Within the optics industry, there is a continuous drive to reduce the size, weight, power consumption and cost of optical systems (known as SWAP-C). A new generation of fabrication technologies for GRadient-INdex (GRIN) materials promise the capability to manufacture GRIN media of arbitrary refractive index distribution (within index variation and spatial resolution limits). This represents an opportunity to further optimise the SWAP-C of lens systems, yet also presents challenges for the optical designer. The necessary optical design tools for arbitary GRINs are not widely implemented, and the potential applications where arbitrary GRINs provide a benefit are not widely explored.

This work addresses these design challenges via two routes. In the first body of work we explore the necessary design tools for generalised GRIN lenses, including efficient mathematical representations for GRIN distributions and tools for the generation of starting points for further optimisation. A powerful new tool is devised that can convert conventional homogeneous lens constructions to generalised GRIN media, which allows the GRIN lens designer to leverage the vast archive available of homogeneous lens solutions as starting points. We also address the aberration correction potential of GRIN lenses with planar surfaces.

In the second body of work we explore the applications that directly benefit from GRIN optics. We demonstrate that layered polymer GRIN lenses of spherical distribution enabled by new extrusion-based manufacture technologies can show comparable performance to conventional cemented doublets and hybrid refractive-diffractive lenses. We also explore the application of a freeform-GRIN distribution to the design of a head-mounted display (HMD), showing that GRIN can significantly reduce the optical complexity of a baseline homogeneous HMD design. Finally, we demonstrate that GRIN can be a powerful tool in the optical design of optical systems with very wide, multispectral infrared wavebands. A short-wave to long-wave (SWIR-LWIR) infrared design study shows a GRIN-based solution can dramatically reduce lens count, size and mass while reducing sensitivity to manufacturing tolerances.

We conclude that the required design infrastructure for arbitrary GRIN lenses is feasible and emerging, and that there are technological challenges in modern optical design that justify ongoing research into GRIN optics. Progress in the optical design of generalised GRINs must be accompanied by refinement in manufacture, metrology, and environmental qualification to enable widespread adoption and deployment.@en

With the continuously growing transistor density in the semiconductor industry, where smaller features and tighter tolerances in the nanometer scale are the norm, there is a growing demand for more advanced metrology tools during manufacturing. While optical metrology in the visible range is the main workhorse, such as scatterometry, its performance is limited by the wavelength. Moving beyond the visible spectrum to extreme ultraviolet (EUV) and soft X-ray (SXR) wavelengths promises higher resolutions, but not without challenges. In this wavelength regime traditional microscopy struggles due to the non-availability of high numerical aperture optics for EUV and SXR at reasonable costs, failing to fully make use of the potential benefits of the shorter wavelength.

This thesis covers an alternative route to traditional microscopy through advanced lensless imaging or coherent diffractive imaging (CDI) techniques, particularly focusing on ptychography within the EUV and soft X-ray ranges demonstrated on a designed EUV beamline. Before we go into details about the setup we start with the basics of diffraction, coherent imaging, and ptychography in chapter 2. In chapter 3 we cover the generation of coherent EUV and SXR light from various sources, ranging from large scale facilities like synchrotrons to table-top High Harmonic Generation (HHG) setups.

From this point we cover the design and construction of a table-top EUV lensless imaging beamline in chapter 4, which has been designed and built from scratch at the Optics Research Group at the Delft University of Technology as part of this thesis. This section covers the design, optimization, and assembly of the beamline tailored for lensless imaging of industry relevant samples in a reflection configuration using EUV and soft X-rays from HHG sources. The beamline is split into several subsystems, a high intensity femtosecond fiber laser, the HHG EUV source, optical components for spectral filtering and illumination, and optomechanical systems required for ptychography which are individually covered in the chapter.

