A. M. Lerer

Full-wave analysis of three-dimensional planar structures

An efficient numerical-analytical approach to the analysis of planar and waveguide three-dimensional structures is presented. To maintain high accuracy and fast convergence of solutions, the technique has been based on Galerkins method in the spectral domain. The following has been achieved: (1) formulation of a diagonalized set of integral equations for problems associated with planar structures on multilayered uniaxial dielectric substrates; (2) development and application of complete orthonormalized sets of basis functions accounting the edge conditions in explicit form; and (3) development of efficient numerical quadratures for evaluating infinite singular integrals and improvement of the convergence of the integrals and series in the matrix elements of the algebraic system. >

Enhanced transmission in microwave arrays of periodic sub-wavelength apertures

Several configurations of aperture arrays have been investigated using a rigorous numerical–analytical technique. The characteristics of optical transmission through a periodic array of sub-wavelength holes in metal films have been simulated and the mechanisms of the transmittance enhancement ar ed iscussed. The effects of topological factors and array arrangement have been explored from the perspective of enhancing microwave transmission through arrays of sub-wavelength apertures. The features and properties of aperture arrays used in quasi-optical filters and wavelength selective structures are presented.

Volume integral method for investigation of plasmonic nanowaveguide structures and photonic crystals

A vector integral–differential equation to describe electromagnetic wave propagation in nanowaveguides and photonic crystals containing thin metal layers is developed. Exact solution of the equation is obtained with the Galerkin method, taking into account the complex dielectric permittivity of metals in the optical range. A simple method for finding complex effective refractive indices for low-loss waveguide structures is developed and proved. Surface plasmon-polariton waves are simulated in the structures under consideration.

Diffraction of electromagnetic waves of optical range on a metallic nanovibrator

A solution of the two-dimensional integro-differential equation describing diffraction of electromagnetic waves on metallic nanovibrators and on nanocrystals coated by a metallic film was obtained. Copper and gold nanoantenna characteristics were studied theoretically in the optical range. It was noted that the dependence of the scattered field on frequency is of a resonant character and the resonant wavelengths of nanovibrators are larger than those of an ideally conducting vibrator of the same size.

Wideband All-Dielectric Diffraction Grating on Chirped Mirror

A method of integral equations (IE) is applied to a simulation of diffraction efficiency (DE) of metal-dielectric and all-dielectric diffraction gratings (DG). Two factors narrowing the spectral band of laser pulse reflection into minus first space harmonics (MFSH) are analyzed. It is found that by using a chirped mirror instead of a multilayer all-dielectric one it is possible to make diffracted spectrum 20-30 nm wider.

The application of integral equations to calculation of diffraction on inhomogeneities in lightguide structures

The numerical code for the simulating of electric fields scattered on two-dimensional bodies of arbitrary shape and either law of nonlinearity is elaborated. In this paper we present results of calculations for cylinders of elliptical cross-section and quadratic nonlinearity law. Due to good convergence of series and integrals it is enough to sum 20-30 terms in series and numerical quadrature to get a deviation up to 0.1%. In this paper we have simulated the power transmitting coefficients for diffraction on: 1) grating made of dielectric rods; 2) dielectric rod set inside of a planar metallic waveguide; 3) dielectric rod situated next to a dielectric planar waveguide layer.

Calculation of periodic metal nanostructures via the method of approximate boundary conditions

Scattering of an H-polarized optical plane wave by a periodic grating of metal strips located on an interface between two dielectrics is analyzed. The scattering problem is solved under the assumption that the material of the strips is characterized by a complex permittivity, which is typical of metals in the optical band. Approximate boundary conditions are used. The results are compared to the data obtained by means of alternative methods.

Solving the problem of diffraction of an optical-band electromagnetic wave by metal nanostructured aperture arrays with the use of the method of impedance boundary conditions

The problem of diffraction of an optical wave by a 2D periodic metal aperture array with square, circular, and ring apertures is solved with allowance for the finite permittivity of a metal in the optical band. The correctness of the obtained results is verified through comparison with experimental data. It is shown that the transmission coefficient can be substantially greater than the corresponding value reached in the case of diffraction by a grating in a perfectly conducting screen.

Electrodynamic analysis of carbon nanotube antenna

The solution of the boundary problem of diffraction and excitation of system of carbon nanotubes-vibrators is reduced to solving of the integral equation with a logarithmic kernel. After regularization, integral equations were solved by means of collocation method. The character of behavior of the current on the vibratorpsilas ends was considered. The existence of resonances at the frequency range 0.1-1.0THz was shown.

All-dielectric diffraction grating for multi-petawatt laser systems

All-dielectric grating with more than 98% efficiency over the reflective band of 40 nm with the central wavelength at 1053 nm is simulated for the angle of incidence 72 degrees. For the grating design we used the fact that chirped mirrors give wider reflective band than usual quarter-wavelength dielectric mirrors. Grating grooves and the very first layer under the grooves in our model is made of fused silica; underneath of the top layer we placed a chirped stack of 13 HfO2/SiO2 layers. Tolerances for groove depth and angle of incidence are estimated, optimal duty-cycle parameter is found out. Electric field distribution inside of the grating is also numerically studied. The model is simulated by two methods: numerical Fourier Modal Method in LightTrans Virtual Lab and semi-analytical Volume Integral Equation Method. The results obtained by both methods show excellent agreement.