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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In this thesis we try to provide novel solutions to key problems related to imaging and imaging system. Imaging is usually referred to as the technique for reproducing the information of the object. In optics, we usually refer the object information to the light field in the object plane due to the interaction of the illumination field and the object. Imaging technique allows the reproduced object information to be recorded by detectors such as human eye, photo resist, or CCD/CMOS sensor. In order to image an object, there must be light. We consider only un polarized quasi-monochromatic light illuminating the object and we approximate the field in the object plane by the multiplication of the transmittance / reflectance of the object and the illumination field (the first Born approximation). However, the results in this thesis can also be generalized to situations beyond the above scope. Here we mainly focus on two aspects: the aberrations, the errors of the imaging system, and the spatial coherence of the light field. In a typical imaging scenario, we consider the object plane field as a source consisting a series of point sources. The field generated by each point source propagates independently to the image plane through the imaging system. Ideally, these fields should all identically have the correct distribution and be centered at the correct location. However, this is not the case in presence of the aberrations. As a result, the image will become blurred. @en

Optical tweezers and associated manipulation tools in the far field have had a major impact on scientific and engineering research by offering precise manipulation of small objects. More recently, the possibility of performing manipulation with surface plasmons has opened opportunities not feasible with conventional far-field optical methods. The use of surface plasmon techniques enables excitation of hotspots much smaller than the free-space wavelength; with this confinement, the plasmonic field facilitates trapping of various nanostructures and materials with higher precision. The successful manipulation of small particles has fostered numerous and expanding applications. In this paper, we review the principles of and developments in plasmonic tweezers techniques, including both nanostructure-assisted platforms and structureless systems. Construction methods and evaluation criteria of the techniques are presented, aiming to provide a guide for the design and optimization of the systems. The most common novel applications of plasmonic tweezers, namely, sorting and transport, sensing and imaging, and especially those in a biological context, are critically discussed. Finally, we consider the future of the development and new potential applications of this technique and discuss prospects for its impact on science.

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This thesis focusses on two aspects of tunable optics: Fabry-Pérot interferometers with a variable distance between their mirrors and electrowetting liquid lenses. The need for a device to detect child abuse has motivated us to design and build a camera that can detect the chemical composition of the upper skin layers of a bruise using a self-made Fabry-Pérot interferometer. The research described in the first part of this thesis has shown that wide-angle spectral imaging can be achieved with compact and cost-effective cameras using Fabry-Pérot interferometers. Designs with a full field of 90◦ in which the Fabry-Pérot interferometer is mounted either in front of an imaging system or behind a telecentric lens system are presented and analysed. The dependency of the spectral resolution on the numerical aperture of the lens system is derived and its value as a design criterion is shown. It is shown that the telecentric camera design is preferable over the collimated design for bruise imaging with a Fabry-Pérot interferometer. The idea to use a liquid lens for spectral imaging has directed the research towards a new concept of controlling surface waves on the surface of a liquid lens. We investigate and model surface waves because they decrease the imaging quality during fast focal switching. We propose a model that describes the surface modes appearing on a liquid lens and that predicts the resonance frequencies. The effects of those surface modes on a laser beam are simulated using geometrical optics and Fresnel propagation, and the model is verified experimentally. The model of the surface oscillations is used to develop a technique to create aspheric surface shapes on commercially available electrowetting liquid lenses. The surface waves on the liquid lens are described by Bessel functions of which a linear combination can be used to create any circularly symmetrical aspheric lens shape at an instant of time. With these surface profiles, one can realise a large set of circularly symmetrical wavefronts and hence intensity distributions of beams transmitted by the lens. The necessary liquid lens actuation to achieve a desired shape is calculated via a Hankel transform and confirmed experimentally. The voltage signal can be repeated at video rate. Measurements taken with a Mach-Zehnder interferometer confirm the model of the surface waves. The capabilities and limitations of the proposed method are demonstrated using the examples of a Bessel surface, spherical aberration, an axicon, and a top hat structure.@en

In many optical measurement methods one aims to retrieve the shape or physical properties of an unknown object by measuring how it scatters an incident optical field. Such an inverse problem is often approached by solving the corresponding direct scattering problem iteratively. Despite the existence of numerical methods, a perturbation approach could be a powerful way to solve those direct problems. In such an approach the field is expressed as a series, known as the Born series, in which the higher-order corrections represent multiplescattering effects. This approach has the advantage that each term of the series has a clear physical meaning and that it can unveil much more about the scattering process than a purely numerical approach. Under (very) weak-scattering conditions the Born series converges and then often the first or first few terms of the series are sufficient to model the scattering. However, except under very special circumstances such as for x-rays where optical contrasts are extremely low, multiple scattering effects are very important and the Born series in general does not converge. Although multiple scattering could, in principle, allow resolving subwavelength details of the unknown object, this is in practice impeded by the divergent nature of the Born series.

