We describe mathematical tools that enable the reflection of light at a diffraction grating applied on a freeform surface to be modeled. To address the problem, we use an analog of the Kirchhoff's method. By way of illustration, reflection at a diffraction grating applied on a spherical surface is analyzed. To enable the modeling of such systems, the software was developed and numerical study was conducted. The feasibility to generalize the results onto freeform diffractive optical elements is studied.
The comparative modeling of focusing of femtosecond Gaussian and Poissonian pulses was presented in this paper. Poissonian spectral shape pulses, as opposed to the Gaussian-shaped ones, allow to avoid negative frequency components. The spectral properties of pulses for various durations are investigated. Calculations showed that a significant difference between the Gauss and Poisson pulses begins only for very short durations (less than 3 fs). A comparative simulation of the focusing of short pulses, as well as the passage of focused pulses through a binary phase plate, is performed. The calculation was carried out on the basis of solutions of the Maxwell equations by the method of finite differences in the time domain.
We propose a geometrical optics approach to calculating the eikonal function of a light field on the assumption of generating a desired intensity distribution in a given focal plane region. To solve the focusing problem in a more efficient way, we modify a conforming rectangles method used to design diffractive optical elements (DOE) to focus into plane regions. The novelty consists in a technique for reconstructing the eikonal function based on the known ray mapping relation between the DOE points and focal plane points. Results of focusing into a rhomb are presented. Simulation results show high quality of focusing, also corroborating the efficiency of the proposed method.
We propose the design of an information-measuring system for evaluating performance parameters of lighting devices.
The system comprises four basic components: a software-hardware complex for designing lighting devices, an emulator
of natural and technogeneous effects on an optical surface, an optical surface condition analyzer, and a lighting-device
laboratory test unit. With this system, the duration of optical device certification tests can be reduced by several orders of
magnitude when compared to full-scale tests.
We consider a differential approach to solving the problem of diffraction of X-rays by crystals within the scalar theory.
Based on this approach we have obtained Laue classical formulas used in X-ray analysis of crystals. The developed
approach can be used to obtain approximate solutions of the diffraction problem.
The article is devoted to hyperspectrometer modeling based on the use of filters with linearly varying parameters. The point spread function depending on the spectral filter parameters is estimated. The results were obtained by decomposition of the incident radiation on vector Bessel modes. Numerical calculations show that significant deterioration in resolution occurs only in wide-angle optical systems
We derive a general nonparaxial analytical representation of the eikonal function for the design of diffractive optical elements (DOE) producing a line focus. The eikonal is given in special curvilinear coordinates. The eikonal’s calculation, from the condition of focusing into a line with prescribed intensity distribution, is reduced to the solution of a first-order explicit differential equation. We design DOEs and nondiffractive refractive optical elements to generate a line-segment focus and a circular-arc focus. The simulation data demonstrates that the designed optical elements produce high-quality lines.
A method for the design of perfectly conducting multiorder diffraction gratings is proposed. The design uses the Rayleigh method and is based on the gradient search algorithm for optimization of grating structure from the condition of the generation of a desired array of diffraction orders. The developed algorithm is more general and for d >> (lambda) , where d is the grating period and (lambda) is the wavelength of incident light, goes over into the familiar gradient algorithms for designing gratings in the Kirchhoff approximation. The designs of multiorder gratings with equal order intensities are reported with the efficiency of more than 90% and root-mean-square errors of 2 - 7%.
A method for the design of perfectly conducting multiorder diffraction gratings is proposed. The design uses the Rayleigh method and is based on the gradient search algorithm for optimization of grating structure from the condition of the generation of a desired array of diffraction orders. The developed algorithm is more general and for d >> (lambda) , where d is the grating period and (lambda) is the wavelength of incident light, goes over into the familiar gradient algorithms for designing gratings in the Kirchhoff approximation. The designs of multiorder gratings with equal order intensities are reported with the efficiency of more than 90% and root-mean square errors of 2 - 7%.
The present work deals with the application of pseudogeometric optics techniques to calculate a light field generated by a focusator of laser radiation into a 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.
A method to compute diffractive elements focusing in a set of lines located in different focal planes along the optical axis is considered. A phase nonlinearity is applied to the phase function of a focusator in a line. It is proven that the selection of the nonlinearity is reduced to the problem of the phase diffraction grating with pre-set energy distribution in the orders. Combined multi-focal elements to focus in two sets of lines simultaneously are considered as well; the first consists of lines located in one plane and the second of lines located in different focal planes along the optical axis.
A new method is investigated for synthesis of computer-generated optical elements to focusate the radial-symmetrical laser beam into the complex focal contours--in particular, into the alphabetical-digital symbols. The method is based on decomposition of the focal contour by segments of the straight lines and half-circumferences, following corresponding spacing out of the focusator on elementary segments with a ring shape and solution of the inverse task of focusing from focusator segments into corresponding element of the focal contour. It was determined in the computer experiment that the theoretical efficiency of synthesized focusators into the letters is above 85%.
The estimation of performance of computer-generated optical elements (CGOE) at the design stage is the actual task. In this paper the mathematical model of laser beam focusing by CGOE is suggested. On the basis of this model, the following results have been obtained: a numerical method for the diffraction computing of the field at the focal region, and also algorithms and software for investigating diffraction characteristics of focusators within the scope of computer simulation. The estimations of power efficiency, focal line width, and light intensity distribution at a focal region for various types of focusators vs physical parameters, number of samples, and number of quantization levels are obtained as a result of computational experiments. CGOE with an elevated depth of focus and focusator at semi-ring are investigated.