In this work we study optical response of noble metal nanoparticles and report how it may be controllably varied over a
wide range of wavelengths. Altering the particle shape and materials we investigate the surface plasmon resonances of
nanostars. To design novel nanostructures possessing diverse optical properties we assemble several plasmonic materials
into a single nanoparticle. With numerical simulation tool based on the spectral boundary integral equation method we
investigate far-field and near-field characteristics of a variety of metal, metal-dielectric and bimetal nanostructures to be
used in a range of applications from disease diagnostics through to the identification of contraband.
Using advanced mathematical techniques for optical computing and combining them with advanced optical engineering
techniques and understanding of physical and chemical processes in plasmonic materials we developed novel boundary
integral equation based numerical simulation tool. The performances of numerical simulation tool were investigated by
means of extensive numerical studies of plasmonic nanostuctures including nanostructures with periodically and
aperiodically spaced nanoparticles embedded in homogenenous medium, isolated homogeneous, layered and
multilayered plasmonic nanoparticles. Selecting the most pormissing particle configurations, we applied the most
efficient hierarchical method to reduce the complexity of calculation schemes for each particular nanostructure
In this work a fully three-dimensional parameterization model for the investigations of gold nanostars by the
ultraspherical Spectral Boundary Integral Equation method has been developed. The set of the numerical results provide
guidelines for a choice of the system parameters for tuning. These can be exploited for new approaches to medical
diagnoses or testing for environmental contaminants.
The work was devoted to the design of advanced plasmonic nanoantennas based on numerical investigation of Surface
Plasmon Polariton resonances in noble metal nanoparticles. Their dependence on the nanoparticle shape and size is
investigated for an efficient manipulation by SPP strength and excitation wavelength. Local near-field plasmon effects
and the impact of SPPs on the directivity of emission in far-field are analyzed simultaneously by means of a boundary
integral equation approach. Various particles including the shapes with gaps and sharp tips were investigated in order to
select the geometries which permit achieving of strong near-field enhancement. The investigation of crescent moon
structures demonstrated the possibility of additional field enhancement because both a gap and sharp tips are realized at
the same time. Analysis of all considered noble-metal nanoparticles revealed a mechanism of efficient manipulation by
SPPs leading to the design of several highly optimized optical nanoantennas.
The optical response of nanostructures that exhibit pronounced plasmonic effects is studied and analyzed. Various
approaches to solve light scattering problems in the time domain and in the frequency domain, using both the domain
and the boundary discretization methods were used. Far-field and near-field characteristics of plasmonic nanostructures
are investigated with several numerical algorithms to study the shape effect and the effects of the illumination angles on
the resonance behavior. Numerical results with high accuracy, reduced complexity and reduced computational time due
to extensive use of semi-analytical solutions are obtained. This set of numerical experiments demonstrates significant
differences in the performances of different numerical methods. We observed that even simple geometries of plasmonic
nanostructures may pose severe problems for various methods. We identify a strong need to select and modify numerical
simulation algorithms according to the plasmonic effects, in addition to the standard selection of numerical method
according to the geometrical settings and length scales.
The optical near field of subwavelength grooves milled in metal surfaces is investigated and channel plasmon polariton
nanoantennas are analyzed with a Spectral Boundary Integral Equation approach. Due to an extensive use of semi-analytical
meshless procedures the numerical simulation tool guaranties the solution with high accuracy and reduced
complexity. The results indicate a strong field enhancement inside the groove and a pronounced dependence of the
antenna characteristics on the groove geometry.
Optical near-field and far-field for coupled plasmonic nanosystems are investigated. Gap plasmon-polaritons are
observed and analyzed with Spectral Boundary Integral Equation based approach. The results indicate pronounced
dependence of the field characteristics on the gap size, the particle shape, the orientation and material properties. The gap
optimization process is performed and the configurations which provide powerful enhancement of the field amplitude
inside the gaps are found. The meshfree procedures of numerical simulation algorithm allow essential flexibility of gap
optimization process in comparison with classical boundary element and finite element based tools. Due to fast
convergence of solution numerical algorithm provides superior accuracy to deal with extremely high field gradients. In
addition reduced complexity and calculation time are guaranteed due to extensive use of Fast Fourier Transforms.
The Spectral Boundary Integral Equation method for the numerical modeling of superlenses formed by metamaterial is
proposed. The corresponding transmission problem is formulated using a classical approach based on layer-potential
technique. The obtained system of integral equations is solved by using the Galerkin's method with approximations
based on spectral harmonics on the unit circle. A singularity subtraction technique is applied to avoid numerical
instabilities caused by the integral equation singularities. The novel idea is the global parameterization of the non-smooth
boundaries of the rods in terms of Fourier series by using a conformal mapping technique. The numerical instabilities
that may be caused by the geometrical singularities of the rods are eliminated. The developed simulation tool based on
this method provides solutions with high accuracy and reduced complexity. These features permit to investigate the
dependence of the lens characteristics on the shape and orientation of its structural details, and their material properties.