In this thesis, we show how Padé approximation can be employed in electromagnetic problems to retrieve an accurate evaluation of the scattered field even under strong-scattering conditions. Padé approximants are rational functions that can offer improvements in two ways, namely, accelerating the rate of convergence of (already) converging series and analytic continuation of series outside its region of convergence. We apply the method to three scalar scattering problems. In one dimension we consider an infinitely thin slab and a slab of finite thickness, and in two dimensions an infinitely long cylinder. In particular, we study cases in the strong-scattering regime for which the Born series diverges. It will be shown that for all cases studied, Padé approximation retrieves an accurate result.

The presented method integrates multiple-scattering effects one by one and can therefore represent an important building block to the application of the Born series to direct and inverse problems, with potential applications in superresolution, optical metrology, and phase retrieval.

Dipoles are all around us and the extent to which it is possible to distinguish two dipoles next to each other is a very important criterion for optical resolution. This report proposes that the resolution can be enhanced by placing a substrate with a film underneath the dipoles. This report specifically looks at the effect on the near and far field using a coupling of the field radiated by the dipole and a guided mode in the film. In an integral over reflected plane waves, in case a guided wave occurs, the integrand has a singularity which has to be dealt with using the Cauchy Principle value technique. Other singularities are dealt with using multiple first order Taylor expansions. With the singularities dealt with, a Matlab function has been constructed that can compute the reflected field of a single dipole. The substrate underneath the dipole has a significant effect on the total field, both in the near and far field areas. Due to the reflection, the polarizability is represented more in the intensity and can be determined more easily. Although the influence of the film on enhancing the resolution requires to investigate to what extent two dipoles can be distinguished better when a film is present, due to lack of time, this report considers the computation of the field of a single dipole only. The extension to the case of two dipoles is in principle easy however.

The ability to apply force and torque directly to micro- and nanoscale particles in optical traps has a wide range of applications. While full control of both force and torque in three dimensions has been realized using top-down fabrication of rod-shaped particles composed of birefringent crystalline materials, widespread usage of such particles is limited as the optical constants of the predominant birefringent materials (quartz SiO2 and rutile TiO2) preclude coverage of the full application space of optical trapping. Here, we show that multilayer metamaterial nanoparticles provide access to a wide range of optical constants that can be specifically tuned for each application. Selecting the material pair Nb2O5/SiO2 from the library of amorphous dielectrics as our metamaterial, we show that its refractive index and birefringence can be designed by adapting the ratio of layer thicknesses. Using a robust top-down fabrication process, we show that uniformly sized, free-floating Nb2O5/SiO2 particles with high birefringence at moderate refractive index are obtained at high yield. Using an optical torque wrench, we show that these particles function as joint force and torque transducers while maintaining excellent stability in aqueous solutions and can be controllably optimized for particular physical characteristics such as maximal torque transfer or rapid response time. We expect that such customizable birefringent metamaterial nanoparticles whose properties surpass those of conventional crystalline particles will provide a means to unleash the full potential of optical trapping applications. @en

Cubic phase wavefront coding technique is applied to an imaging system with the aim of extending the depth of field (DOF). The design is based on the wavefront coding method proposed by Dowski and Cathey1. The method employs a cubic phase mask (CPM) to modify the point spread function (PSF) of the imaging system under incoherent illumination such that the PSF of the system is formed as an isosceles right triangle, which makes the PSF insensitive to defocus. Researchers have found the optimized values of cubic phase coefficient and the exit pupil distance for the given specifications for solving wavefront coded task-based imaging problem2. The extended DOF design is usually based on placing a phase mask exactly in the pupil plane of the imaging system. However, this is not always practical because the complex design of the imaging system leads to a limited practical advantage of this kind of arrangement. In this work, the influence of phase mask position upon wavefront coding technique in the doublet imaging system is studied. The main goal is to find the position where to place the CPM in the imaging system, which type of arrangement can effectively improve the modulation transfer function. Finally, we compare two system configurations, front aperture stop and rear aperture stop in designing the doublet wavefront coded system.@en

