Давид Шапиро - Academia.edu (original) (raw)

Papers by Давид Шапиро

Quantum Electronics, 2015

The microwave absorption properties of single-wall carbon nanotubes (SWNCTs) and barium ferrite n... more The microwave absorption properties of single-wall carbon nanotubes (SWNCTs) and barium ferrite nanocrystalline (SWCNT/BaFe 12 O 19) composites with different doping ratios are investigated in the frequency region of 2-18 GHz. The transmission line theory is used to calculate the reflection loss properties, and microwave absorptive mechanism of the SWCNT/BaFe 12 O 19 composites is discussed. The experiment results reveal that the microwave absorption properties of composite are very sensitive to the volume percentage of SWCNTs. Owing to the multiple absorptive mechanisms, the microwave absorption properties of composite are evidently improved. When SWCNTs are doped with 6 vol % of the sample volume, the maximum reflection loss of the SWCNT/BaFe 12 O 19 composite with a 3 mm thickness reaches 30.79 dB at 10.5 GHz, and the range of resonance absorption peak below À10 dB is about 6 GHz.

The results of both analytical and numerical calculations of the light scattering by periodic arr... more The results of both analytical and numerical calculations of the light scattering by periodic array (either finite or infinite) of gold nanocylinders are compared. Surprisingly, the dipole approximation appears to be well applicable down to the distance between the cylinders only twice exceeding their diameter.

Journal of the Optical Society of America B, 2015

A new method to solve the direct Zakharov-Shabat scattering problem is proposed based on the solu... more A new method to solve the direct Zakharov-Shabat scattering problem is proposed based on the solution for coupled Gel'fand-Levitan-Marchenko integral equations. Speedup of computations is achieved by using the Töplitz symmetry of the matrix and an "inner bordering" procedure. The new algorithm was tested on the exactly solvable potential. It is shown that the suggested algorithm significantly surpasses the traditional transfer matrix method in efficiency.

Optoelectronics, Instrumentation and Data Processing, 2009

A one-dimensional inverse scattering problem for the Helmholtz wave equation is considered. The p... more A one-dimensional inverse scattering problem for the Helmholtz wave equation is considered. The problem consists in reconstruction of the refractive index of transparent inhomogeneous media from a specified complex reflection spectrum. A method previously proposed by the authors for reconstruction of the Bragg gratings in the coupled mode approximation is used. Numerical simulations of the inverse scattering problem for the classical Rayleigh layer and for an exponentially smooth transitional layer are performed. The solutions obtained demonstrate the high efficiency of the proposed approach. The accuracy of refractive index reconstruction turns out to be essentially dependent on the degree of layer smoothness. The proposed approach can be applied in problems of the development of coated and interference optics, in synthesis of the Bragg gratings and multilayer optical mirrors, and in radiophysics and acoustics.

Optics Letters, 2011

The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Hel... more The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Helmholtz equation for two dielectrics with flat interface is found and applied for the numerical calculation of the scattered field by the boundary elements method. The Green function keeps close track of scattering, including multiple reflections. The result may be applicable for the data analysis in near-field optical microscopy.

Journal of the Optical Society of America B, 2006

We examine the problem of fiber Bragg grating reconstruction from its reflection coefficient. A d... more We examine the problem of fiber Bragg grating reconstruction from its reflection coefficient. A direct numerical method of solving the Gel'fand-Levitan-Marchenko integral equations for the problem is developed. The method is based on a bordering procedure, Cholesky decomposition, and piecewise-linear approximation. It is tested using high-reflectance homogeneous and hyperbolic secant profiles. The proposed method is shown to concede the popular discrete layer peeling technique in efficiency but surpasses it in accuracy and stability at high reflectance.

Journal of the Optical Society of America B, 2013

Plasmons, which are excited by an evanescent wave and localized in a narrow slit between two meta... more Plasmons, which are excited by an evanescent wave and localized in a narrow slit between two metallic cylinders overlying a dielectric substrate, are found by numerical solution of Maxwell equations. The simulation is carried out by a modified boundary elements method with the Green function for layered medium. For the wave incident from a dielectric to its border near the angle of total internal reflection, the amplitude of plasmon resonance is shown to change sharply with the incidence angle. The effect allows one to tune up the field enhancement factor. The control over plasmons is promising for applications in "smart" adaptive plasmonic optical elements.

