Since scalar imaging theory treats propagating waves as being scalar, it does not completely describe their physical properties. However, it plays an important role in the field of optical design and applications, such as semiconductor exposure projection optics. Therefore, we establish an accurate and meaningful scalar imaging theory, applicable even for high numerical aperture optics. We call this the consistent scalar imaging theory and consider the following three criteria for consistency. (1) When the wavelength of light becomes close to zero, the point spread function of wave optics coincides with the spot diagram (correspondence principle). (2) When considering point imaging, the total energy incident on the pupil equals that on the image. (3) The reciprocity theorem holds between object and image. These conditions are simultaneously fulfilled by introducing appropriate outgoing and incoming inclination factors. We emphasize that the pupil coordinates should be defined as the direction cosine of the ray.
Structured light beams with extraordinary properties have revolutionized a wide range of applications such as optical manipulation, high-resolution imaging, classical and quantum communications, and so on. These beams can be cleverly shaped with tailored amplitudes, phases, polarizations, and coherences. With advancements in this field, an increasing number of light beams have been uncovered and investigated, including non-diffracting Bessel beams, self-accelerating Airy beams, and abruptly autofocusing circular Airy beams. Pearcey beams, as emerging stars in the field of structured light beams, have garnered considerable attention due to their autofocusing performance and inversion effect. In this review, we provide an overview of the recent advancements in Pearcey beams. We start with the introduction of the prototypical Pearcey beams including the coherent versions that were first proposed and observed in 2012, and their partially coherent counterparts that were reported in 2020. Besides, we describe a virtual source method for generating non-paraxial Pearcey beams. Then, we focus on the diverse Pearcey variants and their remarkable features, including the ring Pearcey, spectrum-engineered Pearcey, chirped Pearcey, and Pearcey pulse, which enrich the Pearcey family. Furthermore, we discuss the practical applications with the Pearcey beams, particularly in particle manipulation and topological charge measurement. These studies serve as a catalyst for our exploration into the realm of higher-dimensional manipulation and broader applications of Pearcey light fields.
Analog-based all-optical computation has recently gained renewed interest due to the growing demand for data processing and the associated need for low-power, high-speed and compact computational platforms. While optical computing platforms based on bulky optical setups—such as 4f systems and pulse shapers—have been studied for decades, their large footprints have prevented their miniaturization and integration. Recently, a new all-optical computing platform has been proposed based on metamaterials—artificially structured materials with morphological features smaller than the radiation wavelength. By accurately tailoring their transfer function, it is possible to design metamaterials that perform computational tasks similar to their macroscopic counterparts, but within subwavelength footprints. In this chapter, we discuss the general working principle of these devices, their advantages and challenges, and the relevant figures of merit to be optimized. We also highlight specific examples and applications, providing a review of recent literature and an outlook on the field.
Rotated reference frames offer fast algorithms for the radiative transport equation (RTE). We review the singular-eigenfunction approach and related numerical methods for the multi-dimensional RTE with rotated reference frames.
Single-photon detectors based on superconducting effects have demonstrated the potential for widespread use in diverse applications such as quantum information, quantum optics, and bioimaging. In this review, we introduce the key technologies of superconducting transition edge sensors, which can be used not only as single photon detectors but also as photon number resolving detectors. We review the latest achievements realized by such devices, in addition to the applications in cutting-edge research areas that have benefited from these advances.
We present the electromagnetic fields of vector Pearcey beams by employing the vector angular spectrum representation. The beams maintain the inherent properties of autofocusing performance and inversion effect. Based on the generalized Lorenz-Mie theory and Maxwell stress tensor approach, we derive the partial-wave expansion coefficients of arbitrary beams with different polarization and the rigorous solution to evaluate the optical forces. Furthermore, we investigate the optical forces experienced by a microsphere placed in vector Pearcey beams. We study the effects on the longitudinal optical force arising from the particle size, permittivity and permeability. This exotic curved trajectory transport of particles by vector Pearcey beams may find applications in the case where the transport path is partly blocked.
The interference phenomenon of light is a common but most important effect in physics. In this article, we compare and analyse the interference effects of both coherent and incoherent light; in particular, the interference of spatially incoherent light sources is described. Thermal light and a two-photon entangled source may both be regarded as incoherent sources which can generate similar second-order interference effects, but their underlying physics is quite different. First-order interference can be realized with both spatially coherent and incoherent sources in the same well-designed experimental setup, but exhibit different interference patterns; their different interference mechanisms will also be clarified.
