Diffractive light attenuators with variable transmission

Abstract

A new application of diffractive optical elements (DOEs) for continuous or multistage adjustment of optical radiation intensity is described. The diffractive attenuators are linear or circular gratings (amplitude or phase) with constant period and diffraction efficiency that varies across the grating. The zero order of diffraction is used as the output and transmitted through the grating without angular deviation. The diffractive attenuators, in distinction to conventional analogues, allow one to change the intensity of the light beam according to predetermined function and have no limitations for power of the regulated light beam. These elements can be used in optical systems as a beam splitter with adjusted splitting coefficient. The experimental results on a circular diffractive attenuator fabricated by direct laser writing on a chromium film are presented. The range of transmission variation was 20 times within a 340° angle of attenuator turn. The possibility to use a phase diffractive attenuator as a light radiation modulator for a powerful technological laser is discussed.     

Diffractive,refractive optics or anything more? Comparative analysis and trends of development

Abstract

The development of diffractive and refractive optics from ancient times (2000 years ago) to the present is traced from a theoretical and practical point of view. A comparative analysis of the possibilities of the two fields in optics is presented. The possibility for achromatization and corrections that exceed the boundary of diffractive and refractive optical elements is pointed out.     

Diffractive optical elements with modulated zone sizes

Abstract

The standard design for phase-only diffractive optical elements comprises a transformation of the continuous phase function into a surface relief by means of wrapping the phase into regular intervals of M2π. This results in a structure with diffractive zones aligned in a horizontal plane. We present an alternative design concept with modulated zone sizes leading to non-periodic boundary positions and non-aligned surface structures. The diffractive properties are compared to those of conventional diffractive optical elements. It can be shown that they are fully equivalent for the design wavelength, but exhibit a different spectral behaviour for deviating wavelengths. These properties are exploited for the improvement of the optical performance of blazed gratings and diffractive lenses under conditions of deviating wavelengths. Special emphasis is put on the optimization of the ratio between diffractive efficiencies of the design order and other orders for blazed gratings and focusing diffractive lenses, as well as the suppression of interference effects within Gaussian beams collimated with diffractive lenses.     

Angular Spectrum of Phase-conjugate Field Generated in Four-wave Mixing

Abstract

The phase-conjugate mirror realized by means of degenerate four-wave mixing in a Kerr-like medium is investigated using the angular spectrum representation of interacting fields. The analysed model is based on the nonlinear mixing of two infinite plane pump waves with the spatially limited probe and signal waves. Relations among harmonic components of the probe and signal fields are derived assuming non-depleted pumping and neglecting the evanescent waves. The influence of the injected signal field on the frequency spectrum of the generated phase-conjugate field is also examined.     

Achromatic fan-out diffractive system for white-light free-space optical interconnects

Abstract

A simple and versatile white-light fan-out diffractive system based on the achromatization of the fractional Talbot effect is proposed. This achromatic configuration is able to interconnect a single polychromatic point source with a 2-D array of optoelectronic microdevices with low residual chromatic aberration even for white light. The whole broadband beamsplitter system is formed by two simple diffractive optical elements, a periodic diffractive lenslet array and a diffractive lens, that are made with a direct laser writing technique giving high light efficiency. The focal amplitude distribution corresponding to the lenslet array produces, by free-space propagation, self-replicas with different density of light points. These patterns, in conjunction with the achromatization process carried out by the additional diffractive lens, are, in short, the key to achieving a set of undistorted white-light spots at the output plane with high uniformity and variable separation between them. Experimental results are also shown.     

Design of non-paraxial array illuminators by step-transition perturbation approach

Abstract

We introduce an efficient Fourier-domain formulation of an approximate method to model non-paraxial diffractive elements. The method is based on evaluation of local field perturbations caused by abrupt surface-profile transitions. It facilitates fast parametric optimization of binary and four-level diffractive array illuminators in the non-paraxial domain of diffractive optics. Comparison with rigorous electromagnetic theory of gratings shows that optimization with the perturbation method gives accurate results if the smallest feature size in the surface profile is larger than one wavelength. Some binary designs are demonstrated using electron beam lithography.     

