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.

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.

A new strategy has been presented to overcome the long-term dilemma of simultaneously achieving high numerical aperture, large aperture size, and broadband achromatism of flat lenses. A stepwise phase dispersion compensation (SPDC) layer is introduced as a substrate on which the meta-atoms are positioned.

In this paper, we study the effects of plasmonic resonances on the Fisher information in the far field, of the position of a silver nanowire with respect to the center of a focused spot. We study theoretically a nanowire embedded in a high refractive index substrate that is illuminated by a dark-field focused spot. The position of the nanowire is determined from the scattered far-field intensities. The Fisher information is computed for both a lateral and longitudinal displacement of the nanowire, and its dependence on the illumination frequency is analyzed. The resonance frequencies of the nanowires are determined. We find that frequencies near a plasmonic resonance can enhance the Fisher information. However, at the resonance frequency itself and very close to it, the scattered far field corresponds to an information dark state. The phenomenon is demonstrated for silver, and the underlying physical mechanism is explained with an analytical model. As is shown, the dark state can be converted into a state with very high Fisher information about the positions of the nanowire by modifying the focused spot.

In this talk, we discuss the effect of plasmonic resonances on the Fisher information in the far field. We consider a metallic nanowire embedded in a silicon substrate, illuminated by a dark-field focused spot, and we investigate how its position can be estimated from the scattered far-field intensities. The Fisher information is computed for both lateral and longitudinal displacements of the nanowire, and the dependence on the illumination frequency is analyzed. We compute the complex resonance frequencies of the nanowires and show that frequencies near the real part of the plasmonic resonance frequency enhance the Fisher information. However, at the resonance frequency itself, the Fisher information drops sharply, leading to an Information Dark State in which the position of the nanowire becomes nearly undetectable. This effect is analyzed and illustrated for both gold and silver nanowires.

Partially coherent light is essential in lithography systems, where it improves illumination homogenization, enhances resolution, and mitigates speckle noise, playing a key role in advanced imaging applications. However, efficiently generating and computing partially coherent beams (PCBs) remains a challenge, particularly in high-precision lithography where computational efficiency is critical. Here, we introduce a novel modal-superposition method for PCB synthesis, termed “few-mode superposition” and demonstrate its effectiveness in achieving PCBs with higher precision and efficiency. The method requires significantly fewer modes compared to conventional techniques while maintaining high accuracy in intensity and coherence. We apply the few-mode superposition method to the efficient generation of partially coherent light sources and computational lithography, showcasing its ability to rapidly produce PCBs with nonconventional cross-spectral density functions. This facilitates fast lithography simulations and other applications involving partially coherent light. Our approach significantly accelerates both the generation and calculation of PCBs and holds promise for integration with on-chip laser sources, as well as for high-energy laser generation and lithographic mask design.

Lensless single-shot dual-wavelength digital holography is resolution limited by the pixel-size of the camera and often has an insufficient depth range. We present a novel dual-wavelength holographic configuration with expanding wavefront illumination that breaks the pixel-limited resolution barrier and achieves diffraction-limited spatial resolution. By implementing expanding wavefront illumination with dual-wavelength digital holography based on a wavelength-tunable laser, we achieve a high-resolution centimeter-scale depth range. A quantitative precision analysis demonstrates that single-shot acquisition reaches the shot-noise-limited depth detection. The proposed holographic scheme provides a robust 3D optical inspection solution for high-throughput, micro-scale resolution industrial inline metrology.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.