Wavefront aberration measurements are required to test an extreme ultraviolet (EUV) imaging system. For a high-NA EUV imaging system, where conventional wavefront-sensing techniques show limitations, ptychography can be used for this purpose. However, at the wavelength region of EUV (i.e., 13.5 nm), the position accuracy of the scanning mask that is defined for ptychography is stringent. Therefore, we propose ptychography combined with mask position correction. The simulated intensity patterns, the ones we use, resemble expected EUV experimental data. Finally, we show the results in the presence of Poisson noise and the tolerance of the position correction method for error in mask positions.@en

The beauty of optical birefringence lies in the fact that it provides an independent control of light over different polarization directions, which leads to many important applications in today's optical systems. This thesis describes the applications of existing naturally-occurring birefringent materials as well as the engineered formed-birefringent meta-materials via nano-fabrication. In particular the application of birefringent materials in optical trapping, waveguide engineering and imaging are discussed. The investigation methods include numerical simulation, nano-fabrication and experimental validation. @en

In this thesis, several phase retrieval methods are discussed. Since the focus will mainly be on theory rather than experiment, the structure has been determined by the similarities and differences of the mathematics of these methods. For example, a distinction is made between non-iterative and iterative methods, and between single-shot iterative phase retrieval and multiple-shot iterative phase retrieval (ptychography). However, it must be noted that phase retrieval methods that are mathematically similar, are suitable for fundamentally different experimental setups. For example, one can consider setups for lensless imaging, of which an interesting application is metrology using Extreme Ultraviolet (EUV) radiation. In such setups, no focusing optics are used, and one typically computes an image from far-field intensity patterns. On the other hand, there are setups for aberrated imaging. In these setups, one does use focusing optics to form images, but by introducing some sort of variations or perturbations, one can generate a set of images from which a complex-valued field can be computed. For example, regular ptychography and Fourier ptychography are mathematically the same, but the former is used for lensless imaging, while the latter is used for aberrated imaging. Mathematically, the only difference between these two ptychographic approaches is that the roles of object space and Fourier space are interchanged.@en

Optical angular momenta (AM) have attracted tremendous research interest in recent years. In this paper we theoretically investigate the electromagnetic field and angular momentum properties of tightly focused arbitrary cylindrical vortex vector (CVV) input beams. An absorptive particle is placed in focused CVV fields to analyze the optical torques. The spin-orbit motions of the particle can be predicted and controlled when the influences of different parameters, such as the topological charge, the polarization and the initial phases, are taken into account. These findings will be helpful in optical beam shaping, optical spin-orbit interaction and practical optical manipulation.@en

HoW do you look inside a box without opening it? How can we know whether or not a heart valve is functioning correctly without cutting a person open? Imaging – the art of seeing the unseeable. A CT-scan at the doctor’s office, crack detection in the wing of an airplane, and medical ultrasound are all examples of imaging techniques that allow us to inspect the interior of an object or person and enable us to observe features that are not directly visible to the naked eye. Science continuously improves upon existing imaging methods and occasionally invents new ones leading to improved image quality and faster image acquisition. Many imaging applications rely on acoustic, electromagnetic, or elastodynamic waves for imaging. These methods use waves to illuminate a penetrable object, and then forman image of its interior from measurements of transmitted or scattered waves. In such imaging problems efficient computation of wavefields in complex geometries is key. New mathematical methods and algorithms are needed to keep up with the demands of the imaging industry – advancements in the computer industry alone cannot respond to the shift towards larger domains, higher resolution, and larger data sets. This thesis is about reduced-order modeling of the equations that describe the dynamics of wave propagation. In reduced-order modeling, the aim is to systematically develop a small model that describes a complex system without losing information that is valuable for a specific application. Evaluating such a model is computationally much more efficient than direct evaluation of the unreduced system and in the context of imaging it can lighten the computational burden associated with imaging algorithms. The central question is, of course: How does one construct a model that describes the wave dynamics relevant to a particular application? Wave equations are partial differential equations that interrelate the spatial and temporal variations of a particular physical wavefield quantity. When we discretize such equations in space, sparse systems of equations with hundreds of thousands or even millions of unknowns are obtained. Via projection onto a small subspace such a largescale system can be reduced to a much smaller reduced system. The solution of this small system is called a reduced-order model. A properly constructed reduced-order model can be easily evaluated and gives an accurate wavefield description over a certain time or frequency interval or parameter range of interest. In this thesis, we discuss different choices for the subspaces that are used for projection in model-order reduction. In particular, we show which types of subspaces are effective for wavefields that are localized and highly resonant and how to efficiently generate such subspaces by exploiting certain symmetry properties of the wave equations. We illustrate the effectiveness of the resulting reduced-order models by computing optical wavefield responses in three-dimensional metallic nano-resonators. Not all wavefields are determined by a few resonances, of course. Waves can also travel over long distances without losing information; a property that is used by mobile phones every day. The reduction methods developed for resonating fields are not efficient for these types of propagation problems and require a different approach. In this thesis, we present a so-called phase-preconditioning reduction method, in which a specific subspace is generated that explicitly takes the large travel times of the waves into account. We demonstrate the effectiveness of this reduction approach using examples from geophysics, where waves with long travel times are frequently encountered or used to probe the subsurface of the Earth. Finally, we show how reduced-order modeling techniques can be incorporated into advanced nonlinear imaging algorithms. Here, we focus on an imaging application in geophysics, where the goal is to retrieve the conductivity tensor of a bounded anomaly located in the subsurface of the Earth, based on measured electromagnetic field data collected on a borehole axis. We demonstrate that the use of reduced-order models in a nonlinear optimization framework does indeed lead to significant computational savings without sacrificing the quality of imaging results. To illustrate the wide applicability of model-order reduction techniques in imaging, an additional example from nuclear geophysical imaging is also presented. @en

