SignificanceThe invention of lasers has led to a boom of laser technology in various science and engineering of many interdisciplinary fields, which have been widely applied in optical manipulation, precision measurement, optical communication, laser processing, microscopy imaging, and so on. However, the simple propagation characteristics of the traditional Gaussian laser mode have hit the bottleneck in the further development of laser technology and failed to meet the ever-increasing needs in the related fields. Consequently, light field manipulation has emerged. By modulating the amplitude, phase, and polarization of the light field, many new types of spatially structured fields with novel physics effects or propagation properties have been proposed. Optical vortices and cylindrical vector beams are among the most well-known examples. To resist beam diffraction and environment disturbance, researchers have discovered a new class of spatially-structured field named “non-diffracting beam”. Theoretically, a non-diffracting beam can maintain its transverse intensity profile during propagation and can propagate over long distances with little beam spreading. Subsequently, a series of non-diffracting beams with different spatial structures, such as Mathieu beams, Weber beams, Airy beams, and Bessel beams, have been proposed, all of which exhibit the common characteristics of non-diffracting beams. As a typical non-diffracting beam, the Bessel beam quickly attracts great attention of research after being proposed as a propagation-invariant solution of the Helmholtz equation. Extensive research has been conducted on non-diffracting beams, including the applications in improving microscopy imaging quality and the performance of optical trapping. With the continuous development of light field manipulation, researchers have gradually attempted to control Bessel beams through different means by modulating or superposing the Bessel beams. Modulated Bessel beams can behave the self-accelerating propagation with nonlinear trajectories, with tunable on-axis intensities and polarizations, or even generate propagation-varied modes, which are different from traditional Bessel beams. Combining Bessel beams with other spatially structured light fields or optical elements for light field modulation would further expand the freedom degree for controlling Bessel beams. In this review, hence, we introduce the basic theory and generation methods of Bessel beams and review the research progress of the propagation control of Bessel beams, including the trajectory control, on-axis intensity management, longitudinally control of polarization, and self-similar Bessel beams.ProgressIn section 2, we introduce the basic characteristics of Bessel beams. Subsection 2.1 presents the solution of Bessel modes from the Helmholtz equation. Typical intensity and phase profiles of Bessel beams with different orders are represented (Fig. 1). The principle and several methods of generating Bessel beams are introduced in subsection 2.2. Fig. 2(a) shows the conical wave vector of Bessel beams, based on which two typical methods of generating Bessel beams with annular aperture and axicon are represented in Figs. 2(b) and 2(c), respectively. Based on the axicon-type phase, we propose a computer-generated hologram [Fig. 2(d)] and dielectric metasurface [Fig. 2(e)] to generate Bessel beams. Additionally, we introduce some other methods with the Fabry-Perot resonator [Fig. 2(f)] and optical fibers. Fig. 3 demonstrates the self-healing properties of Bessel beams. In section 3, we introduce the propagation trajectory control of Bessel beams. Subsection 3.1 presents the spiral Bessel beams, including radially self-accelerating beams (Fig. 4), accelerating rotating beams produced by the superposition of nonlinear vortex beams (Fig. 5), and spiraling zero-order Bessel beams produced by splicing the beam cone (Fig. 6). In subsection 3.2, the Bessel-like beams propagating along arbitrary trajectories based on caustic principle and pure phase modulation are shown in Figs. 7 and 8, respectively. The controllable spin Hall effect of the Bessel beam realized by geometric phase elements is introduced (Fig. 9). Subsection 3.3 represents the nonparaxial self-accelerating beams in Fig. 10, based on which tightly autofocusing beam is proposed (Fig. 11). In section 4, we introduce the axial intensity engineering of Bessel beam. In subsection 4.1, we introduce the theory of “Frozen Waves” (Fig. 12) and the modified “Frozen waves” following spiral and snake-like trajectories (Fig. 13). In subsection 4.2, the on-axis intensity modulation based on the spatial spectrum engineering [Fig. 14(a)] is introduced. By using metasurface, the on-axis intensity with rectangle and sinusoidal profiles are realized [Figs. 14(b) and 14(c)]. The on-axis intensity management is also applied to the self-accelerating Bessel beams to realize the on-demand tailored intensity along arbitrary trajectories [Fig. 14(d)]. Section 5 introduces the longitudinal control