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。     

Efficient encoding algorithms for computer-aided design of diffractive optical elements by the use of electron-beam fabrication

One of the general requirements of a computer-aided design system is the existence of efficient (in data size and running time) algorithms that are generally reliable for the broadest range of design instances. The restricted data formats of the electron-beam machines impose difficulties in developing algorithms for the design of diffractive optical elements (DOE's) and computer-generated holograms (CGH's). Issues that are related to the development of CGH algorithms for e-beam fabrication of DOE's and CGH's are discussed. We define the problems the CGH algorithms need to solve, then introduce general curve drawing algorithms for the e-beam data generation of diffractive optical components. An efficient algorithm for general aspherical DOE's is proposed. Actual design and fabrication examples are also presented.     

Comparison of encoding methods for computer-generated diffractive optical elements

Five modern encoding methods for diffractive optical elements are compared in terms of diffraction efficiency for an f/1 focusing element. It is shown that all five produce similar results for a given value of the minimum feature size delta and number of phase levels N when the grating period is larger than N delta. In contrast, when the grating period is smaller than N delta, the analytic quantization method cannot be employed. When this condition is met, it is shown that the radially symmetric iterative discrete on-axis method can result in diffraction efficiencies as much as 30% higher than those obtained with direct sampling. It is also shown that performance advantages of iterative algorithms improve as the target region in the focal plane increases.     

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.     

Analytic design and solutions for resonance domain diffractive optical elements

A model for designing and analyzing complicated surface relief diffractive elements in the resonance domain is developed. It is based on subdividing the complicated diffractive element into many highly efficient local diffraction gratings whose surface relief modulations can be effectively characterized as slanted volume gratings for which closed form analytic solutions exist. The model is illustrated by finding in the resonance domain the local period, effective slant angle, and groove depth at each location on an off-axis cylindrical diffractive lens.     

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.     

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.     

Iterative algorithm for the design of free-space diffractive optical elements for fiber coupling

We present a design method based on the Gerchberg-Saxton algorithm for the design of high-performance diffractive optical elements. Results from this algorithm are compared with results from simulated annealing and the iterative Fourier-transform algorithm. The element performance is comparable with those designed by simulated annealing, whereas the design time is similar to the iterative Fourier-transform method. Finally, we present results for a demanding beam-shaping task that was beyond the capabilities of either of the traditional algorithms. The element performances demonstrate greater than 85% efficiency and less than 2% uniformity error.     

Theories for the design of diffractive superresolution elements and limits of optical superresolution

We suggest using the theory of linear programming to design diffractive superresolution elements if the upper bound of the intensity distribution on the input plane is restricted, and using variation theory of functional or wide-sense eigenvalue theory of matrix if the upper bound of the radiation flux through the input plane is restricted. Globally optimal solutions can be obtained by each of these theories. Several rules of the structure and the superresolution performance of diffractive superresolution elements are provided, which verify the validity of these theories and set some limits of optical superresolution.     

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.     

Optimal design method for multi-layer diffractive optical elements with consideration of antireflection coatings

An optimal design method for multi-layer diffractive optical elements (MLDOEs) is put forward with consideration of antireflection coatings in actual applications of hybrid optical systems. Taking this method into account for optimal design, it can ensure 100% diffraction efficiency at the designed wavelengths and maximum polychromatic integral diffraction efficiency over the whole waveband. In addition, it can be obtained not only for mechanical durability of soft polymers improvements but increase antireflection coatings functions for hybrid optical systems. Finally, an example for optimal design algorithm process and simulation of MLDOEs used in visible waveband is presented. The results show that this optimal method perfects the MLDOEs design on the basic theory with great practicability for MLDOEs design.     

Extended algorithm for the design of diffractive optical elements around the focal plane

We present a multiplane algorithm for three-dimensional uniform illumination. The large-diameter diffractive optical element simulated by this algorithm homogeneously concentrates more than 86.5% of the incident energy into a 200 microm length of columnar space around the focal plane. The intensity profile in the whole space is nearly flattop, and the beam's quality measured by the root mean square is less than 20.6%. The algorithm is very useful if a great deal of tolerance is required for the installation error of the optical system or if it is used for some particular application, such as uniform illumination on an incline plane.     

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%.     

Design of diffractive optical elements for multiple wavelengths

A method for producing diffractive optical elements (DOE's) for multiple wavelengths without chromatic aberration is described. These DOE's can be designed for any distinct wavelength. The DOE's are produced from two different optical materials, taking advantage of their different refractive indices and dispersions.     

Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements

There is a trade-off between uniformity and diffraction efficiency in the design of diffractive optical elements. It is caused by the inherent ill-posedness of the design problem itself. For the optimal design, the optimum trade-off needs to be obtained. The trade-off between uniformity and diffraction efficiency in the design of diffractive optical elements is theoretically investigated based on the Tikhonov regularization theory. A novel scheme of an iterative Fourier transform algorithm with regularization to obtain the optimum trade-off is proposed.     

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.     

Analytic approach for optimal quantization of diffractive optical elements

One of the most important factors that limit the performance of diffractive optical elements (DOE's) is the depth accuracy of the relief structure. A common procedure for fabricating DOE's is the binary optics procedure, in which binary masks are used for the fabrication of a multilevel relief structure. Here an analytic procedure for calculating the optimal depth levels of DOE's, the phase bias, and the decision levels is presented. This approach is based on the minimization of the mean-squared error caused by the quantization of the continuous profile. As a result of the minimization an optimal value for the etching depth of each photolithographic mask is determined. The obtained depth values are, in general, different from the depth values used by the conventional multilevel approach. Comprehensive mathematical analysis is given, followed by several computer simulations that demonstrate the advantages of the proposed procedure.     

Interference effects in far-field diffractive optical elements

The effects of interference between closely packed diffraction orders in the far field are studied for a number of different scalar-domain diffractive optical elements (DOE's). We demonstrate that there are specific order separations that minimize the observed degradation in the far-field output uniformity. Finally, a DOE that is designed to ensure that the order separation lies near one of these minima is compared with a more general design that produces an equivalent far-field output.     

Polarization-multiplexed diffractive optical elements with liquid-crystal displays

We show experimental results for programmable polarization multiplexing of diffractive optical elements (DOEs) onto two liquid-crystal displays (LCDs). The first LCD encodes the two multiplexed phase-only diffractive optical elements. The second LCD acts as a pixelated polarization rotator to change the polarization state for each of these two DOEs. Although the system requires precise alignment, the DOE's and polarization angles are fully programmable.     

Crossed phase gratings with diffractive optical elements

Orienting two identical or complementary diffractive gratings with a small angle between the grating grooves allows a new crossed-grating device to be constructed. This device has an effective profile that varies locally. For understanding the effects of this variation and the diffraction efficiency of the gratings, the local profiles were correlated with the moiré period of the crossed-grating system by use of various techniques. Asymmetric intensity behavior in the first order of the crossed gratings was seen. Effectively, the diffraction efficiency of the crossed gratings yielded a response equivalent to that of a grating with variable blaze that could be useful in optical computing as a passive optical switching device. One of several models is described that creates greater asymmetric behavior.