In this article we have considered the situation when a conical wave illuminates an astigmatic lens. Since the task to be solved is to estimate the degree of astigmatism, it is not necessary to determine the total amplitude distribution, it is sufficient to obtain an analytical expression for the field amplitude on the optical axis. On its basis, the boundaries of the shadow region, the number of zeros of intensity and their positions are calculated. The astigmatic coefficient was calculated based on the positions of zeros were found in numerical modeling. The obtained value is quite consistent with the given a priori, which proves the practical applicability of the proposed method.
An investigation of behavior of different types of vortical laser beams in parabolic media widens a set of optical signals used for the telecommunication. Generally, Laguerre-Gauss modes and Bessel ones are regarded as vortical. However, lately researchers examine other types of laser modes which primordially not have the vortical phase singularity (for example, Hermite-Gauss modes or Airy beams) but the singularity is embedded into these beams additionally. The embedding of the vortical phase into an arbitrary laser field may be realized by means of diffractive optic tools. <p> </p>In this paper the transformation of Hermite-Gauss (HG) beams with embedded vortex phase by lens system is investigated theoretically and numerically. A particular attention is attended to the formation of vortex phase singularities in focal area. It is shown, that under appointed relations between HG mode indices and the number of embedded optical vortex, the vortex phase singularity in a focal plane centre may be disappeared. The modeling of the vortical HG beams propagation through a waveguide with a parabolic dependence of the refractive index is implemented on base of the fractional Fourier transformation (FrFT).
We have considered effect of fill factor of circular binary phase grating on intensity distribution in the focal plane. A theoretical analysis is performed in two approaches. One of them allows us to describe the general distribution structure in the focal plane, but it is not suitable for solving the inverse problem. The second approach allows us to explain the fine structure in the intensity maxima corresponding diffraction orders. In particular, this approach explains the possibility of focal ring splitting and allows us to calculate the ratio of the intensities of the two rings. The theoretical calculations and numerical simulation are confirmed by experimental studies. As a result, we have shown the ability to dynamically change the focal structure due to regulation of the grating’s fill factor by means of a spatial light modulator.
An action survey of the optical elements class named by generalized parabolic lens is cited in this paper. The approximately-analytical and numerical analysis of radiation transformation realized by the generalized parabolic lens is described within the limits of different theories: geometrical-optics and wave (paraxial and nonparaxial). The types of refracting aspherical surfaces described with power function are defined on base of the geometrical-optics analysis. The surfaces allow forming characteristic intensity distributions on an optical axis. A paraxial propagation of laser beam with an initial arbitrary power phase function is described with approximate analytical expressions which are agreed qualitatively with the geometrical-optics analysis. The obtained expressions are precise for exponents 1 and 4. A nonparaxial analysis is implemented on base of calculation of the Rayleigh-Sommerfeld integral with qualifying corrections. It is shown that essential growth of intensity in the focus happens at the exponent value from 1 to 2, and the maximal intensity is achieved in a middle of the range.
The paper considers the action of radial-layered lenses with a linear dependence of refractive index. The effect of such lenses depending on their thickness investigated. Numerical simulation based on the finite-difference time-domain method showed the possibility of sub-wavelength focusing singular Gaussian beams through such lenses.
We consider nanofocusing of electromagnetic field in the near-field using sharp metallic and dielectric particles with little radius of surface curvature. An ability of extraordinary field confinement is shown theoretically using integral equations and modelling in Comsol. We have offered the scheme of focusing, which consists of prefocuser and nanofocuser. We consider different composition of prefocuser and nanofocuser. It is shown that a size of a focal spot extremely depends on radius of surface curvature. A refractive axicon can be used as prefocuser and metal or silicon nanoparticle can be used as nanofocuser. If the radius of aluminum spherical nanofocuser is 20 nm the radius of the focal spot is λ 400 . That is smaller than it is achieved in previous works.