The paper considers a method for quantizing the phase of a vortex lens by the defined level which makes it possible to control the generation of diffraction orders (local foci) containing vortex phases. Two-level and three-level quantization examined in detail.
This report presents results for focusing a field with an inhomogeneous polarization distribution: the incident field has elliptical polarization with parameters of the ellipse of polarization depending on the position. We primarily consider the case of fixed value of inclination of the polarization ellipse and the varying ratio of the semi-axes. Calculations were performed using the Richards-Wolf formulas. Results show the ability to obtain various distributions when changing the initial parameters. Special attention is paid to the properties of the Umov-Poynting vector.
The report presents a theoretical and numerical analysis of the sharp focusing of a displaced Laguerre-Gauss single-ring mode with circular polarization based on the Richards-Wolf formulas. Expressions for the amplitude of the field components in the focal plane are obtained, while the case of “+”-polarization is considered in more detail. In addition to the general expression, the formula for intensity along the horizontal axis is given separately. It is more convenient for determining the displacement parameters than tracking them from the intensity pattern. Expressions are given for calculating the displacement value based on the intensity profile of the longitudinal component for large values of the vortex order. It is shown that for explicit asymmetry visualization it is advisable to use modes with a small but non-zero number.
This report theoretically and numerically investigates the properties of autofocusing of chip beams based on a more accurate analytical model. It is shown that the refinement of the model made it possible to obtain a caustic of the second type. At the same time, caustics of the first and second types "do not intersect": in two-parameter beams, they are formed in different ranges of values of the exponent; and in three-parameter ones they are formed in the same range, but they are spatially separated.
We studied the autofocusing properties of chirp beams whose phase has an arbitrary power-law dependence on the radius. Two types of such beams were considered (theoretically and numerically): two-parameter beams corresponding to a generalized lens, and three-parameter beams corresponding to a displaced generalized lens. On the basis of theoretical analysis, the conditions imposed on the parameters of the beams, under which the off-axis caustic is formed, are revealed and the equation of the caustic line is obtained. It is shown how changing the beam parameters affects the autofocusing properties. The results of numerical simulation are consistent with theoretical calculations. Thus, we can form beams with controlled autofocusing properties, which are in demand in various applications of optics and photonics.
In this paper, several methods of forming a spiral intensity distribution are mentioned and it is noted that they mainly form a spiral in the far diffraction zone. To form a spiral intensity distribution in the near zone, the authors propose to illuminate a helical diffractive microaxicon. The results of numerical simulation within the limits of strict electromagnetic theory visually confirm that a spiral structure is formed. In this case, the formation is more qualitative and more reliable compared to the illumination of the binary spiral axicon.
The configurations of rays passing through the axicon are considered, which take into account the presence of both reflected and refracted rays at the boundary of the media. This is important for such values of the angle at the apex of the axicon, when the Fresnel coefficient for the reflected beam is greater than for the refracted one. The passage of rays through the semi-axicon is also considered. An example of quantitative calculation is given, showing that this effect allows forming two divergent conical beams having comparable amplitude at once.
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.
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.
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