Eqs. (23), (24), and (28)]. Figures 2(a) and 2(b) depict σ LD and σ CD of a silver dimer as a function of λ for various ε m , respectively. ...
We study the magneto-optical response of planar clusters of hollow silver nanoparticles. We use the coupled-dipole equations to describe the interaction of the electromagnetic wave with particles. The simplest achiral and anisotropic cluster, a dimer, exhibits magnetic-field-induced linear and circular dichroism. For particular directions of the magnetic field and light wave vector, the magnetic circular dichroism of a planar cluster is considerable. We find that the hollow size can be invoked to tailor the overall shape of the spectrum, in particular its peak position, bandwidth, and FWHM.
... The current understanding of interactions of nonmagnetic metal nanocomposites with the electromagnetic (EM) waves has been significantly advanced and enabled new exciting engineering applications mostly in the band of EM spectrum corresponding to the optical frequency range. [1][2][3][4][5][6][7][8][9] EM waves passing through a metal nanoparticle excite the oscillations of the charge carries, plasmons. Plasmon oscillations, in turn, change the properties of EM waves. ...
... Since the imaginary part of l m for the plus-wave is almost zero (Figure 2), only minus-wave will induce the magnetic losses. The magnetic field h m 6 of microwave inside the nanoparticle is determined by Eq. (8). Since the damping coefficient a is unknown for the materials listed in Table I except of cobalt, we consider cobalt as an example and estimate the heat production rate P h k/P 0 induced by the minus-wave. ...
... h m 6 is related to h 0 through Eq. (8) and h 0 is related to P 0 as P 0 ¼ c 0 l 0 h 2 0 =2. As a result, considering a linear polarized microwave which is composed of equal amount of minuswave and plus-wave, the heating rate can be interpreted in terms of P 0 as K T ¼ xP 0 2c 0 qC p Im l m ð Þ 3 2 þ l m 2 : ...
We theoretically study Ferromagnetic Resonance (FMR) in nanocomposites focusing on the analysis of heat production. It is demonstrated that at the FMR frequency, the temperature of nanoparticles can be raised at the rate of a few degrees per second at the electromagnetic (EM) irradiation power equivalent to the sunlight power. Thus, using FMR, one can initiate either surface or bulk reaction in the vicinity of a particular magnetic inclusion by purposely delivering heat to the nanoscale at a sufficiently fast rate. We examined the FMR features in (a) the film with a mixture of nanoparticles made of different materials; (b) the laminated films where each layer is filled with a particular type of magnetic nanoparticles. It is shown that different nanoparticles can be selectively heated at the different bands of EM spectrum. This effect opens up new exciting opportunities to control the microwave assisted chemical reactions depending on the heating rate.
... FR and FE have been studied for inorganic materials such as glasses or materials including paramagnetic ions, 125, 126 metallic nanoparticles, 127,128 semi-conductors, 129 and organic materials such as small molecules, 130 ...
... Wysin et al. further investigated the effect of interband transitions in metallic nanoparticles on their Faraday rotation response. 128 The authors concluded that these transitions need to be included in a full description of the magneto-optical activity of metallic nanoparticles. ...
To achieve the societal and technological ambitions set for nanotechnology in general, multifunctional magnetic-plasmonic nanostructures can be a great asset. Such multifunctional materials, in which magnetic and plasmonic functionalities are combined at the nanoscale, can be used to unravel fundamental interactions between light and magnetism at that same scale. Further, they can also be applied in e.g. biomedicine for cancer therapy, catalysis for improved reaction rates at lower temperatures, sensors for magnetic field strength and miniaturized optical components such as optical isolators.
In the first part of this work we present the calculated optical properties of core-shell magnetic-plasmonic nanospheres and nanorods as a function of nanostructure composition, size, and shape with a focus on biomedical applications. With this knowledge it is possible to rationally design and synthesize structures that possess a plasmon band in the advantageous biomedical near-infrared spectral window region and other optical properties such as scattering and absorption cross sections as desired for potential application in life sciences.
To deal with the disadvantages of previously used synthesis protocols for nanoparticle-based thin film magnetic-plasmonic materials, a novel synthetic protocol was devised. The protocol itself, the resulting materials and their linear, nonlinear and magneto-optical properties are described in the second part of this work.
Using short bifunctional molecular linkers, we produced magnetic-plasmonic nanoparticle multilayers by a novel layer-by-layer (LbL) synthesis on glass substrates. No polymers or polyelectrolytes were required during synthesis. Resulting nanocomposites, incorporating gold, silver and magnetite nanoparticles were homogeneous over a large area, had large nanoparticle filling fractions and showed tunability of the plasmon wavelength over a very broad spectral range by changing composite thickness through the number of added nanoparticle layers.
Theoretical calculations were performed to verify and explain the observed optical properties of these magnetic-plasmonic assemblies. The calculations and the comparison with experimental observations lead us to a more nuanced view of the LbL self-assembly process as a function of layers. Nonlinear optical microscopy images confirmed homogeneity of the sample and the generated nonlinear optical signals. Spectral nonlinear optical measurements showed that gold-magnetite nanoparticle multilayers combine and simultaneously enhances second and third order nonlinear optical processes. Large magneto-optical responses were measured for gold-magnetite composites and the influence of the plasmonic gold nanoparticles was established.
These results show that the developed layer-by-layer synthesis protocol can be used to produce homogeneous thin films of good quality. Advantageous and tuneable optical properties, large magneto-optical responses and the observed nonlinear optical resonance enhancements of such thin films make them attractive candidates for further fundamental research into e.g. magnetoplasmonics and for application in sensors or optical components.
