On-axis diffractive elements with improved signal quality in the presence of fabrication errors and wavelength tolerances

The optical function of diffractive elements is usually strongly dependent on systematic fabrication errors as well as the illumination wavelength which do not only affect the diffraction efficiency but also the intensity distribution in the signal region. In the paper a design and fabrication method for on-axis diffractive elements with significantly improved signal quality in the presence of wavelength changes and fabrication tolerances is discussed. An example of an experimentally realized beam shaper is presented.     

Multilevel phase-only array generators with a trapezoidal phase topology

The implementation of a two-stage design process for the design of diffractive optical elements for array illumination is described. Results are presented for on-axis two-dimensional array illuminators for which this method is used. The final designs are theoretically within 5% of the calculated diffraction efficiency upper bound, and theoretical signal reconstruction error is below 1%. Experimental verification of the design theory is given, with experimental diffraction efficiencies within 4% of design values and signal reconstruction error below 6%.     

Coherent diffractive imaging using short wavelength light sources

Techniques that recover images from diffraction data obtained using coherent short-wavelength light sources are currently under active development for applications in nanotechnology and structural biology. In this review, an outline of paraxial optics is provided in a form that is sufficiently general to incorporate the coherence properties and frequency structure of illumination sources used in diffractive imaging applications. The Fourier phase problem is formulated in the context of imaging algorithms that are designed to obtain uniquely-determined phase distributions from measurements of diffraction data. The properties of several iterative phase retrieval algorithms for both coherent and partially-coherent diffractive imaging applications are presented in a unified formalism, together with a brief discussion of a non-iterative technique. Approaches to diffractive imaging based on Fraunhofer and Fresnel diffraction configurations are compared. Applications are described utilising quasi-monochromatic third-generation synchrotron X-ray sources and polychromatic high-harmonic generation table-top soft X-ray sources. The review concludes with a consideration of proposed applications of diffractive imaging approaches to the determination of biomolecular structures from isolated molecules using fourth-generation X-ray free-electron laser sources.     

Analysis of the influence of the passive facet of blazed transmission gratings in the intermediate diffraction regime

Blazed diffraction gratings are of enormous practical importance for imaging and analyzing hybrid optical systems. The intermediate diffraction regime is characterized by the transition from the scalar to the rigorous electromagnetic theory. An effect known as shadowing occurs and reduces the diffraction efficiency. Based on rigorous calculations for optimized sawtooth-shaped and binary-multilevel blaze profiles, we deduce a semianalytical model describing the shadowing phenomenon for the general case of oblique incidence. We discuss illumination both from air and from the substrate. Though a multilevel blaze possesses a discrete substructure, our shadowing model remains valid, if substructural effects are neglected. We find that electromagnetic effects due to the passive blaze facet lead to the efficiency reduction, and the blazing efficiency shows a linear dependence on the ratio of blaze wavelength to grating period. Our shadowing model is applied to predict the performance of a Littrow-like blazing condition in transmission geometry as, e.g., for a diffractive solid immersion lens.     

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.     

Design of a Binary Grating with Subwavelength Features that Acts as a Polarizing Beam Splitter

A binary diffractive optical element, acting as a polarizing beam splitter, is proposed and analyzed. It behaves like a transmissive blazed grating, working on the first or the second diffraction order, depending on the polarization state of the incident radiation. The grating-phase profile required for both polarization states is obtained by means of suitably sized subwavelength groups etched in an isotropic dielectric medium. A rigorous electromagnetic analysis of the grating is presented, and numerical results concerning its performances in terms of diffraction efficiency as well as frequency and angular bandwidths are provided.     

基于DILL模型的SU8厚胶曝光仿真

基于DILL经典曝光模型,对其分别在深度轴和时间轴上进行扩展:在深度轴上,以基尔霍夫衍射公式为基础,引入复折射率,利用光束传输法的思想计算了某曝光时刻下胶体内部的光场分布;在时间轴上,分析SU8光刻胶的特点及曝光反应过程,建立合适的光交联反应动力学模型,计算不同曝光时刻下的光场分布,通过整个曝光模型的建立,最终给出一定曝光时间后的光场分布;结果表明,在曝光阶段,胶内深层光场整体分布随时间变化不大,曝光时间对曝光阶段光场分布的影响较小,这种影响将在后烘阶段得以放大.     

