Tatiana I. Kuznetsova

Localization of light energy on the nanometer scale in a silicon cone

The spatial structure of light fields in a metallized cone filled with a medium with complex dielectric function was studied on the basis of the exact solution of the eigenwave problem. It is suggested that silicon can be used as a core of optical probe in the visible spectral region. It is shown that the density of light energy at the output of optical probe can be drastically increased if silicon is used instead of glass fiber.

Subwavelength diameter of light beams in active waveguides

It is shown that there is no frequency cutoff in a uniform cylindrical waveguide containing an amplifying medium. Waves of any frequency grow in the direction of propagation, and for small transverse sections the growth rate is inversely proportional to the waveguide diameter.

Transmission of Electric-Type Waves Through a Subwavelength-Sized Exit Hole of a Metallized Cone

The spatial structure of light waves of the electric type in a cone with perfectly reflecting metal walls is studied. Exact formulas defining dependences of energy densities of various field components inside the cone on the radial coordinate and polar angle are presented. Simple asymptotic expressions for the field components are derived. They are applicable when the distances from the cone vertex significantly exceed the wavelength of the light wave. The behavior of the field near the vertex as a function of its taper angle and the wavelength of the light wave for the fundamental electric-type mode is studied in detail. A theoretical approach for the quantitative description of wave reflection at the interface of the truncated cone and free space is proposed. The reflection effects of light waves in a truncated cone at the exit aperture of the subwavelength cross section are calculated on the basis of this approach. Particular attention has been concentrated on calculations and analysis of the dependences of the transmission coefficient of the truncated cone on the wavelength and geometric parameters of the system. The results obtained cover the spectral region from 400 nm up to 1000 nm and a wide range of cone taper angles and exit aperture diameters up to about 1/20 of the wavelength. The possibility of obtaining a high coefficient of light transmission in a metallized truncated cone is theoretically demonstrated.

Magnetic-Type Waves in a Tapered Waveguide of Subwavelength Cross Section

The characteristics of electromagnetic waves in a narrowing waveguide are investigated. A method for field analysis is developed based on the application of transverse modes parametrically dependent on the longitudinal coordinate. For a circular cross section waveguide, a system of equations for the wave amplitudes is obtained, the waves being coupled owing to a variable tilt of the walls. It is shown that in the adiabatic approximation, there exist independent eigenwaves whose structure reflects the field energy density variation due to the waveguide radius variation. A detailed analytical and numerical investigation of these fields has been carried out for a waveguide with a special profile of “hypergeometric” type. The applicability of the adiabatic approximation is studied and conversion of the fundamental mode into higher-order modes is assessed. The amplitudes of the higher-order modes are obtained using the Green function for ordinary differential equations. The region of the waveguide parameters is found where the higher-order mode amplitudes are not great and the adiabatic approximation is highly accurate. The dependence of the transmittance of a semi-infinite waveguide on the input radiation characteristics is obtained. It is established that the field amplitudes at the waveguide output strongly depend on the wavelength of the input radiation, on its transverse structure, and the waveguide profile steepness. The greatest output fields take place in the case of an abrupt dependence of the waveguide radius on the longitudinal coordinate.

Light Penetration through a Tapered Waveguide

An approximate pattern of calculation of the field behavior in waveguides of variable radius is proposed. It is based on the assumption of a slow dependence of the radius on the longitudinal coordinate and is reduced to the solution of an ordinary differential equation. The dependences of the waveguide transmission on the frequency of radiation, entrance and exit radii, as well as the rate of radius variation along the axis are studied. The analysis is carried out within the range of parameters typical for optical fibers used in optical near‐field microscopy. It is shown that the increase in the rate of radius variation with the longitudinal coordinate will cause the transmission coefficient of the tapered waveguide to increase.

Spectrotemporal technique for enhancement of resolution in studies of ultrashort pulses

A new technique is proposed for the characterization of ultrashort optical pulses. The technique includes a simple mathematical treatment of the time-resolved spectrum of the signal that is obtained using an image converter camera. The theoretical description of the technique and several numerical examples modeling the ultrashort pulse reconstruction are presented. The dependence of the reconstruction result on the noise level is evaluated. It is shown that the temporal resolution of the technique can be up to two orders of magnitude higher than that for the used electro-optic device.

Spectro-temporal expansions in optical measurements and signal reconstruction from spectrograms

A mathematical method of reconstruction of a function from its Gabor transform is described. The reconstruction requires data only on the modulus of the Gabor expansion. An analysis is made of transformations of light signals that are produced in some optical systems including the spectral expansion. It is shown that the combination of these systems with appropriate mathematical processing is able to provide a very high time resolution in the analysis of arbitrary signals.