In chapter 5 we demonstrate one of the first ptychography reconstructions obtained on the EUV beamline, as presented in chapter 4, by illuminating an object with EUV light at 17.3 nm and 17.9 nm in a grazing reflection orientation of 20 degrees. The object, a silicon substrate which has been patterned with a 20 nanometer thick gold layer with feature sizes from a few microns down to 15 nanometers, has been reconstructed. This reconstruction has been generated with an in-house developed ptychography algorithm, based on automatic differentiation, for the ptychography reconstruction process. The experimental results demonstrate the feasibility of achieving high resolution reconstructions.

Line features down to 50 nanometers were retrieved with this method, close to the diffraction limit given an imaging NA of 0.17 at 18 nm wavelength. A reconstructed structure height of 23.6 ± 0.62 nm agrees well with the 20 nm nominal design value and the height retrieved from an atomic force microscope (AFM) measurement of 22.8 ± 1.45 nm.

The results in chapter 5 are quite promising, though there are certain challenges which need to be solved to further improve the reconstruction quality. One of these challenges are intensity stability issues which are typically associated with EUV sources based on high harmonic generation. Chapter 6 proposes a simple computational method to mitigate intensity fluctuations during ptychography scans by introducing a scanning position dependent multiplication factor. The algorithm effectively corrects for power fluctuations, enabling object reconstruction even in the presence of significant intensity variations up to 50 percent during the overall scan.

Chapter 7 presents a compact schlieren (from the German word ’streak’) imaging system integrated within the HHG EUV source, enabling quantitative density retrieval of the gas jet used to drive the high harmonic generation process. Schlieren imaging provides a straightforward alternative to vibration sensitive techniques like interferometry and can be used as a standardized tool for HHG sources, allowing for a better comparison among different HHG setups and for the optimization of HHG light sources.

In summary, this thesis does not only cover the field of lensless EUV microscopy but also covers the design process of such a beamline and the challenges associated with HHG EUV sources. This work presents a starting point for experimental EUV metrology within the Optics Research Group at the Delft University of Technology and enables future academic research relevant for the semiconductor industry.
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We demonstrate a broadband implementation of coherent Fourier scatterometry (CFS) using a supercontinuum source. Spectral information can be resolved by splitting the incident field into two pulses with a variable delay and interfering them at the detector after interaction with the sample, bearing similarities with Fourier-transform spectroscopy. By varying the time delay between the pulses, a collection of diffraction patterns is captured in the Fourier plane, thereby obtaining an interferogram for every camera pixel. Spectrally resolved diffraction patterns can then be retrieved with a per-pixel Fourier transform as a function of the delay. We show the physical principle that motivates the two-pulse approach, the experimental realization, and results for a silicon line grating. The presented implementation using a supercontinuum source offers a cost-effective way to acquire multi-wavelength CFS data over a wide wavelength range, with the potential to improve reconstruction robustness and sensitivity in applications such as dimensional metrology.@en

Optical trapping of metallic nanoparticles has diverse applications because metallic nanoparticles have unique properties. One significant advantage is that the optical force exerted on metallic nanoparticles is considerably larger than that on dielectric nanoparticles of the same size and shape. This results in a significantly deeper optical potential well compared to the optical trapping of dielectric nanoparticles.
In this thesis, our central objective is to delve into the underlying physical mechanisms behind an exceptional and enhanced optical trapping phenomenon that is referred to as"nonlinear optical trapping". To achieve this, we extensively investigated the third-order nonlinear effects that come into play in this intriguing optical trapping behavior. This investigation aimed to shed light on the underlying principles and mechanisms that enable the manipulation of nanoparticles beyond the diffraction limit, opening up exciting possibilities for various applications in nanotechnology and beyond....@en

We present the realization of a vectorial perturbation method based on the Born series applied to strong electromagnetic scattering problems. We present the general theoretical formalism and show a semianalytical implementation for scattering by diffraction gratings. We are particularly interested in the strong scattering regime, where the Born series is known to wildly (namely, exponentially) diverge. By applying Padé approximation to the vectorial Born series, we are able to obtain accurate results from divergent Born series. The method we present has the inherent benefit of being close to the actual physical mechanism behind the formation of a scattered signal, as the solution is built step by step from a sequence of multiple-scattering events. This helps in the understanding of signal formation, which is a key element in inverse scattering problems that are relevant to optical metrology, among others.@en