Laser Physics, 2009

The similarity between one-dimensional Schrödinger and Helmholtz equations is discussed. The Helm... more The similarity between one-dimensional Schrödinger and Helmholtz equations is discussed. The Helmholtz equation in optical coordinate is shown to reduce to the Schrödinger equation with an effective potential. Two examples of scattering problem are considered: sinusoidal Bragg grating with deep modulation and smooth hyperbolic secant layer. The inverse scattering problem is solved numerically for both cases. For the layer an analytical solution is presented as well. The analysis of the effective potential allows one to qualitatively predict some properties of the reflection spectrum.

Laser Physics, 2007

Page 1. 1317 ISSN 1054-660X, Laser Physics, 2007, Vol. 17, No. 11, pp. 1317–1322. © MAIK “Nauka /... more Page 1. 1317 ISSN 1054-660X, Laser Physics, 2007, Vol. 17, No. 11, pp. 1317–1322. © MAIK “Nauka /Interperiodica” (Russia), 2007. Original Text © Astro, Ltd., 2007. 1. INTRODUCTION Direct and inverse scattering problems for fiber Bragg gratings (FBG) are widely studied in ...

Journal of Optics, 2013

The scattering of electromagnetic wave by a periodic array of nanowires is calculated by the boun... more The scattering of electromagnetic wave by a periodic array of nanowires is calculated by the boundary element method. The method is extended to the infinite grating near the interface between two dielectrics. A special Green function is derived that allows to study the evanescent wave. The Rayleigh-Wood's anomalies are found in the period-to-wavelength dependence of the average Pointing vector in the wave zone. For thin wires the calculations are shown to agree with the twodimensional coupled dipole approximation.

EPL (Europhysics Letters), 2012

Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near th... more Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved numerically by boundary integral equations method. A special Green function was proposed to avoid the infinite integration. A pattern with a circular and a prolate elliptic cylinders, respectively, is suggested to simulate the sample and the probe in near-field optical microscopy. The energy flux in the midplane of the probe-cylinder is calculated as a function of its position.

Journal of the Optical Society of America B, 2007

A new numerical method is developed for solution of the Gel'fand-Levitan-Marchenko inverse scatte... more A new numerical method is developed for solution of the Gel'fand-Levitan-Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it noticeably in accuracy at high reflectance.

The scattering of electromagnetic wave by a periodic array of nanowires is calculated by the boun... more The scattering of electromagnetic wave by a periodic array of nanowires is calculated by the boundary element method. The method is extended to the infinite grating near the interface between two dielectrics. A special Green function is derived that allows to study the evanescent wave. The Rayleigh--- Wood's anomalies are found in the period-to-wavelength dependence of the average Pointing vector in the wave zone. For thin wires the calculations are shown to agree with the two-dimensional coupled dipole approximation.

Journal of the Optical Society of America B, 2006

A numerical method is developed for solution of the Gel'fand-Levitan-Marchenko inverse scattering... more A numerical method is developed for solution of the Gel'fand-Levitan-Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz-Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it noticeably in accuracy at high reflectance.

Laser Physics, 2010

The similarity between one dimensional Schrödinger and Helmholtz equations is discussed. The Helm... more The similarity between one dimensional Schrödinger and Helmholtz equations is discussed. The Helmholtz equation in optical coordinate is shown to reduce to the Schrödinger equation with an effective potential. Two examples of scattering problem are considered: sinusoidal Bragg grating with deep modulation and smooth hyperbolic secant layer. The inverse scattering problem is solved numerically for both cases. For the layer an analytical solution is presented as well. The analysis of the effective potential allows one to qual itatively predict some properties of the reflection spectrum.

A new method to solve the direct Zakharov–Shabat scattering problem is proposed based on the solu... more A new method to solve the direct Zakharov–Shabat scattering problem is proposed based on the solution for coupled Gel'fand–Levitan–Marchenko integral equations. Speedup of computations is achieved by using the Töplitz symmetry of the matrix and an " inner bordering " procedure. The new algorithm was tested on the exactly solvable potential. It is shown that the suggested algorithm significantly surpasses the traditional transfer matrix method in efficiency.

Optics Letters, 2011

The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Hel... more The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Helmholtz equation for two dielectrics with flat interface is found and applied for the numerical calculation of the scattered field by the boundary elements method. The Green function keeps close track of scattering, including multiple reflections. The result may be applicable for the data analysis in near-field optical microscopy.