Multi-wavelength optical pickup with diffractive optical elements

Abstract

A novel, to our knowledge, multi-wavelength diffractive optical pickup is presented. The pickup enables multi-focus imaging and increases the data transfer rate considerably. Parallel reading of two or more memory layers is possible. The different spots can be controlled independently. The optical pickup consists of different diffractive optical elements (DOEs). The measured full-width at half-maximum (FWHM) spot intensity for the DOE-pickup is 0.76 μm—close to the diffraction limited predicted value of 0.71 μm—indicating good optical performance. The measured highest diffraction efficiencies of the realized DOEs are about 92%.     

Compensation of beam ellipticity and astigmatism based on holographic diffractive elements recorded onto spherical substrates

Abstract

Edge emitting diode lasers with their divergent, highly elliptical and astigmatic beams in the visible spectrum are widely used in all branches of photonics. Usually the beams must be transformed into circular anastigmatic beams for the majority of applications. Holographic diffractive elements on spherical substrates are devised for transformation of beams to circular collimated beams. An off-axis holographic set-up is used to record diffractive elements into a thin photoresist layer as shallow surface-relief gratings working in reflection mode with curved and chirped grooves. The elements are destined for the diode lasers emitting at a suitable wavelength and with appropriate ellipticity and astigmatism. The performance of the elements is tested on the basis of intensity patterns and the elements produced at a focal plane on their illumination with a collimated expanded beam of a HeNe laser.     

High-order Harmonic Generation During Multiphoton Ionization of Gases

Abstract

We present theoretical work on high-order harmonic generation accompanying multiphoton ionization of atoms in intense laser fields. We first review some elements of the theory of harmonic generation, particularly the limitations imposed by perturbation theory and some aspects of phase-matching at high pump intensities. A new non-perturbative approach to the theory based on the direct numerical solution of the time-dependent Schrödinger wave equation is described.

Selected results of this theory are presented, including: (a) evidence for a plateau of high-order harmonic peak intensities and a relatively abrupt cut-off of this plateau, closely similar to what has been reported experimentally in noble gas atoms, (b) specific predictions for harmonic production by H, He and Xe atoms, and (c) analytical and numerical evidence for the correlation of harmonic production spectra with above-threshold photoelectron spectra under certain circumstances.     

Implementation of ordinary and extraordinary beams interference by application of diffractive optical elements

Abstract

We apply diffractive optical elements in problems of transformation of Bessel beams in a birefringent crystal. Using plane waves expansion we show a significant interference between the ordinary and extraordinary beams due to the energy transfer in the orthogonal transverse components in the nonparaxial mode. A comparative analysis of the merits and lack of diffractive and refractive axicons in problems of formation non-paraxial Bessel beams has shown the preferability of diffractive optics application in crystal optics. The transformation of uniformly polarised Bessel beams in the crystal of Iceland spar in the nonparaxial mode by application of a diffractive axicon is investigated numerically and experimentally.     

Diffractive elements designed to suppress unwanted zeroth order due to surface depth error

Abstract

We consider a design approach to reduce unwanted zero-order intensity due to profile depth error in diffractive elements. Our method is based on addition of local bias phase to a binary element phase, leading to the introduction of a third phase level. We show theoretically and experimentally that gratings obtained with such modifications are more tolerant to profile depth error than conventionally designed binary or multilevel elements, thus reducing the appearance of unwanted zero order.     

Fourier array illuminators with 100% efficiency: Analytical Jones-matrix construction

Abstract

Fourier-type spot-array illuminators are designed for electromagnetic fields in the paraxial domain of diffractive optics. An analytical construction of the periodic, spatially variable Jones matrix is presented, which produces 100% conversion efficiency from an arbitrarily polarized incident plane wave into M × N=2 ^P × 2 ^Q (P and Q are integers) diffraction orders. Such perfect performance is not possible within the scalar theory of paraxial diffractive optics.     

