Efficient diffractive optical elements from glass with continuous surface profiles

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.

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.

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.

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.

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

We propose a technique for calculating the color separation gratings aimed at separating plane light beams of different wavelengths into different diffraction orders. The technique is based on a special-type optimization criterion. With this criterion, the problem of calculating the piecewise-constant grating profile is reduced to sequentially solving independent problems of optimization of the step heights. We derived an analytical expression for the profile of a color separation grating that generalizes the familiar analytical solutions. The criterion introduced is used to design a diffractive optical element (DOE) that generates required light beams when it is illuminated by different wavelengths. Design of color separation gratings able to separate three and five different wavelengths and DOEs to demultiplex and focus the two- and three-wavelength beams is presented.

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.

Efficient diffractive optical elements in chalcogenide glass layers fabricated by direct DUV laser writing

Recent advances in compression molding of glass optical elements for mass production offer the potential of extending this technology to elements with micro and nano scale features. In this research, glass diffractive optical elements (DOEs) with lateral features in the order of 10 µm and vertical height of 330 nm were fabricated using a fused silica glass mold and a special low Tg (glass transition temperature) glass material K-PG325. Molded DOEs were studied using an atomic force microscope (AFM) and scanning electron microscope (SEM) to evaluate the glass molding process capability. Optical testing of the molded DOEs was a further demonstration of the effectiveness of the molding process for high volume micro and diffractive optical component fabrication. The combination of two high-precision, high-volume processes, i.e., semiconductor batch process for optical mold making and glass molding for DOE replication, is an effective alternative manufacturing method for high-quality, low-cost optical components. The reported experiment is a detailed illustration of the glass molding process capability. With further process optimization a robust manufacturing process can be developed for mass production of diffractive and micro glass optical elements.

LEDs have long been hailed as a sustainable light source. Indeed, its adoption in recent decades has greatly improved the efficiency of artificial light sources. Nonetheless, the sustainability claims are challenged by mounting evidence pointing to the detrimental impact of light pollution due to blue-rich white LEDs on wildlife, human health, and astronomy. A potential solution to this is the use of holographically recorded diffractive optical elements (DOEs) to redirect LED light to regions where illumination is required. However, current limitations on the use of DOEs are high costs, low angular working range (Δθ), and relatively narrow spectral working range (Δλ). This restricts their efficient use to narrow wavelength range light sources at highly specific ranges of incident angles. In order for DOEs to be operational with broad Δθ and Δλ, a low thickness and suitably high refractive index modulation (Δn) are required, but it must still operate in the Kogelnik regime and not lose energy to higher diffraction orders. The aim of this review is to identify candidate materials for the design of a novel low-cost DOEs with higher Δn.

A new method of calculation of binary-phase and quantized diffractive optical elements (DOEs) is proposed. The design uses a specific series expression for the quantized DOE transmission function and is based on the gradient search algorithm for the optimization of truncated series approaching the quantized complex transmission function. Fast designs of binary beam shapers and multiorder binary gratings with equal order intensities are reported with the efficiency in the range of 70 - 75% and the root-mean-square errors of 3 - 5%. The design of binary DOEs that transform the gaussian beam into Gauss-Hermite (0,1) and (1,1) complex amplited distributions is also presented.

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.

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.

Phase retrieval in optical imaging refers to the recovery of a complex signal from phaseless data acquired in the form of its diffraction patterns. These patterns are acquired through a system with a coherent light source that employs a diffractive optical element (DOE) to modulate the scene, resulting in coded diffraction patterns (CDPs) at the sensor. Recently, the hybrid approach of a model-driven network or deep unfolding has emerged as an effective alternative to conventional model- and learning-based phase-retrieval techniques because it allows for bounding the complexity of algorithms while also retaining their efficacy. Additionally, such hybrid approaches have shown promise in improving the design of DOEs that follow theoretical uniqueness conditions. There are opportunities to exploit novel experimental setups and resolve even more complex DOE phase-retrieval applications. This article presents an overview of algorithms and applications of deep unfolding for bootstrapped—regardless whether near, middle, or far zones—phase retrieval.