The discovery of high-order harmonic generation in the late 1980s and the subsequent realization of attosecond temporal confinement of the emitted radiation, have stimulated significant interest in the study of attosecond phenomena in atoms, molecules, and solids. In the last two decades, technological advances in laser technology have permitted the development of isolated attosecond pulse sources spanning the extreme ultraviolet and extending into the soft X-ray region of the spectrum, and have stimulated the development of time-resolved spectroscopies and sophisticated theory techniques capable of following the electron dynamics of quantum systems in the time domain. In particular, attosecond science has allowed unique insight into laser-driven dynamics occurring on sub-optical cycle time scales, including ionization, high-order harmonic generation, Stark shifts, and other processes. The techniques are now sufficiently sophisticated to follow non-adiabatic electronic processes in gas-phase molecules, and to probe the dynamics of quantum phase transitions in solids. In this chapter, we review the techniques and technologies for generating attosecond pulses through high-order harmonic generation, and highlight some recent advances in the applications of attosecond pulses to study dynamics in atoms, molecules, and solids.
The unrestricted shape of freeforms has opened the possibility of finding solutions clearly exceeding the performance of their rotationally symmetric counterparts. This applies especially to systems where the specifications (either optical or geometrical) deviate from rotational symmetry. For instance, short throw distance multimedia projectors cannot be placed in front of the center of the projected image without blocking the spectators’ view. This requires the projection to be done from the side. Offset rotational symmetric solutions are not optimal: a freeform projector can improve the image quality on the target area with the same number of surfaces or can match the quality with fewer optical surfaces. Similar problems arise in head-worn displays when trying to make the headsets sleeker while providing excellent image quality. In nonimaging applications, low-beam headlamps of cars also need to produce an asymmetric pattern on the road to avoid blinding the incoming drivers. Freeforms permit to solve these design problems both efficiently and matching aesthetic constraints at the same time. The continuous progress in the technology to produce and test freeforms, as occurred in the past with rotationally symmetric aspherics, is pushing optical designers to include tailored freeforms in their designs. However, the likewise higher complexity of these unrestricted surfaces introduces multiple new challenges in their design. These challenges range from finding the best mathematical description of the optical surfaces to the design algorithms themselves. In this article, we’ll review a wide range of state-of-the-art freeform design techniques and illustrate their use in specific examples for a wide range of applications.
Polarization is one of light’s most versatile degrees of freedom for both classical and quantum applications. The ability to measure light’s state of polarization and changes therein is thus essential; this is the science of polarimetry. It has become ever more apparent in recent years that the quantum nature of light’s polarization properties is crucial, from explaining experiments with single or few photons to understanding the implications of quantum theory on classical polarization properties. We present a self-contained overview of quantum polarimetry, including discussions of classical and quantum polarization, their transformations, and measurements thereof. We use this platform to elucidate key concepts that are neglected when polarization and polarimetry are considered only from classical perspectives.
Focusing light into a small spot is vital in many research and industrial fields. In principle, the diffraction nature of light restricts the achievable size of a focal spot referred to as the diffraction limit. Cylindrical vector beams have a promising feature that can surpass this limit in tight focusing conditions. This small focal spot characteristics of vector beams are being extensively applied to optical imaging for spatial resolution enhancement. This study reviews the fundamentals and the recent progress of the small focal spot formation by vector beams. Some advanced features, including superoscillation focusing, dark spot formation, and utilization in laser scanning microscopy, will be discussed in detail herein.
Optical coherence tomography (OCT) is a noninvasive, three-dimensional imaging technique that offers close-to-histology-level image quality. Based on broadband spectral interferometry, OCT has enabled clinical applications ranging from ophthalmology to cardiology that revolutionized in vivo medical diagnostics. Considering the size and cost of a commercial OCT system, it is essential to investigate different approaches for realizing a compact and low-cost OCT system in order to make it accessible to a significantly larger group of applications and users. Exploiting integrated optics, several central components of an OCT system have been assembled on a microchip so far. Silicon based designs have the advantage of complementary metal-oxide-semiconductor (CMOS) compatible high-volume production while indium phosphate (InP) based designs have the possibility of monolithic integration of the light source and the detector with other components. In this chapter, the design considerations, theoretical analysis and experimental results of the passive integrated optical components of an on-chip OCT system including interferometer, spectrometer, reference arm, and sample arm will be presented. Active components (light source and detectors) are beyond the scope of this chapter.
