On-axis beam extinction through diffraction design and analysis

To optimize the functions of the surface-relief diffractive optical elements for optical limiters and other applications, we present a systematic design and analysis with numerical illustrations of the transmission properties of different surface-relief phase gratings and Fabry-Perot elements. The spectral response and the tolerance of fabrication errors have been included. An analysis shows that the blazed grating and the echelon grating, a multilevel element as a substitute of the blazed grating, can make the on-axis transmittance very low (less than 1% with one grating) over the broad visible band with a large tolerance of fabrication errors. The results are highly significant for the design of optical-limiting devices.     

Transition between diffractive and refractive micro-optical components

Optical components are usually classified into diffractive and refractive elements. In this classification, refractive components are defined as elements that are sufficiently described by geometrical optics. For micro-optics this distinction is very often not applicable. Our goal is to understand which parameters control the transition from elements that can be interpreted as refractive to those elements that are called diffractive. We investigate the linear blazed grating and focus on the wavelength dependence of its properties. For this we adopt an approach well known from the theory of echelette gratings. Our results can easily be transferred to other blazed components, such as Fresnel lenses.     

Characterization of 1D diffractive optical elements by phase inversion

Abstract

We consider the feature dimensions of selected 1D diffractive optical elements (DOE) such that the Fourier transform based Gerchberg-Saxton (GS) iterative scalar phase retrieval algorithm, as calibrated by the results of vector coupled-wave theory, may be used for phase reconstruction. We consider examples only of continuous surface relief and binary (two level, not multi-level) phase-only DOE. Experimental phase distribution for rectangular and blazed gratings with ～ 5λ period agree within experimental limits with scalar theory, and, for the rectangular grating, were shown to agree also with the vector theory. Phase distributions are considered for a continuously varying linear blazed grating with 10λ periodicity, its sampled binary equivalent with minimum feature sizes of 0.1λ and for continuous linear blazed gratings with period varied from ～ 16λ to ～ 2λ. The vector calculations show an average linear dependence of the phase on grating period, but the vector curves are displaced to lower values from the scalar results by an increasing amount as the grating period is reduced. Grating performance is more influenced by the size of the grating period than the subwavelength size of the features in a binary representation. Reasonable equivalence is found in the prediction of correct phase distributions between scalar and vector theory for grating periods > ～ 5λ.     

Static and dynamic Fresnel zone lenses for optical interconnections

Abstract

Static and dynamic Fresnel zone lenses were fabricated in quartz glass by means of microstructuring techniques. Two types of on-axis and offaxis lenses with different focal lengths and of different apertures were designed to operate at wavelengths of 1·52 μm and 633 nm. The blazed profile of the onaxis and off-axis lenses was approximated by up to 16 and up to four discrete levels respectively. Dynamic, that is electrically switchable, lenses have been realized by filling the structured surface with liquid crystal. The optical properties of the lenses, such as the focal spot sizes and the diffraction efficiencies, were investigated. Further the switching behaviour of the dynamic lenses was studied. The design and fabrication of the static and dynamic, on-and off-axis Fresnel zone lenses as well as their optical and switching properties will be presented.     

Achromatic fourier processor with holographic optical lenses

An optical Fourier processor that allows the use of broadband light sources and colored inputs is designed, fabricated, and tested. We develop a design technique based on phase manipulation in the Fourier plane to construct an image processor that provides a chromatically corrected image making use of the good aberrations behavior of symmetrical optical systems. Only a small number of diffractive lenses and one achromatic refractive lens are required to obtain a real image. We verify our design experimentally using holographic lenses, which are presented, owing to their versatility, as a good alternative to expensive blazed diffractive elements.     

Sapphire-GaN-based planar integrated free-space optical system

We report on the design and fabrication of a planar integrated free-space optical system working on the basis of binary phase diffractive optical elements (DOEs) realized in GaN on a sapphire substrate. Group III-nitride/sapphire substrates enable the parallel monolithic integration of passive microoptical elements like lenses and gratings as demonstrated here and optoelectronic devices like light emitters and photodetectors on a single wafer. We present an approach for the simultaneous optimization of the efficiency of transmissive and reflective diffractive optical elements processed in a single lithographic etching step.     

Application of an interferometric phase contrast method to fabricate arbitrary diffractive optical elements

A novel approach for the fabrication of diffractive optical elements is described. This approach is based on an interferometric phase contrast method that transforms a complex object wavefront into an intensity pattern. The resulting intensity pattern is used to expose a photoresist layer on a substrate. After development, a diffractive phase object with an on-axis diffraction pattern is achieved. We show that the interferometric phase contrast method allows a precise control of the resulting intensity pattern. An array of blazed Fresnel lenses is realized in photoresist by using kinoform or detour-phase computer holograms for the interferometric phase contrast setup.     