This book treats optics at the level of students in the later stage of their bachelor or the beginning of their master. It is assumed that the student is familiar with Maxwell’s equations. Although the book takes account of the fact that optics is part of electromagnetism, special emphasis is put on the usefulness of approximate models of optics, their hierarchy and limits of validity. Approximate models such as geometrical optics and paraxial geometrical optics are treated extensively and applied to image formation by the human eye, the microscope and the telescope. Polarisation states and how to manipulate them are studied using Jones vectors and Jones matrices. In the context of interference, the coherence of light is explained thoroughly. To understand fundamental limits of resolution which cannot be explained by geometrical optics, diffraction theory is applied to imaging. The angular spectrum method and evanescent waves are used to understand the inherent loss of information about subwavelength features during the propagation of light. The book ends with a study of the working principle of the laser.@en

This book treats optics at the level of students in the later stage of their bachelor or the beginning of their master. It is assumed that the student is familiar with Maxwell’s equations. Although the book takes account of the fact that optics is part of electromagnetism, special emphasis is put on the usefulness of approximate models of optics, their hierarchy and limits of validity. Approximate models such as geometrical optics and paraxial geometrical optics are treated extensively and applied to image formation by the human eye, the microscope and the telescope. Polarisation states and how to manipulate them are studied using Jones vectors and Jones matrices. In the context of interference, the coherence of light is explained thoroughly. To understand fundamental limits of resolution which cannot be explained by geometrical optics, diffraction theory is applied to imaging. The angular spectrum method and evanescent waves are used to understand the inherent loss of information about subwavelength features during the propagation of light. The book ends with a study of the working principle of the laser.@en

Chiral objects are abundant in nature, and although the enantiomers have almost identical physical properties apart from their handedness, they can exhibit significantly different chemical properties and biological functions. This underscores the importance of sorting chiral substances. In this Letter, we demonstrate that chirality-sorting optical force pairs can be inversely generated in a tightly focused Gaussian beam by tailoring the input polarization state. We provide a detailed method for constructing the polarization state of the incident light to create the desired chiral optical field that generates the chirality-sorting optical force pairs. These force pairs precisely trap two opposite enantiomers at distinct predetermined positions within the same equilibrium plane, enabling their simultaneous identification and separation. Notably, the trapping positions and separation distances can be freely adjusted by altering the incident polarization parameters.@en

We demonstrate lensless single-shot dual-wavelength digital holography for high-speed 3D imaging in industrial inspection. Single-shot measurement is realized by combining off-axis digital holography and spatial frequency multiplexing of the two wavelengths on the detector. The system has 9.1 µm lateral resolution and a 50 µm unambiguous depth range. We determine the theoretical accuracy of off-axis dual-wavelength phase reconstruction for the case of shot-noise-limited detection. Experimental results show good agreement with the proposed model. The system is applied to industrial metrology of calibrated test samples and chip manufacturing.@en

The Born series applied to the Lippmann-Schwinger equation is a straightforward method for solving optical scattering problems, which however diverges except for very weak scatterers. Replacing the Born series by Padé approximants is a solution of this problem. However, in some cases it is rather difficult to obtain an accurate Padé approximant. In this paper we aim to understand the cause by studying the scattering by a cylinder. We find that there is a strong connection between eigenvalues of the Lippmann-Schwinger operator that are close to the real axis, the occurrence of a near-resonance, and the problematic behavior of the Padé approximant. The determination of these eigenvalues provides a general method to obtain, for any given geometry, materials for which near-resonances occur.@en

