Design of diffractive optical elements for multiple wavelengths

Diffractive optical elements (DOE) utilize diffraction to manipulate light in optical systems. These elements have a wide range of applications including optical interconnects, coherent beam addition, laser beam shaping and refractive optics aberration correction. Due to the wide range of applications optimal design of DOE has become an important research problem. In the design of the DOEs, existing techniques utilize the Fresnel diffraction theory to compute the phase at the desired location at the output plane. Since this process involves solving nonlinear integral equations, various numerical methods along with robust optimization algorithms have been proposed. However all the algorithms proposed so far assume that the size and the spacing of the elements as independent variables in the design of optimal diffractive gratings. Therefore search algorithms need to be called every time the required geometry of the elements changes, resulting in a computationally expensive design procedure for systems utilizing a large number of DOEs. In this work, we have developed a novel algorithm that uses neural networks with multiple hidden layers to overcome this limitation and arrives at a general solution for the design of the DOEs for a given application. Inputs to this network are the spacing between the elements and the input/output planes. The network outputs the phase gratings that are required to obtain the desired intensity at the specified location in the output plane. The network was trained using the back-propagation technique. The training set was generated by using genetic algorithm approach as described in literature. The mean square error obtained is comparable to conventional techniques but with much lower computational costs.

Modification of the Gerchberg-Saxton algorithm for the generation of specle-reduced intensity distributions of micrometer and submicrometer dimensions

Diffractive optical element (DOE) design techniques can be applied to the generation of pattern recognition filters for optical correlators, in which case the spatial light modulator (SLM) in the filler plane is thought of as a real-time DOE. The designer must first select the desired complex pattern recognition filter and then apply DOE design techniques to map the fully complex function onto the limited dynamic range SLM. To illustrate the procedure, we apply the techniques to the problem of implementing a matched filter with limited dynamic range Fourier plane SLM’s. We use computer simulations to evaluate the effectiveness of the technique. We quantify the performance by measuring the mean squared error between the ideal matched output and output from quantized filters. Numerical simulations indicate that the DOE method yields a significant improvement over direct quantization. The improvement in mean squared error comes, however, at the expense of light efficiency. The DOE technique has been applied to design of matched filters with binary phase, ternary phase, and phase-only SLM’s for coherent as well as incoherent optical correlators. The additional phase freedom in the incoherent design results in improved performance, but incoherent systems are limited to correlation with real positive reference scenes. A proof-of-principle laboratory experiment has been constructed to complement the numerical simulations.

A lot of source shapes have been proposed for resolution enhancement in semiconductor exposure field, and so-called OAI (OAI: Off Axis Illumination) in them improves not only the resolution but also defocus behavior. Such kind of small window illumination was realized aperture filter at first stage but there were issues of efficiency of light source and complex OPC due to higher coherency. The advantages of use DOE (DOE : Diffractive Optical Element ) are not only the flexible illumination shape available but also the controllability of intensity profile in addition to the higher efficiency of light source. However DOE design and fabrication to obtain enough resolution are difficult due to the huge design load and leading-edge fabrication. Not enough design and fabrication error lead unintended intensity distribution, and the distribution degrades the resolution and makes OPC less effective so that photomask specification shall be tighter. In this paper, as one example, dipole source shape named "Soft-Dipole" is optimized considering intensity distribution targeting 90nm with simulator and is estimated the impact to resolution and OPC. Then actual DOE is fabricated for the intended distribution and evaluated the behavior with the simulator of the DOE using captured intensity distribution. The result showed Soft-Dipole illumination had possibilities to reduce OPC load with enough resolution. Then the DOE design, the fabrication and the evaluation are discussed in this paper.

We consider the calculation of a diffractive optical element (DOE) generating a required intensity distribution in a given plane. For the calculation, we propose a version of the supporting quadric method widely used in similar geometrical optics problems. The method is based on minimizing the root-mean-square error in a certain class of functions using a gradient method and leads to a DOE with a quasi-regular surface relief. We derive explicit expressions for the gradient and Hessian of the root-mean-square error, which makes it possible to efficiently apply the gradient method and provides the theoretical basis for using the methods of the second order. The obtained theoretical results are illustrated by a DOE design example.

The design and optimization of meso-scopic diffractive optical elements (DOEs) is complicated by the fact that electromagnetic models of diffraction must be used to accurately analyze the behavior of candidate DOE profiles. Although recent years have seen steady progress in the development of electromagnetic models, in particular those formulated for the analysis of finite and aperiodic DOEs, few of these methods have been applied to DOE synthesis. This is due, in large part, to the computational resources needed to implement electromagnetic models of diffraction. For instance, the time required to analyze a DOE using scalar models is typically on the order of fractions of a second, while that for electromagnetic models ranges from several minutes to a few hours. As a result, optimization algorithms developed for scalar applications are generally of limited value in the electromagnetic domain due to their inability to arrive at an optimal solution in reasonable time frames. As a result, in this paper we present an optimization algorithm developed explicitly for electromagnetic applications.

