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

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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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

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

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

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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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

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

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

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

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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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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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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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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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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Shortly after their inception, superconducting nanowire single-photon detectors (SNSPDs) became the leading quantum light detection technology. With the capability of detecting single-photons with near-unity efficiency, high time resolution, low dark count rate, and fast recovery time, SNSPDs outperform conventional single-photon detection techniques. However, detecting lower energy single photons (<0.8 eV) with high efficiency and low timing jitter has remained a challenge. To achieve unity internal efficiency at mid-infrared wavelengths, previous works used amorphous superconducting materials with low energy gaps at the expense of reduced time resolution (close to a nanosecond), and by operating them in complex milliKelvin (mK) dilution refrigerators. In this work, we provide an alternative approach with SNSPDs fabricated from 5 to 9.5 nm thick NbTiN superconducting films and devices operated in conventional Gifford-McMahon cryocoolers. By optimizing the superconducting film deposition process, film thickness, and nanowire design, our fiber-coupled devices achieved >70% system detection efficiency (SDE) at 2 μm and sub-15 ps timing jitter. Furthermore, detectors from the same batch demonstrated unity internal detection efficiency at 3 μm and 80% internal efficiency at 4 μm, paving the road for an efficient mid-infrared single-photon detection technology with unparalleled time resolution and without mK cooling requirements. We also systematically studied the dark count rates (DCRs) of our detectors coupled to different types of mid-infrared optical fibers and blackbody radiation filters. This offers insight into the trade-off between bandwidth and DCRs for mid-infrared SNSPDs. To conclude, this paper significantly extends the working wavelength range for SNSPDs made from polycrystalline NbTiN to 1.5-4 μm, and we expect quantum optics experiments and applications in the mid-infrared range to benefit from this far-reaching technology.

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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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Single photon detectors are indispensable tools in optics, from fundamental measurements to quantum information processing. The ability of superconducting nanowire single photon detectors (SNSPDs) to detect single photons with unprecedented efficiency, short dead time, and high time resolution over a large frequency range enabled major advances in quantum optics. However, combining near-unity system detection efficiency (SDE) with high timing performance remains an outstanding challenge. In this work, we fabricated novel SNSPDs on membranes with 99.5-2.07+0.5% SDE at 1350 nm with 32 ps timing jitter (using a room-temperature amplifier), and other detectors in the same batch showed 94%-98% SDE at 1260-1625 nm with 15-26 ps timing jitter (using cryogenic amplifiers). The SiO2/Au membrane enables broadband absorption in small SNSPDs, offering high detection efficiency in combination with high timing performance. With low-noise cryogenic amplifiers operated in the same cryostat, our efficient detectors reach a timing jitter in the range of 15-26 ps. We discuss the prime challenges in optical design, device fabrication, and accurate and reliable detection efficiency measurements to achieve high performance single photon detection. As a result, the fast developing fields of quantum information science, quantum metrology, infrared imaging, and quantum networks will greatly benefit from this far-reaching quantum detection technology.

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A new method for fast, high resolution interrogation of an array of photonic sensors is proposed. The technique is based on the integrated Fourier transform (FT) interrogator previously introduced by the authors. Compared to other interferometric interrogators, the FT-interrogator is very compact and has an unprecedented tolerance to variations in the nominal values of the sensors’ resonance wavelength. In this paper, the output voltages of the interrogator are written as a polynomial function of complex variables whose modulus is unitary and whose argument encodes the resonance wavelength modulation of the photonic sensors. Two different methods are proposed to solve the system of polynomial equations. In both cases, the Gröbner basis of the polynomial ideal is computed using lexicographical monomial ordering, resulting in a system of polynomials whose complex variable contributions can be decoupled. Using an NVidia graphics processing card, the processing time for 1 026 000 systems of algebraic equations takes around 9 ms, which is more than two orders of magnitude faster than the interrogation method previously introduced by the authors. Such a performance allows for real time interrogation of high-speed sensors. Multiple solutions satisfy the algebraic system of equations, but, in general, only one of the solutions gives the actual resonance wavelength modulation of the sensors. Other solutions have been used for optimization, leading to a reduction in the cross-talk among the sensors. The dynamic strain resolution is 1.66 nε/√Hz.

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