Optical tweezers have proved to be a powerful tool with a wide range of applications. The gradient force plays a vital role in the stable optical trapping of nano-objects. The scalar method is convenient and effective for analyzing the gradient force in traditional optical trapping. However, when the third-order nonlinear effect of the nano-object is stimulated, the scalar method cannot adequately present the optical response of the metal nanoparticle to the external optical field. Here, we propose a theoretical model to interpret the nonlinear gradient force using the vector method. By combining the optical Kerr effect, the polarizability vector of the metallic nanoparticle is derived. A quantitative analysis is obtained for the gradient force as well as for the optical potential well. The vector method yields better agreement with reported experimental observations. We suggest that this method could lead to a deeper understanding of the physics relevant to nonlinear optical trapping and binding phenomena.

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Next-generation metrology solutions in various technology areas require to image sample areas at the nanoscale. Coherent diffractive imaging based on ptychography is the route towards EUV imaging of nanostructures without lenses. A key component in a table-top EUV beamline is a high-brightness high-harmonic generation (HHG) source. Since our research is mainly directed towards wafer metrology for lithography in the semiconductor industry, we adhere to a reflection setup: the EUV light is scattered by the nanostructures at the surface of the sample, and is reflected towards a CCD camera, where a far-field diffraction pattern is recorded. A data-set comprising a multitude of these diffraction patterns is generated for partially overlapping positions of the focused probe on the sample. This provides the necessary redundancy for phase retrieval of the complex-valued field of the sample. Recent advancements in both hardware and software for computation enable the development of advanced algorithms. In particular, the benefits of automatic differentiation are exploited in order to cope with a drastic growth in model complexity. Our computational imaging algorithms realize wavelengthmultiplexed reconstruction and a modal approach for the spatial coherence of the source.@en

Ptychographic extreme ultraviolet (EUV) diffractive imaging has emerged as a promising candidate for the next generationmetrology solutions in the semiconductor industry, as it can image wafer samples in reflection geometry at the nanoscale. This technique has surged attention recently, owing to the significant progress in high-harmonic generation (HHG) EUV sources and advancements in both hardware and software for computation. In this study, a novel algorithm is introduced and tested, which enables wavelength-multiplexed reconstruction that enhances the measurement throughput and introduces data diversity, allowing the accurate characterisation of sample structures. To tackle the inherent instabilities of the HHG source, a modal approach was adopted, which represents the cross-density function of the illumination by a series of mutually incoherent and independent spatial modes. The proposed algorithm was implemented on a mainstream machine learning platform, which leverages automatic differentiation to manage the drastic growth in model complexity and expedites the computation using GPU acceleration. By optimising over 200 million parameters, we demonstrate the algorithm's capacity to accommodate experimental uncertainties and achieve a resolution approaching the diffraction limit in reflection geometry. The reconstruction of wafer samples with 20-nm high patterned gold structures on a silicon substrate highlights our ability to handle complex physical interrelations involving a multitude of parameters. These results establish ptychography as an efficient and accurate metrology tool.@en

The terahertz frequency region of the electromagnetic spectrum is crucial for understanding the formation and evolution of galaxies and stars throughout the universe's history, as well as the process of planet formation. Detecting the unique spectral signatures of molecules and atoms requires terahertz spectrometers, which must be operated in space observatories due to water vapor absorption in the Earth's atmosphere. However, current terahertz spectrometers face challenges such as low resolution, limited bandwidth, large volume, and complexity. In this paper, the issues of size and weight are addressed by demonstrating a concept for a centimeter-sized, low-weight terahertz spectrometer using a metasurface. The design of the metasurface spectrometer is first discussed for the 1.85 to 2.4 THz range, followed by its fabrication. Next, an array of quantum cascade lasers operating at slightly different frequencies around 2.1 THz is utilized to characterize the spectrometer. Finally, a spectrum inversion method is applied to analyze the measured data, confirming a resolution R (λ/Δλ) of at least 273. This concept can be extended to other application areas, such as planetary observations and various wavelengths in the far-infrared (FIR) and near-infrared (NIR) ranges.