Quantum Electronics, 2015

The microwave absorption properties of single-wall carbon nanotubes (SWNCTs) and barium ferrite n... more The microwave absorption properties of single-wall carbon nanotubes (SWNCTs) and barium ferrite nanocrystalline (SWCNT/BaFe 12 O 19) composites with different doping ratios are investigated in the frequency region of 2-18 GHz. The transmission line theory is used to calculate the reflection loss properties, and microwave absorptive mechanism of the SWCNT/BaFe 12 O 19 composites is discussed. The experiment results reveal that the microwave absorption properties of composite are very sensitive to the volume percentage of SWCNTs. Owing to the multiple absorptive mechanisms, the microwave absorption properties of composite are evidently improved. When SWCNTs are doped with 6 vol % of the sample volume, the maximum reflection loss of the SWCNT/BaFe 12 O 19 composite with a 3 mm thickness reaches 30.79 dB at 10.5 GHz, and the range of resonance absorption peak below À10 dB is about 6 GHz.

The results of both analytical and numerical calculations of the light scattering by periodic arr... more The results of both analytical and numerical calculations of the light scattering by periodic array (either finite or infinite) of gold nanocylinders are compared. Surprisingly, the dipole approximation appears to be well applicable down to the distance between the cylinders only twice exceeding their diameter.

Journal of the Optical Society of America B, 2015

A new method to solve the direct Zakharov-Shabat scattering problem is proposed based on the solu... more A new method to solve the direct Zakharov-Shabat scattering problem is proposed based on the solution for coupled Gel'fand-Levitan-Marchenko integral equations. Speedup of computations is achieved by using the Töplitz symmetry of the matrix and an "inner bordering" procedure. The new algorithm was tested on the exactly solvable potential. It is shown that the suggested algorithm significantly surpasses the traditional transfer matrix method in efficiency.

Optoelectronics, Instrumentation and Data Processing, 2009

A one-dimensional inverse scattering problem for the Helmholtz wave equation is considered. The p... more A one-dimensional inverse scattering problem for the Helmholtz wave equation is considered. The problem consists in reconstruction of the refractive index of transparent inhomogeneous media from a specified complex reflection spectrum. A method previously proposed by the authors for reconstruction of the Bragg gratings in the coupled mode approximation is used. Numerical simulations of the inverse scattering problem for the classical Rayleigh layer and for an exponentially smooth transitional layer are performed. The solutions obtained demonstrate the high efficiency of the proposed approach. The accuracy of refractive index reconstruction turns out to be essentially dependent on the degree of layer smoothness. The proposed approach can be applied in problems of the development of coated and interference optics, in synthesis of the Bragg gratings and multilayer optical mirrors, and in radiophysics and acoustics.

Optics Letters, 2011

The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Hel... more The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Helmholtz equation for two dielectrics with flat interface is found and applied for the numerical calculation of the scattered field by the boundary elements method. The Green function keeps close track of scattering, including multiple reflections. The result may be applicable for the data analysis in near-field optical microscopy.

Journal of the Optical Society of America B, 2006

We examine the problem of fiber Bragg grating reconstruction from its reflection coefficient. A d... more We examine the problem of fiber Bragg grating reconstruction from its reflection coefficient. A direct numerical method of solving the Gel'fand-Levitan-Marchenko integral equations for the problem is developed. The method is based on a bordering procedure, Cholesky decomposition, and piecewise-linear approximation. It is tested using high-reflectance homogeneous and hyperbolic secant profiles. The proposed method is shown to concede the popular discrete layer peeling technique in efficiency but surpasses it in accuracy and stability at high reflectance.

Journal of the Optical Society of America B, 2013

Plasmons, which are excited by an evanescent wave and localized in a narrow slit between two meta... more Plasmons, which are excited by an evanescent wave and localized in a narrow slit between two metallic cylinders overlying a dielectric substrate, are found by numerical solution of Maxwell equations. The simulation is carried out by a modified boundary elements method with the Green function for layered medium. For the wave incident from a dielectric to its border near the angle of total internal reflection, the amplitude of plasmon resonance is shown to change sharply with the incidence angle. The effect allows one to tune up the field enhancement factor. The control over plasmons is promising for applications in "smart" adaptive plasmonic optical elements.

