Sergey I. Kharitonov

A method of designing diffractive optical elements focusing into plane areas

We propose a numerical method for designing phase function of diffractive optical elements (DOEs) aimed at focusing into a plane area of complex shape. The method is applied to factorable intensity distribution in the domain of focusing and factorable illuminating beam of arbitrary cross-section. The diffraction analysis of a direct problem of focusing into the plane region is carried out. Based on a specially developed software, the numerical experiment was carried out, which allowed us to find that the theoretical power efficiency of typical DOEs is no less than 85%.

Design of diffractive lenses for focusing surface plasmons

We present a method of designing diffractive optical elements for transforming and focusing surface plasmons. The method is based on a phase modulation of the surface plasmon provided by the dielectric block with varying geometric parameters located on the interface. The problem of SP diffraction by a dielectric block is solved using the rigorous coupled wave analysis. We demonstrate that the modulation can be implemented not only by changing the length of the dielectric block at fixed height, but also by changing the height at fixed length as well as by simultaneous changing of both parameters. The height modulation and combined height–length modulation are believed to be considered for the first time. As an example, the design of diffractive elements for focusing surface plasmons is considered. It is demonstrated that combining the height and length modulations allows us to increase the diffraction efficiency by more than 10%.

A DOE to form a line-shaped directivity diagram

Abstract Diffractive optical elements to form one-parameter directivity diagrams are designed using the geometric optics. The field ray structure corresponding to the line-shaped directivity diagram is analyzed and curvilinear coordinates for calculating the eikonal are proposed. A new simplified formula for the eikonal function in the curvilinear coordinates is derived. The calculation of the eikonal function is exemplified by the line-shaped and arc-shaped directivity diagram.

Computer Generated Diffractive Multi-focal Lens

The method has been proposed for computing Fresnel-type multi-focal lenses on the basis of special-type phase nonlinearity. A multi-focal lens is represented as a mathematical superposition of a thin lens and nonlinearity distorted Fresnel lens. Selection of the nonlinearity type is reduced to the problem of the groove form determination for the phase diffraction grating with pre-set energy distribution between orders. In particular, bi-focal lens and seven-focal lens have been investigated.

Designing reflectors to generate a line-shaped directivity diagram

A novel method of designing a mirror surface to generate a directivity diagram represented as a vector function of one argument is presented. A general relationship for the mirror surface for an arbitrary illuminating beam wavefront is derived as an envelope of a parametric family of surfaces. Each surface in the family transforms the input beam into a beam with plane wavefront of desired direction. For the spherical illuminating beam the mirror surface is given as the envelope of the family of rotational paraboloids. The envelope is represented as a family of curves given by the intersections of paraboloids with circular cones of rays from the point source.

Focusators for laser-branding

Abstract A new method is investigated for synthesis of computer-generated optical elements: focusators that are able to focus the radial-symmetrical laser beam into complex focal contours, in particular into alphanumeric symbols. The method is based on decomposition of the focal contour into segments of straight lines and semi-circles, following corresponding spacing out of the focusator on elementary segments (concentric rings or sectors) and solution of the inverse task of focusing from focusator segments into corresponding elements of the focal contour. The results of numerical computing of the field from synthesized focusators into the letters are presented. The theoretical efficiency of the focusators discussed is no less than 85%. The amplitude masks and the results of operational studies of synthesized focusators are presented.

Comparative investigation of nonparaxial mode propagation along the axis of uniaxial crystal

We compare nonparaxial propagation of Bessel and Laguerre–Gaussian modes along the axis of anisotropic media. It is analytically and numerically shown that the nonparaxial laser modes propagating along the crystal axis are periodically oscillating owing to polarization conversion. The oscillation period for Bessel beams is inversely proportional to the square of the spatial frequency of the laser mode and the difference between the dielectric constants of an anisotropic crystal. So, for higher spatial frequency of Bessel beams, we will get shorter period of oscillations. For a linearly polarized light, there is a periodic redistribution of the energy between the two transverse components, and for a beam with the circular polarization, the energy is transferred from the initial beam to a vortex beam and backward. Similar periodic behavior is observed for the high-order in radial index Laguerre–Gaussian beams. However, it is true only at short distances. As the distance increases, the frequency of periodicity slows down and the beam is astigmatically distorted. We show that high-spatial-frequency nonparaxial beams can provide spin-orbit conversion efficiency close to 100% on small distances (tens of microns) of propagation along the axis of uniaxial crystals. It provides an opportunity of miniaturization of mode optical converters.

Application of a pseudogeometrical optical approach for calculation of the field formed by a focusator

The present work deals with the application of pseudogeometric optics techniques to calculating a light field generated by a focusator of laser radiation into the rectangular domain. We have derived an analytical expression for the principal term of the asymptotic expansion in the focal plane including the geometric-optics shadow domain.

An analog of the Rayleigh–Sommerfeld integral for anisotropic and gyrotropic media

In this work, the integral representations of Maxwell’s equations solutions for anisotropic and gyrotropic media with separable longitudinal and transverse components are derived in a complete analytic form. In particular cases, the integral expressions are reduced to an analog of the Rayleigh–Sommerfeld integral.

Synthesis of a binary DOE focusing into an arbitrary curve, using the electromagnetic approximation

We discuss methods for the generation of desired phase distributions based on the representation of DOEs as an array of diffraction gratings with different direction of grooves and different periods. The formulated problem is solved with due regard for the vector character of the electromagnetic radiation.