Effect of multiple equidistant imaging: analyzing the techniques of its monochromatic reproduction and the forms of manifestation

Monochromatic imaging systems with spatial-frequency filters in the form of Fabry-Perot interferometers, concentric ring masks, and diffractive multifocal lenses are shown to realize the same effect of multiple equidistant imaging. However, the forms of manifestation of this effect are not identical due to the difference in spectral content of generated wave fields. Self-imaging fields with a discrete angular spectrum inherent in the systems with masks and interferometers are found to comprise a subclass of periodically focused fields with a continuous angular spectrum peculiar to the systems with diffractive multifocal lenses. The advantages of the latter systems are the extremely high total light efficiency and the sharply defined longitudinal localization of generated wave fields, which enhance the brightness of the reproduced images and decreases their parasitic diffraction dispersion, background noise, and blurring.     

High-efficiency production of propagation-invariant spot arrays

Tailoring of the transverse intensity profiles of propagation-invariant optical fields is considered. The design of diffractive elements capable of realizing such fields by Fourier synthesis is discussed. High-efficiency realization of finite-aperture approximations of the constructed fields is demonstrated in a system consisting of two multilevel diffractive elements. The first element is a diffractive toroidal lens, which focuses the incident field into a ring pattern. The second diffractive element, located at the focal plane of the first element, introduces the phase modulation necessary to realize the desired transverse intensity profile behind a separate collimating lens. The influence of the fabrication errors of the diffractive elements on the fidelity of the propagation-invariant spot array is simulated, and system-integration aspects based on substrate-mode planar-integrated optics are considered.     

Elastic Collision Studies in Caesium/noble Gas Systems Using Two-pulse Echoes

Abstract

Measurements are presented of the collisional relaxation of two-pulse echoes on the 455 nm and 459 nm D-lines of atomic caesium perturbed by low pressures of He, Ar and Xe using the echo-polarisation rotation technique, with interpulse times up to approximately 200 ns. The line broadening constants are measured to about 3% and show significant discrepancies with line profile measurements. For τ ? 100ns there is evidence for the diffractive velocity-changing aspects of the collisions. The mean collisional velocity changes and the cross-sections for diffractive velocity-changing collisions are estimated from the data. The results are found to be insensitive to variations of axial magnetic fields and optical densities.     

Diffractive-refractive hybrid doublet to achromatize the human eye

Abstract

In this work, we show the design of a diffractive-refractive hybrid doublet to achromatize the human eye. It takes advantage of the achromatizing properties of diffractive elements combined with conventional optics. The performance of the doublet has been compared with conventional systems, which have more elements. The results show that it is a useful alternative to those systems.     

Importance of Initial Distribution for Iterative Calculation of Quantized Diffractive Elements

Abstract

The significance of the initial distribution for three iterative calculation techniques of diffractive elements; simulated annealing, direct binary search, and Fourier transform algorithm, is investigated. Depending on the initial distributions, convergence problems may occur. Techniques to calculate special initial distributions for the three methods are described: these significantly improve the capabilities of the iterative techniques.     

Rotation of multimode Gauss-Laguerre light beams in free space

An iterative algorithm is presented for calculating diffractive phase optical elements that form light beams which are an effective superposition of a small number of nonradially symmetric Gauss-Laguerre modes with a prescribed energy contribution from each mode. Pis’ma Zh. Tekh. Fiz. 23, 1–6 (September 12, 1997)     

Two-element diffractive systems for generation of Bessel fields

We demonstrate experimentally a combination of two apodizing diffractive elements, which generate nearly propagation-invariant Bessel fields efficiently with almost uniform axial intensity distributions over the specified region recently introduced by two of the present authors. Strongly reduced intensity fluctuations near both ends of the propagation-invariant range are verified. Various design and alignment issues of the two-element systrem are addressed numerically.     

Zeroth-order complex-amplitude modulation with dielectric Fourier-type dififractive elements

Abstract

Diffraction by a lamellar grating with slowly modulated groove width and depth is considered. By mathematical design of the diffractive microstructure the zeroth diffraction order of the carrier grating may be modulated in amplitude and phase and thereby split into some specified on-axis far-zone diffraction pattern. The noise, which in diffractive optics normally appears in the immediate neighbourhood of the signal, is shifted angularly into the surroundings of the higher diffraction orders of the carrier grating. Therefore a large frame of virtually zero intensity can be formed around the original signal without brute force optimization. This is of interest in, for example, several space-invariant optical interconnection and photonic switching schemes that employ diffractive beam-splitter elements.