Laser Physics, 2009

The similarity between one-dimensional Schrödinger and Helmholtz equations is discussed. The Helm... more The similarity between one-dimensional Schrödinger and Helmholtz equations is discussed. The Helmholtz equation in optical coordinate is shown to reduce to the Schrödinger equation with an effective potential. Two examples of scattering problem are considered: sinusoidal Bragg grating with deep modulation and smooth hyperbolic secant layer. The inverse scattering problem is solved numerically for both cases. For the layer an analytical solution is presented as well. The analysis of the effective potential allows one to qualitatively predict some properties of the reflection spectrum.

Laser Physics, 2007

Page 1. 1317 ISSN 1054-660X, Laser Physics, 2007, Vol. 17, No. 11, pp. 1317–1322. © MAIK “Nauka /... more Page 1. 1317 ISSN 1054-660X, Laser Physics, 2007, Vol. 17, No. 11, pp. 1317–1322. © MAIK “Nauka /Interperiodica” (Russia), 2007. Original Text © Astro, Ltd., 2007. 1. INTRODUCTION Direct and inverse scattering problems for fiber Bragg gratings (FBG) are widely studied in ...

Journal of Optics, 2013

The scattering of electromagnetic wave by a periodic array of nanowires is calculated by the boun... more The scattering of electromagnetic wave by a periodic array of nanowires is calculated by the boundary element method. The method is extended to the infinite grating near the interface between two dielectrics. A special Green function is derived that allows to study the evanescent wave. The Rayleigh-Wood's anomalies are found in the period-to-wavelength dependence of the average Pointing vector in the wave zone. For thin wires the calculations are shown to agree with the twodimensional coupled dipole approximation.

EPL (Europhysics Letters), 2012

Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near th... more Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved numerically by boundary integral equations method. A special Green function was proposed to avoid the infinite integration. A pattern with a circular and a prolate elliptic cylinders, respectively, is suggested to simulate the sample and the probe in near-field optical microscopy. The energy flux in the midplane of the probe-cylinder is calculated as a function of its position.

Journal of the Optical Society of America B, 2007

A new numerical method is developed for solution of the Gel'fand-Levitan-Marchenko inverse scatte... more A new numerical method is developed for solution of the Gel'fand-Levitan-Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it noticeably in accuracy at high reflectance.

The scattering of electromagnetic wave by a periodic array of nanowires is calculated by the boun... more The scattering of electromagnetic wave by a periodic array of nanowires is calculated by the boundary element method. The method is extended to the infinite grating near the interface between two dielectrics. A special Green function is derived that allows to study the evanescent wave. The Rayleigh--- Wood's anomalies are found in the period-to-wavelength dependence of the average Pointing vector in the wave zone. For thin wires the calculations are shown to agree with the two-dimensional coupled dipole approximation.

Journal of the Optical Society of America B, 2006

A numerical method is developed for solution of the Gel'fand-Levitan-Marchenko inverse scattering... more A numerical method is developed for solution of the Gel'fand-Levitan-Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz-Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it noticeably in accuracy at high reflectance.

Laser Physics, 2010

The similarity between one dimensional Schrödinger and Helmholtz equations is discussed. The Helm... more The similarity between one dimensional Schrödinger and Helmholtz equations is discussed. The Helmholtz equation in optical coordinate is shown to reduce to the Schrödinger equation with an effective potential. Two examples of scattering problem are considered: sinusoidal Bragg grating with deep modulation and smooth hyperbolic secant layer. The inverse scattering problem is solved numerically for both cases. For the layer an analytical solution is presented as well. The analysis of the effective potential allows one to qual itatively predict some properties of the reflection spectrum.

A new method to solve the direct Zakharov–Shabat scattering problem is proposed based on the solu... more A new method to solve the direct Zakharov–Shabat scattering problem is proposed based on the solution for coupled Gel'fand–Levitan–Marchenko integral equations. Speedup of computations is achieved by using the Töplitz symmetry of the matrix and an " inner bordering " procedure. The new algorithm was tested on the exactly solvable potential. It is shown that the suggested algorithm significantly surpasses the traditional transfer matrix method in efficiency.

Optics Letters, 2011

The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Hel... more The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Helmholtz equation for two dielectrics with flat interface is found and applied for the numerical calculation of the scattered field by the boundary elements method. The Green function keeps close track of scattering, including multiple reflections. The result may be applicable for the data analysis in near-field optical microscopy.