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.     

Replication of continuous-relief diffractive optical elements by conventional compact disc injection-molding techniques

Continuous-relief diffractive optical elements have been replicated by use of conventional compact disc injection-molding techniques. Two continuous-relief microstructures, a blazed grating and a fan-out element, were chosen to evaluate the replication process. Original elements were fabricated by direct-write electron-beam lithography. Optical measurements and atomic force microscopy were used for investigating the replication fidelity.     

Analysis of multimask fabrication errors for diffractive optical elements

As design algorithms for diffractive optical elements improve, the limiting factor becomes the fabrication process. It is hoped a better understanding of fabrication errors will allow elements with greater tolerance to be designed. This is important for high-power laser fiber coupling, where hot spots lead to failure. We model seven different fan-out gratings applying misetch, misalignment, and feature rounding. Our main findings are that misetch can lead to improved results, misalignment is strongly asymmetric, and both the pi and pi/2 masks can dominate misalignment. Rounding has a r(2) dependence and potentially can be incorporated into the design stage. Finally we present some experimental data for misalignment.     

衍射光学元件灰度掩模板激光制作系统研究

根据灰度掩模的制作理论,提出了由PP8000胶片输出仪、远心成像透镜组、平行准直He-Cd激光器构成的精缩投影曝光灰度掩模制作系统。通过灰度掩模平面不同位置处提供可变的透过率,经一次光刻后得到所需的衍射光学元件。该系统不仅可采用黑白胶片制作高分辨率灰度掩模板,还可根据彩色灰度等效理论,利用彩色等效胶片实现256灰度级的扩展细分,以进一步提高灰度掩模板制作的分辨率。对于16台阶灰度掩模,其分辨率可以从0~255扩展到0~1280灰度级。利用该系统给出了二元光栅精缩后的感光图片。     

Excimer laser micromachining for rapid fabrication of diffractive optical elements

We demonstrate the fabrication of binary, multilevel, and blazed diffractive structures by a fast and flexible direct-write process by using an excimer-laser-based tabletop micromachining workstation with an integrated optical surface profiler.     

Design and fabrication of diffractive optical elements by use of gray-scale photolithography

Diffractive optical elements (DOEs) are key components in the miniaturization of optical systems because of their planarity and extreme thinness. We demonstrate the fabrication of DOEs by use of gray-scale photolithography with a high-energy-beam sensitive glass photomask. We obtained DOE lenses with continuous phase profiles as small as 800 microm in diameter and 5.9 microm in the outermost grating pitch by selecting a suitable optical density for each height level and optimizing the process variables. Microlenses patterned with eight levels and replicated by UV embossing with the polymer master mold showed a diffraction efficiency of 81.5%, which was sufficiently high for the devices to be used as optical pickups. The effects of deviations in diffraction efficiency between the DOE height and profile design were analyzed.     

遗传算法用于衍射光学元件的优化设计

提出了一种基于遗传算法的衍射光学元件优化设计方法;在衍射光学元件设计中遗传算法运行参数对遗传算法性能有一定的影响:采用较大的群体规模,遗传算法越容易获得最优解;交叉算子越大,遗传算法全局搜索能力越强;选择算子对遗传算法的影响不是太大;如果要进一步提高解的精度,可选取较大的终止代数。数值计算结果表明,用遗传算法优化设计的衍射光学元件,其误差小于 5.2%,衍射效率达到 91.2%。遗传算法很适合衍射光学元件的优化设计。     

Photoresist characterization and linearization procedure for the gray-scale fabrication of diffractive optical elements

We present a procedure for the characterization and the linearization of the photoresist response to UV exposure for application to the gray-scale fabrication of diffractive optical elements. A simple and reliable model is presented as part of the characterization procedure. Application to the fabrication of surface-relief diffractive optical elements is presented, and theoretical predictions are shown to agree well with experiments.     

Rapid fabrication of diffractive optical elements by use of image-based excimer laser ablation

We describe a method of fabricating multilevel diffractive optics by excimer laser ablation. A portion of a chrome mask containing many patterns is illuminated by 193-nm laser light and imaged by an objective lens onto a poly(imide) substrate. Ablation of an entire single pattern is achieved in a single laser pulse. Multiple pulses are used to vary the ablation depth, and multiple patterns are used to create a variety of multilevel optics. We have successfully fabricated arrays of eight-level diffractive microlenses with varying focal lengths and decenters. The optics performed with diffraction-limited focusing and near-theoretical diffraction efficiency (92%).     

Genetic local search algorithm for optimization design of diffractive optical elements

We propose a genetic local search algorithm (GLSA) for the optimization design of diffractive optical elements (DOE's). This hybrid algorithm incorporates advantages of both genetic algorithm (GA) and local search techniques. It appears better able to locate the global minimum compared with a canonical GA. Sample cases investigated here include the optimization design of binary-phase Dammann gratings, continuous surface-relief grating array generators, and a uniform top-hat focal plane intensity profile generator. Two GLSA's whose incorporated local search techniques are the hill-climbing method and the simulated annealing algorithm are investigated. Numerical experimental results demonstrate that the proposed algorithm is highly efficient and robust. DOE's that have high diffraction efficiency and excellent uniformity can be achieved by use of the algorithm we propose.     