Multilevel diffractive elements in SiO2 by electron beam lithography and proportional etching with analogue negative resist

Abstract

A negative low-contrast electron beam resist X AR-N 7700/18 is introduced, which provides a nearly linear dose-to-depth curve at electron acceleration voltages below 20 kV, and is therefore an excellent material for fabrication of multilevel diffractive optics. Direct electron beam recording at 12.5kV is used to pattern analogue surface profiles in this resist, and proportional reactive ion etching (RIE) is employed to transfer the profile into the SiO₂ substrate. It is shown that errors in resist-profile scale can be corrected by proper adjustment of the radio-frequency power or chamber pressure in RIE. The reproducibility of the profile scale is better than 2%. Transmission-type blazed gratings, array illuminators, and pattern projection elements are demonstrated.     

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.     

Gray-scale masks for diffractive-optics fabrication: I. Commercial slide imagers

Fabrication of diffractive optics with binary masks requires multiple photolithographic processes to produce high-efficiency elements. Alignment or etching errors at any stage of fabrication decrease the efficiency of the element. We developed an easily accessible procedure that reduces fabrication complexity and costs by using a single gray-scale mask. The gray-scale patterns are generated by commercial slide imagers and are then photoreduced onto low-contrast film plates. Multiple-level or continuous relief structures (kinoforms) may be constructed by use of the photoreduced gray-scale patterns as lithographic masks. Diffractive-optic lenses and blazed gratings were fabricated in photoresist with this procedure. First-order diffraction efficiencies as high as 85% were measured for the blazed gratings. The advantages and the limitations of this technique are discussed.     

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.     

Fabrication and simulation of diffractive optical elements with superimposed antireflection subwavelength gratings

With the aim of reducing surface reflections and increasing the diffraction efficiency we investigated the superposition of subwavelength phase gratings onto blazed phase gratings. With direct-write electron-beam lithography bare blazed gratings and blazed gratings carrying subwavelength gratings were fabricated and their optical performances compared. For TE polarization the subwavelength-carrying gratings showed a maximum diffraction efficiency of 90.6%, whereas the corresponding maximum value for the bare grating was 86.3%. The experiment was simulated with rigorous diffraction theory.     

Generation and selection of laser beams represented by a superposition of two angular harmonics

Abstract

The properties of fields generated by diffractive phase-only optical elements that generate combinations of two angular harmonic fields with different harmonic indices in Fraunhofer and Fresnel regions are investigated theoretically and experimentally. Camomile shaped diffraction patterns are predicted and observed. It is shown that multi-order diffractive phase elements can be used to both generate these beams and to identify the weights of different angular harmonics in a given incident laser beam.     

Spectral properties of multiorder diffractive lenses

Diffractive lenses have been traditionally designed with the first diffracted order. The spectral characteristics of diffractive lenses operating in higher diffracted orders differ significantly from the first-order case. Multiorder diffractive lenses offer a new degree of freedom in the design of broadband and multispectral optical systems that include diffractive optical elements. It is shown that blazing the surface-relief diffractive lens for higher diffraction orders enables the design of achromatic and apochromatic singlets. The wavelength-dependent optical transfer function and the associated Strehl ratio are derived for multiorder diffractive lenses. Experiments that illustrate lens performance in two spectral bands are described, and the results show excellent agreement with the theoretical predictions.     

A Blazed Holographic Concave Grating for Monochromators

Abstract

The theory of blazed holographic gratings given in a previous paper is applied to the design of a blazed holographic aberration-corrected spherical concave grating. Two solution types are found which cover different ranges of blaze wavelength and aberration. The use of the refractive indices of the substrate, and the medium in front of the photoresist, as optimising parameters is demonstrated. Four ray-traced solution examples are given which include the distributions of blaze angle and wavelength across the grating surface.     

The generation of phase singularities at millimetre wavelengths by the use of a blazed grating

Abstract

A specially configured reflection blazed grating has been designed for operation at millimetre wavelengths to enable the efficient conversion of an incident plane wave into a beam with a phase singularity.     

Iterative calculation of diffractive optical elements focusing into a three-dimensional domain and onto the surface of the body of rotation

Abstract

The present paper deals with algorithms for calculating phase diffractive elements aimed at focusing the laser light into three-dimensional domains or onto the surface of the body of rotation. The algorithms are based on the expansion of the desired transmission function of the optical element in terms of a suitable orthogonal basis. The moduli of the expansion coefficients are assumed to be pre-given, whereas the arguments are free parameters of the task. Calculational results of focusing onto the surface of a diverging and a converging cone and onto the surface of a circular cylinder are presented.     

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.     

Harmonic diffractive lenses

The harmonic diffractive lens is a diffractive imaging lens for which the optical path-length transition between adjacent facets is an integer multiple m of the design wavelength λ(o). The total lens thickness in air is mλ(o)/(n - 1), which is m times thicker than the so-called modulo 2π diffractive lens. Lenses constructed in this way have hybrid properties of both refractive and diffractive lenses. Such a lens will have a diffraction-limited, common focus for a number of discrete wavelengths across the visible spectrum. A 34.75-diopter, 6-mm-diameter lens is diamond turned in aluminum and replicated in optical materials. The sag of the lens is 23 μm. Modulation transfer function measurements in both monochromatic and white light verify the performance of the lens. The lens approaches the diffraction limit for 10 discrete wavelengths across the visible spectrum.     

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.