Diffractive variable beam splitter: optimal design

The analytical expression of the phase profile of the optimum diffractive beam splitter with an arbitrary power ratio between the two output beams is derived. The phase function is obtained by an analytical optimization procedure such that the diffraction efficiency of the resulting optical element is the highest for an actual device. Comparisons are presented with the efficiency of a diffractive beam splitter specified by a sawtooth phase function and with the pertinent theoretical upper bound for this type of element.     

Diffractive phase elements for pattern formation: phase-encoding geometry considerations

Space-invariant, multilevel, diffractive phase elements are designed for large-scale pattern-formation tasks. The importance of the design algorithm and the phase-encoding geometry of the diffractive element is discussed with regard to the performance of both on- and off-axis reconstruction, notably for pixelated gratings. A new phase-encoding scheme is presented that results in an increase of the diffraction efficiency for the off-axis case.     

Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display

We present an analysis of the diffraction efficiency of diffractive lenses displayed on spatial light modulators that depends on the modulation response of the display. An ideal display would produce continuous phase-only modulation, reaching a maximum phase-modulation depth of 2pi. We introduce the concept of modulation diffraction efficiency that accounts for the effect of nonlinearities only in the phase modulation of the display. We review a diffractive model with which to evaluate this modulation efficiency, including modulation defects such as nonlinear phase modulation, coupled amplitude modulation, phase quantization, and a limited modulation depth. We apply this diffractive model to Fresnel lenses and show that these modulation defects produce a lens multiplex effect. Finally we demonstrate that the application of a minimum Euclidean projection principle leads to high modulation diffraction efficiency even if the phase-modulation depth is much less than 2pi. We demonstrate that the modulation efficiency can exceed 90% for a modulation depth of 1.4pi and can exceed 40% (the equivalent for a binary phase element) for a modulation depth of only 0.7pi. Experimental results from use of a twisted nematic liquid-crystal display are presented to confirm these conclusions.     

Design of space-variant diffractive polarization elements

Improved diffraction efficiencies can be obtained in the paraxial domain of diffractive optics by considering light explicitly as an electromagnetic rather than a scalar field because of the extra freedoms provided by the state of polarization. For example, diffractive beam splitters with 100% efficiency are made possible by means of space-variant subwavelength-carrier surface-relief elements. Some aspects of the general design theory of polarization-modulating elements for vector fields, including design freedoms and constraints, are presented. Upper bounds of diffraction efficiency are derived and compared with those for the scalar case. Iterative design algorithms are developed. Several design examples with different constraints are presented, and the effects of replacing continuous-fringe structures by pixel structures containing locally linear gratings are evaluated.     

Single-point diamond turning and replication of visible and near-infrared diffractive optical elements

High-fidelity diffractive surfaces have been generated with single-point diamond-turning techniques. A key to the success of this technique is the ability to shape the diamond tool tip to provide the optimum phase-relief profile, given manufacturing constraints. Replication technology is used to transfer the phase-relief surface into a thin epoxy or photopolymer layer on a glass substrate. Diffraction efficiency results for a wide range of zone widths are presented to provide the reader with a baseline of expected performance for replicated visible and near-infrared diffractive optical elements. In addition, a new method for analyzing diffractive surface structures is presented. The ray-trace algorithm quickly provides accurate results of predicted diffraction efficiency for arbitrary zone profiles, which is extremely valuable in predicting manufacturing errors.     

Analysis of blazed diffractive optical elements formed with artificial dielectrics

A new hybrid method for the analysis of diffractive optical elements, which combines fully vectorial and scalar theories, is presented. It is suitable for use with elements of arbitrary large zone, even when the local feature size is of the order of the wavelength. To assess its applicability, we have performed cross-checking tests. The model is shown to accurately predict many optical properties of diffractive optical elements based on two-dimensional artificial dielectrics, like the useful energy diffracted into the order of interest or the deterministic loss into high diffraction orders for an illumination with a wavelength different from the design wavelength or for highly oblique incidence.     

Design of diffractive axicons producing uniform line images in Gaussian Schell-model illumination

We present a design method for diffractive axicons in spatially partially coherent Gaussian Schell-model illumination. The method of stationary phase applied to the Fresnel diffraction integral for on-axis intensity leads, on requiring a uniform axial image profile, to a second-order differential equation for the optimal axicon phase function. The first integral can be formally performed, and the phase function is subsequently obtained numerically. The correctness of the synthesized phase profiles is confirmed by numerical simulations using partially coherent Fresnel diffraction theory. The effects of input-beam spot size and coherence width are assessed, and influences of different forms of apodization, including asymmetric functions for narrow incident beams, in annular-aperture diffractive axicons are examined.     