Electromagnetic fields carry a linear and an angular momentum, the first being responsible for the existence of the radiation pressure and the second for the transfer of torque from electromagnetic radiation to matter. The angular momentum is considered to have two components, one due to the polarization state of the field, usually called spin angular momentum (SAM), and one due to the existence of topological azimuthal charges in the field phase profile, which leads to the orbital angular momentum (OAM). These two contributions to the total angular momentum of an electromagnetic field appear, however, to not be independent of each other, something which is described as spin-orbit coupling. Understanding the physics of this coupling has kept scientists busy for decades. Very recently it has been shown that electromagnetic fields necessarily carry also invariant radial charges that, as discussed in this Letter, play a key role in the angular momentum. Here we show that the total angular momentum consists in fact of three components: one component only dependent on the spin of the field, another dependent on the azimuthal charges carried by the field, and a third component dependent on the spin and the radial charges contained in the field. By properly controlling the number and coupling among these radial charges it is possible to design electromagnetic fields with a desired total angular momentum. Remarkably, we also discover fields with no orbital angular momentum and a spin angular momentum typical of spin-3/2 objects, irrespective of the fact that photons are spin-1 particles.@en

A noise-robust extension of iterative phase retrieval algorithms that does not need to assume a noise model is proposed. It works by adapting the intensity constraints using the reconstructed object. Using a proof-of-principle ptychographic experiment with visible light and a spatial light modulator to create an object, the proposed method is tested and it compares favorably to the Extended Ptychographic Iterative Engine (ePIE) with reduced step size. The method is general, so it can also be applied to other iterative reconstruction schemes such as phase retrieval using focus variation.

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A technique to create aspheric surface shapes on commercially available electrowetting liquid lenses is demonstrated. Based on a previously published surface oscillation model a technique using a Hankel transform is proposed and tested experimentally. An alternating actuation voltage is applied to the liquid lens to stimulate surface oscillations, that temporarily add up to the desired surface shape. The voltage signal can be repeated at video rate. The measurements were taken with a Mach-Zehnder interferometer and confirm the previous results. The capabilities and limitations of the proposed method are demonstrated using the examples of a Bessel surface, spherical aberration, an axicon, and a top hat structure.@en

'Silicon Photonics: Electromagnetic theory' is a concise introduction to the fundamental theories of integrated optics that focuses on modern silicon photonic technology. It includes well-known general theories on properties of waveguides and couplers as well as new theories on high-index contrast waveguides, directional couplers, and micro-ring resonators. The book may be used as a first introduction to integrated optics, with only basic electrodynamics as prerequisite. It would fit well as lecture material in a short introduction course, as additional material in an extensive electrodynamics course, or as fundamental background material in a more applied course. The later chapters are of interest to experts in the field of integrated optics that want to learn the latest theories for high-index contrast waveguides such as silicon photonic waveguides.@en

Coherent Fourier scatterometry is an optical metrology technique that utilizes the measured intensity of the scattered optical field to reconstruct certain parameters of test structures written on a wafer with nano-scale accuracy. The intensity of the scattered field is recorded with a camera and this information is used to retrieve the grating parameters. To improve sensitivity in the parameter reconstruction, the phase of the scattered field can also be acquired. Interferometry can be used for this purpose, but with the cost of cumbersomeness. In this paper, we show that iterative phase retrieval methods can be applied to retrieve the scattered complex fields from only intensity measurement data. We show that the accuracy of the retrieved complex fields using phase retrieval is comparable to that measured directly using interferometry.@en