The magneto-plasmonic response in planar multilayer with prism coupling composed from Fe and Au bilayer supplied by photonic crystal (Ta2O5 / SiO2) is studied. Modeled structure is intended as a sensor unit combining magneto-optical (MO) and surface-plasmon-resonance (SPR) effects. The sensitivity of MO-SPR system by small variations of analyte refractive index is tested to obtain optimal resolution ability.
We demonstrate the model specification of the MO-SPR coupling-prism system consisting of the Ag film deposited between two garnet layers; the water is supposed as an analyte. The bismuth-doped gallium-gadolinium iron garnet offers low optical losses as well as strong MO response from visible to near infrared optical region. We apply two different response functions that detect a change of analyte refractive index that operate either directly with reflectance change at appropriate incidence angle or with the magneto-optically highlighted SP resonance dip shift. Suggested sensitivity criteria lead to the sensitivity about 120 1/RIU or 75 deg/RIU with the resolution of the order 10-5 RIU by experimentally acceptable variation of response factors.
The non-reciprocity of magneto-optical reflection response by surface plasmon excitation in the planar Au/Fe/Au/glass nano-systems with prism coupling is studied. These structures are intended as magnetic field sensor units combining magneto-optical (MO) and surface-plasmon-resonance (SPR) effects. The ability of MO-SPR systems to magnetic field sensing is analysed using incidence-angle-depending response function (Rpp(+) – Rpp(-))/(Rpp (+) + Rpp (-)), where Rpp denotes the reflectance of p-polarized beam; and, the sign in upper index relates to the orientation of external magnetic field. The proposed sensitivity criteria F and K (the magnitude and inflexed tangent of the response function oscillation) are applied in transverse MO configuration. Mathematical model based on the own matrix algorithm is applied to simulate the diffraction response to varying external magnetic field at the wavelength 632.8 nm. Obtained theoretical results are compared with experiments realized using the measuring device Multiskop (Optrel GbR, Germany).
A measurable magneto-optical activity of nanoparticles made out of noble metals is observed when the localized plasmon waves are excited in the presence of external magnetic field. We confirmed these observations for quite general Au nanostructure on SiO2/Si substrate theoretically and by experimental way. The heterogeneous layer is formed as a field of cylindrical or spheroidal nanodots of various size having the same height and parallel symmetry axis. These properties enable to apply the Bruggeman’s model of effective medium approximation, for which the size of dots (height, diameter) and fill-factor of nanodots were specified using the transmission electron microscopy image processing. Actually, this model is extended about the interaction of magnetic dipole moments simulated using discrete dipole approximation via geometrical averaging. Derived computational algorithm leads to better agreement with experimental data in the form of Kerr angles in polar configuration at visible spectral region. Obtained out-puts also illustrate the fact that extinction peak of plasmon excitation is located at the resonance wavelength of permittivity.
The paper is devoted to Au/Fe/Au/glass and Au/Fe/glass structures intended as MO SPR sensor units. The model approach based on matrix algebra is used to describe the response of discussed structures to external magnetic field. The theoretical results are confirmed by experiments realized by Multiscope device. The attention has been focused on a sensitivity of proposed response factors ρ±(Φ) and F to magneto-optical effects. The application of ρ±(Φ) response factor for our structures description is limited. The F factor has practically linear character such as change of external magnetic field and ferromagnetic thin film thickness.
Presented study brings some theoretical results derived for Kretschmann SPR configuration with gold patterned structure
at coupling prism (SF 10 glass). As the analyzed medium, air or water with simulated contamination are considered. The
thickness of Au nano-layer is fixed at 44 nm, its patterning is supposed to have planar or lamellar feature with variable
governing parameters (i.e. period, shape and fill-factor). The reflectivity is calculated for wavelength of 632.8 nm in the
incidence angle interrogation by rigorous coupled wave algorithm (RCWA) implemented in own Matlab code. The
partially new view to sensitivity criteria is applied to optimize SPR systems of various kinds.
In the presented paper we summarize some results obtained by testing the recently prepared mathematical model for an inverse optical scattering problem. The computational scheme is based on the matrix model of the multilayer [1] and implemented in Matlab-code which uses the built-in Nelder-Mead algorithm for non-linear regression.
The characteristic matrix T and total matrix M have been determined for isotropic prism coupling gap and anisotropic
one with magnetic ordering in linear magneto-optical approximation. On the base of these matrices the reflection and
transmission coefficients of structure have been specified. The effect of gap thickness, index of refraction and linear
transverse anisotropy of coupling media is discussed. Special attention is devoted to the ultra-thin approximation.
The parameters of two dispersion models for Si3N4 dots of multilayer 2D grating are established by the fitting procedures. The Gauss-Newton and Levenberg-Marquardt fitting algorithms are compared. Spectral ellipsometric measurements as the resource of experimental data are reported. In the objective function, various weighting coefficients corresponding to ellipsometric angles are tested.
The Kerr reflection is studied on various cases of binary magneto-optical grating with circular dots. Proposed grating schemes correspond to irregular grating preparation. Kerr rotation is calculated using theoretical model based on coupled wave method. Obtained results are compared with experimental data and discussed to find conditions of optimal coincidence.
The coupled wave method (CWM) has been applied to the description of electromagnetic wave propagation in binary optic gratings. The electromagnetic field and the permittivity profile are expanded into two-fold Fourier series. The reflection coefficients of 2D periodical structures have been specified and the ellipsometric angles of discussed shapes have been computed. The theoretical results computed for SiO2 and Si3N4 dots are compared with experimental data obtained for the square silicon nitride dots on the Si substrate. The measurements were performed using computer controlled four zone null ellipsometer in spectral range from 240 nm to 700 nm. The influences of Si02 ultrathin oxidation layer and dot thickness on spectral ellipsometric angles are also discussed.
The prism coupler allows the resonant excitation of leaky modes whose transverse field distribution in the guiding structure is close to that of guided waves. The paper is concentrated on the study of the influence of the associated electromagnetic resonances on the linear response of this distributed coupler while taking into account the width of coupling gap and the induced anisotropy of waveguiding media. The characteristics of prism coupling into anisotropic thin films are calculated by 4×4 matrix algebra.
The extended description of magneto-optical effects in reflection is developed. Two special case are studied -- linear bi-gyrotropic and quadratic gyrotropic Kerr effect in the principal configurations according to magnetization. Obtained polarization states are presented in the form of polarization vectors. The 2D and 3D graphical output is used to the demonstration some important examples.
The theoretical analysis of second-order magneto-optical effects is presented. A material anisotropy is introduced by relative permittivity tensor whose components are expressed using Voigt magneto-optical parameter Q and Lissberger's parameter f. The permeability corresponds to isotropic medium. Three principal configurations are studied according to the magnetization-transversal, polar and longitudinal. The governing wave equation for the field vector leads to four polarization states described by complex polarization vectors. Their components have been derived in closed form. The eignemode polarization states in planar structures with magnetic ordering for the classical materials applied for magneto-optical media are analyzed in detail.
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