Fabrication of phase masks with variable diffraction efficiency using HEBS glass technology

A new fabrication method of apodized diffractive optical elements is proposed. It relies on using high energy beam sensitive glass as a halftone mask for variable diffraction efficiency phase masks generation in a resist layer. The presented technology is especially effective in mass production. Although fabrication of an amplitude mask is required, it is then repeatedly used in a single shot projection photolithography, which is much simpler and less laborious than the direct variable-dose pattern writing. Three prototypes of apodized phase masks were manufactured and characterized. The main advantages as well as limitations of the proposed technology are discussed.     

Calculation and evaluation of narcissus for diffractive surfaces in infrared systems

In infrared optical systems, the narcissus effect for diffractive surfaces should be calculated with specific diffraction orders based on the diffraction efficiency. It is shown in this work that the diffraction order of maximum diffraction efficiency varies with the change of the incident angle and wavelength of the backward-traced narcissus flux. Meanwhile, yni, which is the paraxial evaluation criterion of narcissus intensity for a refractive surface, is modified considering diffraction when a ray passes through diffractive surfaces, and a practical example has been given. The analysis can be used to calculate and control the narcissus intensity in infrared optical systems with diffractive surfaces.     

Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements

Enhancing the diffraction efficiency of continuous-relief diffractive optical elements fabricated by direct laser writing is discussed. A new method of zone-boundary optimization is proposed to correct exposure data only in narrow areas along the boundaries of diffractive zones. The optimization decreases the loss of diffraction efficiency related to convolution of a desired phase profile with a writing-beam intensity distribution. A simplified stepped transition function that describes optimized exposure data near zone boundaries can be made universal for a wide range of zone periods. The approach permits a similar increase in the diffraction efficiency as an individual-pixel optimization but with fewer computation efforts. Computer simulations demonstrated that the zone-boundary optimization for a 6 microm period grating increases the efficiency by 7% and 14.5% for 0.6 microm and 1.65 microm writing-spot diameters, respectively. The diffraction efficiency of as much as 65%-90% for 4-10 microm zone periods was obtained experimentally with this method.     

角谱理论用于衍射光学元件数字仿真

本文采用衍射角谱理论对衍射光学元件的光场分布进行数字计算。该理论包括两种表达方式:既可用含有传递函数的等式表达,也可用含有点扩散函数的等式表达。这两种计算方法在本质上是一致的。然而,在MATLAB计算过程中,它们又具有不同的适用条件,通过分析,将它们分为近场算法和远场算法,并且展示了它们的计算实例。结果表明,在标量衍射理论成立的条件下,不改变衍射元件抽样间隔和抽样点数,利用这两种算法能够快速、准确计算不同位置处的衍射图样。该方法对衍射光学元件像面光场分布的精确计算具有重要的意义。     

Design and fabrication of a high-efficiency extreme-ultraviolet binary phase-only computer-generated hologram

As the development of extreme-ultraviolet (EUV) lithography progresses, interest grows in the extension of traditional optical components to the EUV regime. The strong absorption of EUV by most materials and its extremely short wavelength, however, make it very difficult to implement many components that are commonplace in the longer wavelength regimes. One such component is the diffractive optical element used, for example, in illumination systems to efficiently generate modified pupil fills. The fabrication and characterization of an EUV binary phase-only computer-generated hologram is demonstrated, allowing arbitrary far-field diffraction patterns to be generated. Based on reflective architecture, the fabricated device is extremely efficient. Based on an identically fabricated null hologram, the absolute efficiency into one diffracted order of 22% has been demonstrated. In the case where axially symmetric diffraction patterns are desired (both positive and negative diffraction orders can be used), the efficiency can be twice as high.     

The Constant-thickness Zone Plate as a Variational Solution

The diffractive properties of constant-thickness zone plates composed of arbitrary materials are presently well known. Less well known, however, is the fact that the constant-thickness zone plate is the best possible profile that can be created for maximizing the throughput diffraction efficiency of a zone plate system which has a certain symmetry constraint imposed on its geometry. The formal statement of this claim is set forth in this Letter as a variational exercise and the derived optimum constant-thickness solutions are shown to hold for materials of arbitrary complex indices of refraction ?.