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.     

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.     

Optimization design of diffractive phase elements for beam shaping

An improved approach called the weighted YG algorithm for the design of the diffractive phase element (DPE) that implements beam shaping in the fractional Fourier transform domain and free space is presented. Modeling designs of the DPE are carried out for several fractional orders and different parameters of the beam for optimally converting a Gaussian profile into a uniform beam. We found that our algorithm can improve the beam shaping effect, reduce the error function, and increase uniformity of light intensity.     

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.     

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.     

Stray-light effects of diffractive beam-shaping elements in optical microsystems

The use of diffractive beam-shaping elements in hybrid or monolithic microsystems is investigated. Compact optical systems require diffractive structures with small grating periods for creating large deflection angles. Such elements are difficult to fabricate while a low stray-light level is maintained. In addition, because of the small geometrical dimensions and the short propagation lengths in an optomechanical microsystem, any stray light generated by the diffractive structure critically affects the overall optical performance. A model for the estimation of the interference effects between the designed and the unwanted diffraction orders is developed and applied to an example of a collimating diffractive optical element. On the basis of theoretical and experimental results, design rules for the application of diffractive beam-shaping elements in microsystems are derived.     

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。     

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.     

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.     

Comparison of simulated quenching algorithms for design of diffractive optical elements

We compare the performance of very fast simulated quenching; generalized simulated quenching, which unifies classical Boltzmann simulated quenching and Cauchy fast simulated quenching; and variable step size simulated quenching. The comparison is carried out by applying these algorithms to the design of diffractive optical elements for beam shaping of monochromatic, spatially incoherent light to a tightly focused image spot, whose central lobe should be smaller than the geometrical-optics limit. For generalized simulated quenching we choose values of visiting and acceptance shape parameters recommended by other investigators and use both a one-dimensional and a multidimensional Tsallis random number generator. We find that, under our test conditions, variable step size simulated quenching, which generates each parameter's new states based on the acceptance ratio instead of a certain theoretical probability distribution, produces the best results. Finally, we demonstrate experimentally a tightly focused image spot, with a central lobe 0.22-0.68 times the geometrical-optics limit and a relative sidelobe intensity 55%-60% that of the central maximum intensity.     

Analysis and optimization of fabrication of continuous-relief diffractive optical elements

The fabrication of continuous-relief diffractive optical elements by direct laser beam writing in photoresist is analyzed. The main limitation and tolerances are identified, and their influence on optical performance is quantified. Fabricated structures show rounded profile steps resulting from the convolution of the desired profile with the writing beam. This leads to a reduction in diffraction efficiency. Optimization techniques are presented to minimize this effect. Scaling the profile depth by a factor of mu > 1 increases the first-order diffraction efficiency for blazed elements. This method is also applied to suppress the zeroth diffraction order in computer-generated holograms. A nonlinear compensation of the exposure data for the Gaussian beam convolution results in an 18% increase of the diffraction efficiency for a blazed grating with a 10-mum period to a value of 79%.     

Implementation of high-resolution diffractive optical elements on coupled phase and amplitude spatial light modulators

We propose the optical implementation of diffractive optical elements onto electrically addressed liquid-crystal spatial light modulators. We compare the classic implementations onto amplitude-only or phase-only domains with the implementations onto coupled phase and amplitude (spiral) domains. We demonstrate that the coupling between amplitude and phase provides a trade-off between diffraction efficiency and the signal-to-noise ratio in the reconstruction. Furthermore, when investigating the influence of the maximum dephasing on phase domains and spiral domains through the use of optimal trade-off design, we show that phase-only domains with limited maximum dephasing can provide satisfactory performance. Finally, optical implementations are provided.     

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.     

Blazed-binary diffractive elements with periods much larger than the wavelength

Blazed-binary optical elements with only binary ridges or pillars are diffractive components that mimic standard blazed-echelette diffractive elements. We report on the behavior of one-dimensional blazed-binary optical elements with local periods much larger than the wavelength. For this purpose, an approximate model based on both scalar and electromagnetic theory is proposed. The model is tested against electromagnetic-theory computational results obtained for one-dimensional blazed-binary gratings with large periods. An excellent agreement is obtained, showing that the model is able to predict quantitatively the wavelength and the incidence-angle dependences of the diffraction efficiency of blazed-binary structures.     

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.     

On the zero-thickness model of diffractive optical elements

In a recent paper [J. Opt. Soc. Am. A 16, 113 (1999)] a thin-element approximation of diffractive optical elements was used to describe diffraction of oblique incident wave fronts. This expression motivated by a ray optical analysis is shown to be incorrect. I discuss how the thin-element approximation can be generalized to arbitrary diffraction geometries. This includes an intuitive interpretation of the results.     

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.     

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.     

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.     

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.