Iterative optimization of diffractive phase elements simultaneously implementing several optical functions

The design of diffractive optical elements that incorporate several optical functions in a single element is discussed. The technique used involves iterative optimization. Aprevious paper is continued, in which initial results with few sampling points were reported. Here new results that involve a large number of sampling points are reported. Because the algorithm is computationally intensive with a large number of data points, the parallel implementation of the algorithm on a MASPAR machine is described. MASPAR is a single-instruction multiple-data machine with 16,384 processors. The computer simulations discussed involve simultaneous wavelength demultiplexing, focusing, and the filtering out of a particular wavelength component. It is shown that satisfactory designs of diffractive optical elements can be achieved by the assignment of only a small number of sampling points on the output plane that adequately specify what is required at each wavelength.     

Computer-generated stratified diffractive optical elements

We present what is to our knowledge a new type of diffractive optical element (DOE), the computer-generated stratified diffractive optical element (SDOE), a hybridization of thin computer-generated DOEs and volume holograms. A model and several algorithms for calculating computer-generated SDOEs are given. Simulations and experimental results are presented that exhibit the properties of computer-generated SDOEs: the strong angular and wavelength selectivity of SDOEs makes it possible to store multiple pages in a computer-generated SDOE, which can be read out separately (multiplexing). The reconstruction of an optimized SDOE has a higher quality than the reconstruction of optimized one-layer DOEs. SDOEs can be calculated to have only one diffraction order.     

Polar coordinate laser pattern generator for fabrication of diffractive optical elements with arbitrary structure

A precision laser pattern generator for writing arbitrary diffractive elements was developed as an alternative to Cartesian coordinate laser/electron-beam writers. This system allows for the fabrication of concentric continuous-relief and arbitrary binary patterns with minimum feature sizes of less than 0.6 mum and position accuracy of 0.1 mum over 300-mm substrates. Two resistless technologies of writing on chromium and on amorphous silicon films were developed and implemented. We investigated limit characteristics by writing special test structures. A 58-mm f/1.1 zone plate written directly is demonstrated at a lambda/50 rms wave-front error corresponding to a 0.06-mum pattern accuracy. Several examples of fabricated diffractive elements are presented.     

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%.     

Efficient optimization of diffractive optical elements based on rigorous diffraction models.

An efficient optimization strategy for the design of diffractive optical elements that is based on rigorous diffraction theory is described. The optimization algorithm combines diffraction models of different degrees of accuracy and computational complexity. A fast design algorithm for diffractive optical elements is used to yield estimates of the optimum surface profile based on paraxial diffraction theory. These estimates are subsequently evaluated with a rigorous diffraction model. This scheme allows one to minimize the need to compute diffraction effects rigorously, while providing accurate design. We discuss potential applications of this scheme as well as details of an implementation based on a modified Gerchberg-Saxton algorithm and the finite-difference time-domain method. Illustrative examples are provided in which we use the algorithm to design Fourier array illuminators.     

Iterative optimization of phase-only diffractive optical elements based on a lenslet array

We describe the design of Fourier-type phase-only array generators. The numerical optimization employs the Fienup algorithm, where the parageometric design of the phase retardation profile, with the form of a lenslet array, is used as the initial guess of the optimization process. This approach provides designs with high performance that can be obtained with comparatively low computing effort. This is particularly true for elements generating large spot arrays. For symmetric reconstruction fields, the optimized phase profile typically has the same symmetry as that for the reconstruction field and can be easily unwrapped.     

Fan-out diffractive optical elements designed for increased fabrication tolerances to linear relief depth errors

The intensity uniformity of the spots generated by fan-out diffractive optical elements (DOEs) (or kinoforms) is often highly sensitive to any fabrication error that leads to a deviation of the surface-relief depth of the DOE from its design value. Many of the fabrication errors, such as those that are due to insufficient control of development or etch rates, increase almost linearly with the desired relief depth in every position of the DOE. We present an algorithm for designing fan-out DOEs with a significantly reduced sensitivity of the intensity uniformity to such errors. The reduced sensitivity can be obtained without reducing the efficiency of the DOE. Experimental results for fabricated DOEs show that reduced sensitivity is also obtained in practice.     

Multilayer technology for diffractive optical elements

The proposed multilayer technology makes it possible to approximate a continuous phase distribution by discrete phase steps. Compared with binary techniques, a higher diffraction efficiency can be achieved. In most known processes a bulk substrate is used and etched directly; therefore it is difficult to control the height of the phase steps. We propose applying layers of a well-known thickness and structuring them with a selective etching process. In this new multilayer process for reflecting elements a system of metal and dielectric layers is used that can easily be produced by standard methods.     

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.     

Asymptotic analysis and design of diffractive optical elements

The problem of light diffraction by a micro-optical diffractive element is investigated. The method of stationary phase is applied to obtain approximate values of the integrals in the Kirchhoff approximation. The accuracy of the asymptotic approximation is studied in detail. As an application, the obtained approximate formulas are used to solve a design problem of constructing a diffractive optical element with a desired intensity distribution.