Nikolay L. Kazanskiy

Design of high-efficient freeform LED lens for illumination of elongated rectangular regions

We propose a method for the design of an optical element generating the required irradiance distribution in a rectangular area with a large aspect ratio. Application fields include streetlights, the illumination of halls or corridors, and so forth. The design assumes that the optical element has a complex form and contains two refractive surfaces. The first one converts a spherical beam from the light source to a cylindrical beam. The second one transforms an incident cylindrical beam and generates the required irradiance distribution in the target plane. Two optical elements producing a uniform irradiance distribution from a Cree® XLamp® source in rectangular regions of 17 m × 4 m and 17 m × 2 m are designed. The light efficiency of the designed optical element is larger than 83%, whereas the irradiance nonuniformity is less than 9%.

Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system

An analysis was performed into the possibility of reducing the lateral size and increasing the longitudinal size of a high-aperture focal system focus using a vortex phase transmission function for different types of input polarisation (including the general vortex polarisation). We have shown both analytically and numerically that subwavelength localisation for individual components of the vector field is possible at any polarisation type. This fact can be important when considering the interaction between laser radiation and materials that are selectively sensitive to different components of an electromagnetic field. In order to form substantially subwavelength details in total intensity, specific polarisation types and additional apodisation of pupil function, such as masking by a narrow annular slit, are necessary. The optimal selection of the slit radius allows balance of the trade-off between focus depth and focal spot size.

Design of DOEs for wavelength division and focusing

We propose a technique for calculating the color separation gratings aimed at separating plane light beams of different wavelengths into different diffraction orders. The technique is based on a special-type optimization criterion. With this criterion, the problem of calculating the piecewise-constant grating profile is reduced to sequentially solving independent problems of optimization of the step heights. We derived an analytical expression for the profile of a color separation grating that generalizes the familiar analytical solutions. The criterion introduced is used to design a diffractive optical element (DOE) that generates required light beams when it is illuminated by different wavelengths. Design of color separation gratings able to separate three and five different wavelengths and DOEs to demultiplex and focus the two- and three-wavelength beams is presented.

Computer-aided design of diffractive optical elements

A number of iterative algorithms for calculating kinoforms are discussed: a multiplicative adaptive algorithm allowing the rate of iterative process to be increased, fast algorithms for interpolating and extrapolating the kinoform phase pixels, an algorithm for calculating kinoforms forming radially symmetrical images and axial light segments, an algorithm for calculating formators of Gauss-Hermite modes in required diffraction orders, and an algorithm for calculating formators of reference wavefronts. The results of computer simulation are given.

Coupled-resonator optical waveguides for temporal integration of optical signals

In this paper, we propose and numerically investigate an all-optical temporal integrator based on a photonic crystal cavity. We show that an array of photonic crystal cavities enables high-order temporal integration. The effect of the value of the cavitys free spectral range on the accuracy of the integration is considered. The influence of the coupling coefficients in the resonator array on the integration accuracy is demonstrated. A compact integrator based on a photonic crystal nanobeam cavity is designed, which allows high-precision integration of optical pulses of subpicosecond duration.

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.

Fibre sensors based on transverse mode selection

Use of diffractive optical elements (DOEs) in fibre sensors is very promising. This work is dedicated to the investigation of dependence of the transverse mode content in step-index fibres on the microbending value by means of diffractive optical elements. We describe the experimental set-up and methods of experimental data processing that afford precise measurements of mode power. The LP mode power dependencies on the fibre microbending value are obtained. The results obtained allow the designing of fibre sensors with advanced characteristics such as the dynamic range and accuracy.

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.

Vortex phase elements as detectors of polarization state

We suggest vortex phase elements to detect the polarization state of the focused incident beam. We analytically and numerically show that only the types of polarization (linear, circular, or cylindrical) can be distinguished in the low numerical aperture (NA) mode. Sharp focusing is necessary to identify the polarization state in more detail (direction or sign). We consider a high NA micro-objective and a diffractive axicon as focusing systems. We show that the diffractive axicon more precisely detects the polarization state than does the micro-objective with the same NA.