Generally, uniformity can be improved at the cost of a low diffraction efficiency in the design of diffractive optical elements by the conventional iterative Fourier transform algorithm. This trade-off is a fundamental limitation of the conventional iterative Fourier transform algorithm. However in this letter, a novel iterative Fourier transform algorithm with adaptive regularization parameter distribution for alleviating the trade-off between uniformity and diffraction efficiency and for improving uniformity is devised on the basis of the theoretical analysis of the trade-off property in the conventional iterative Fourier transform algorithm scheme. The validity of the proposed algorithm is proved by numerical experiments.

In this paper, we examine the effect of applying bias phase on the design of diffractive optical elements for two colour far-field pattern formations. We also explain how critical the choice of the two wavelengths on the quality of the generated output patterns and the effect of changing the ratio of the wavelengths.

Diffractive optical elements (DOE) are used for various purposes, such as a beam shaper, beam splitter and so on. In order to design DOEs, iterative Fourier transform algorithm (IFTA) is widely used. IFTA is fast and effective optimization method and can handle large size data. In the IFTA, propagation in the far field and near field is described by Fourier transform and Fresnel transform, respectively. Iterative angular spectrum approach (IASA) is one of iterative methods based on angular spectrum technique. IASA adopt angular spectrum technique as expression of propagation in near field instead of Fresnel transform. Angular spectrum technique is based on scalar diffraction theory and satisfies Helmholtz equation; therefore angular spectrum technique is the accurate method for the calculation of diffraction. We designed a DOE by using IASA and evaluated its diffraction characteristics based on vector diffraction theory. In this paper, we report on the outcome.

Diffractive optical elements (DOEs) can realize beam shaping with higher light efficiency, strong flexibility of diffraction pattern, and is suitable to be used in optical interconnections to split beams. In order to increase the intensity uniformity of the split beams, a hybrid algorithm merging Gerchberg-Saxton (GS) algorithm with gradient method is presented based on the sampling rule different from the existing optimization algorithms. By controlling N extra points with zero amplitude besides the original N sampling points on the input plane, and finally the sampling pitch on the Fourier plane is half of that of the conventional sampling rule. Then the N extra points on the Fourier plane will be controlled. Finally spot array with high intensity uniformity can be realized with the proposed algorithm. Simulation results demonstrate the good performance of the proposed algorithm.

The finite-difference time-domain (FDTD) method as realized in the Yee algorithm is very useful for solving the analytically intractable diffraction problems that arise in the design of diffractive optical elements (DOE). The error, e, of the Yee algorithm is rather large. We introduce a new high accuracy version of the Yee algorithm based on nonstandard finite differences. We have verified its performance by comparing with known analytical solutions. We have used this algorithm to study the near field (0 - 10 wavelengths) diffraction patterns of three binary phase gratings. Grating (1) has a constant period, while grating (2) has a variable one. Grating (3) is generated by interlacing grating (1) with (2). The period of grating (1) is on the order of a wavelength. Some of these computed fields display interesting and possibly useful Fourier spectra.

Artificial intelligence (AI) is transforming diffractive optics development through its advanced capabilities in design optimization, pattern generation, fabrication enhancement, performance forecasting, and customization. Utilizing AI algorithms like machine learning, generative models, and transformers, researchers can analyze extensive datasets to refine the design of diffractive optical elements (DOEs) tailored to specific applications and performance requirements. AI-driven pattern generation methods enable the creation of intricate and efficient optical structures that manipulate light with exceptional precision. Furthermore, AI optimizes manufacturing processes by fine-tuning fabrication parameters, resulting in higher quality and productivity. AI models also simulate diffractive optics behavior, accelerating design iterations and facilitating rapid prototyping. This integration of AI into diffractive optics holds tremendous potential to revolutionize optical technology applications across diverse sectors, spanning from imaging and sensing to telecommunications and beyond.

Using a laser light source in imaging devices provides a wide color gamut, high brightness, resolution, and efficiency. At the same time, it creates a speckle pattern that deteriorates the image quality. This paper is related to the application of the moving binary code diffractive optical element (DOE) for speckle suppression in a laser display. Analytical optimization of DOE parameters is made in this paper. The optimal DOE pitch is found analytically. Limitation of the DOE code length is shown, and the highest possible code length is estimated. Application of the compound Barker code for the DOE design is suggested. As an alternative, the M-sequence and minimum peak side-lobe codes are considered. The expected residual speckle contrast ratio after application of those codes is estimated for the number of codes. A comparison of the different codes is done, and recommendations for speckle suppression DOE design are provided.

The boundary element method (BEM) is a numerical technique to solve the boundary integral for the vector analysis of diffraction.1,2 Boundary integral methods model the interaction between an incident field and a diffractive optical element (DOE) using distributions induced on the surface of the DOE by the incident field. For a conductor the surface distribution is a current and, for a dielectric, it is a polarization field. Re-radiation from the surface distribution, in turn, generates a diffracted field. The objective of the BEM is the determination of the surface distribution given the incident field and DOE.

Phase and intensity control through diffractive optical elements in X-ray microscopy