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We use a rigorous vector Born series to solve electromagnetic scattering by a diffraction grating. To deal with possible divergence of the Born series, we compute Padé approximants of the Born series to retrieve the solution regardless. Besides results of the Born-Padé method for an example grating, for which the Born series diverges, we show analytical expressions for a two-layer grating in the case of s polarization. This gives insight into the convergence behavior of the Born series as function of the angle of incidence, for instance.

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When redistributing the light emitted by a source into a prescribed irradiance distribution, it is not guaranteed that, given the source and optical constraints, the desired irradiance distribution can be achieved.We analyze the problem by assuming an optical black box that is shift-invariant, meaning that a change in source position does not change the shape of the irradiance distribution, only its position. The irradiance distribution we can obtain is then governed by deconvolution. Using positive-definite functions and Bochner s theorem, we provide conditions such that the irradiance distribution can be realized for finite etendue sources.We also analyze the problem using optimization, showing that the result heavily depends on the chosen source distribution.

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Nonlinear responses of nanoparticles induce enlightening phenomena in optical tweezers. With the gradual increase in optical intensity, effects from saturable absorption (SA) and reverse SA (RSA) arise in sequence and thereby modulate the nonlinear properties of materials. In current nonlinear optical traps, however, the underlying physical mechanism is mainly confined within the SA regime because threshold values required to excite the RSA regime are extremely high. Herein, we demonstrate, both in theory and experiment, nonlinear optical tweezing within the RSA regime, proving that a fascinating composite trapping state is achievable at ultrahigh intensities through an optical force reversal induced through nonlinear absorption. Integrated results help in perfecting the nonlinear optical trapping system, thereby providing beneficial guidance for wider applications of nonlinear optics.

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We show that composite nanoparticles can be designed to scatter light into a desired direction. By choosing the materials of the nanoparticle carefully, the phase of the scattered light by the different components can be controlled. This leads to constructive interference is certain directions and destructive interference in others, resulting in directional scattering obtainable for a large bandwidth. FEM simulations were used to validate the theory. Furthermore, SiO2/Au nanoparticles were fabricated and measured confirming the directional scattering.

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Stable optical trapping of gold nanoparticles is essential and desirable because of its wide applications in nanotechnology. While several factors have been proposed to affect optical trapping stability, the sample's volume fraction during optical trapping has often been neglected. To address this, by utilizing the effective medium theory, we analyze the stability of optical trapping of a gold nanoparticle in human serum albumin solutions, HIV-1,virus solutions, and gold nanoparticle solutions in this article. Our comparative analysis of the optical force and potential on a single gold nanoparticle in solutions of varying volume fractions reveals that both parameters decrease with increasing volume fraction. This finding can aid in more effective control of gold nanoparticles in various applications.

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As a two-dimensional planar material with low depth profile, a metasurface can generate non-classical phase distributions for the transmitted and reflected electromagnetic waves at its interface. Thus, it offers more flexibility to control the wave front. A traditional metasurface design process mainly adopts the forward prediction algorithm, such as Finite Difference Time Domain, combined with manual parameter optimization. However, such methods are time-consuming, and it is difficult to keep the practical meta-atom spectrum being consistent with the ideal one. In addition, since the periodic boundary condition is used in the meta-atom design process, while the aperiodic condition is used in the array simulation, the coupling between neighboring meta-atoms leads to inevitable inaccuracy. In this review, representative intelligent methods for metasurface design are introduced and discussed, including machine learning, physics-information neural network, and topology optimization method. We elaborate on the principle of each approach, analyze their advantages and limitations, and discuss their potential applications. We also summarize recent advances in enabled metasurfaces for quantum optics applications. In short, this paper highlights a promising direction for intelligent metasurface designs and applications for future quantum optics research and serves as an up-to-date reference for researchers in the metasurface and metamaterial fields.

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