Generalized design of diffractive optical elements using neural networks

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

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.

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.

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.

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.

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.

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.

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.

We propose a design method for dense surface-relief diffraction gratings with high efficiency in transmission mode. Closed-form analytical relations between diffraction efficiency, polarization, and grating parameters are derived and verified in the resonance domain of diffraction under general three-dimensional angles of incidence traditionally termed conical mounting. A powerful tool for rigorous design of computer-generated holograms and diffractive optical elements with spectroscopic scale periods is now enabled.

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.

Diffractive optical elements (DOE) play an important role for laser beam shaping in industry, for example in lithography or parallel laser material processing. Typically such applications require high damage threshold and low background illumination (high contrast and efficiency). Usual DOE with binary phase (step-like) profiles are made microlithographically and suffer from substantial scattering on profile derivative discontinuities. That gives also tendency to lower damage threshold as compared to intrinsic material values. The LIMO approach is based contrarily on a proprietary, non etching material processing and is suitable for manufacturing of high-precision free programmable continuous surface profiles in optical glasses and crystals. We report on linear symmetric diffractive beam splitter 1:11 with high homogeneity and efficiency > 95% and discuss also other DOE designs. The design data, simulations with measured surface profiles and experimental intensity distributions are in very good agreement. Furthermore we report on a new type of optical attenuator composed from two DOE gratings. Its dynamic transmission range is 0.3% to 98%. The required lateral DOE shift is only 5 - 10 μm in the present design, so that the device can be very fast and applicable for dynamic intensity stabilization.

Applications may vary with time, and so may the technical realization of these applications. Lasers change and consequently application wavelengths, due to requirements imposed by material changes, power constraints, scaling of lateral features, or other parameters and specifications. In applications where diffractive optical elements (DOEs) are employed a change in laser or wavelength usually demands not only a new fabrication batch but a redesign of the diffractive structure. This is almost always the case in the special application of laser beam shaping where a DOE is designed to redistribute the energy of a specific laser beam profile, generally into a flat-top intensity profile (either round or square). In this paper we will describe how a mono-mode beam shaping DOE design for 355 nm was adapted to compensate a wavelength change to 532 nm. A preliminary telescope is necessary to ensure that the input beam retains the initial properties of beam waist and beam diameter. In this case, the original DOE design can be maintained with some minor compensation in phase depth for the wavelength change and in positioning of the elements to compensate the scaled diffraction angles. Further data will be shared showing a side by side comparison of testing results of the 355 nm and 532 nm designs.

Optical lithography with its 193nm technology is pushed to reach and shift its limits even further. There is strong demand on innovations in illumination part of exposure tools. Current illumination systems consisting of diffractive and refractive optical elements offer numerous benefits such as optimized laser beam shape with high homogeneity and high numerical aperture enabling high efficiency. LIMO's unique production technology is capable to manufacture free form surfaces on monolithic arrays larger than 250mm with high precision and reproducibility. Different kinds of intensity distributions with best uniformities or customized profiles have been achieved by using LIMO's refractive optical elements. Recently LIMO pushed the limits of this lens production technology and was able to manufacture first diffractive optical elements (DOE) based on continuous relief's profile. Beside for the illumination devices in lithography, DOEs find wide use in optical devices for other technological applications, such as optical communications and data processing. Up to now DOE designs follow the principle of phase diffraction gratings. Its diffraction structure with a periodic phase profile performs a superposition of beams with predefined energy ratios. Due to the application for high precise laser-beam shaping and beam splitting in optical technologies and optical fiber networks, number of grating orders is increased up to some tens or even hundreds. Classic lithographic technologies lead to quantized (step-like) profiles of diffractive micro-reliefs, which causes a decrease of beam splitter's diffractive efficiency. The newest development of LIMO's microlens fabrication technology allows us to make a step from free programmable microlens profiles to diffractive optical elements with high efficiency. Our first results of this approach are demonstrated in this paper. Diffractive beam splitters are presented. A special mathematical method is used to design diffractive optical elements with continuous surface profiles. Comparison between theoretical simulations and experimental results shows very good correlation.