of the polarization of the Bessel beam. In subsection 5.1, the Bessel beams with propagation-varied polarization state are proposed based on the transverse- longitudinal mapping (Fig. 15). Based on the mapping, the vector Bessel-Gauss beams with propagation-variant polarization state and the corresponding self-healing are introduced (Fig. 16). In subsection 5.2, polarization oscillating beams constructed by superposing the copropagating optical frozen waves are shown in Fig. 17. In subsection 5.3, we introduce the longitudinal polarization control via the Gouy phases of beams. The self-accelerated optical activity in free space according to the Gouy phase difference between the Bessel beam and Laguerre-Gauss beam is shown in Fig. 18. We introduce the analogous optical activity in free space using a single Pancharatnam-Berry phase element, which can highly resemble the on-axis circular birefringence of beams. Fig. 19(a) shows the polarization rotator based on the theory. In addition, the off-axis circular birefringence, triggered by a tilted input Bessel beam, can generate the photonic spin Hall effect, which can be enhanced by inputting a self-accelerating Bessel-like beam [Fig. 19(b)]. In section 6, we introduce the self-similar Bessel-like beam, including self-similar beams with different scaling factors by solving the paraxial wave equation (Fig. 20), self-similar arbitrary-order Bessel-like beams based on the Fresnel integral (Fig. 21), and constructing arbitrary self-similar Bessel-like beams via transverse-longitudinal mapping (Fig. 22).Conclusions and ProspectsModulated Bessel beams exhibit increased controllability during propagation while retaining the non-diffracting and self-healing properties. The trajectory, intensity, polarization state, and beam width can be flexibly controlled in the propagation direction. These characteristics have significant potential in various applications, including optical manipulation, microscopy imaging, and precision machining.

SignificanceTo help humans explore and understand the world, researchers have been committed to exploring diverse techniques of optical field manipulation to accomplish a variety of applications since the inception of the field of optics, including imaging, detection, sensing, communications, and so on.With the rapid development of modern micro-nanofabrication techniques, there is increasing interest in manipulating multiple degrees of freedom of light flexibly. However, at the nanoscale, there are close couplings and interactions among classical degrees of freedom such as intensity, phase, and polarization, making it difficult to achieve flexible and independent control of these degrees of freedom. Whereas, momentum and angular momentum degrees of freedom of light, which are a fundamental dynamic physical quantity of elementary particles and class wave fields and play important roles in the light-matter interactions, offer extreme advantages in manipulating the light in the nanoscale. For example, through the spin-momentum equation, spin and orbit angular momentum can be individually controlled, allowing for more precise manipulation and utilization of the spin properties of photons individually. The numerous advantages of controlling the spin angular momentum of photons bring new opportunities for nanophotonics, particularly in the areas of optical manipulation, detection, information processing, chiral quantum optics, and quantum entanglement.Plenty of novel and interesting optical phenomena and applications have been proposed connecting to the interactions between optical spins and matters or nanostructures, and a new research field of spin optics has been born in recent years. Previously, most of the researchers mainly focused on the optical longitudinal spin parallel to the direction of the mean wave vector. In recent years, by studying the spin-orbit couplings of confined fields, such as focused fields, guided waves, and evanescent waves, researchers have discovered a new class of optical spins that are perpendicular to the direction of the mean wave vector, which are also known as optical transverse spins. Optical transverse spin possesses the properties of spin-momentum locking, so it has been widely studied by researchers since discovered. Moreover, the discovery of optical transverse spin expands the content of optical spin-orbit interactions, and it has potential in the applications of optical manipulation, ultrahigh-precision optical detection, chiral quantum optics, and optical spin topological states. Here, we introduce the recent progress of spin optics in detail from three aspects: theory, characterizations, and applications. These theoretical concepts and frameworks of spin optics can play a critical role in further developing applications based on optical spins in optical imaging, detection, communications, and quantum technology, and they can be flexibly expanded to other classical wave fields, such as fluid waves, sound waves, and gravitational waves.ProgressIn this paper, we provide a comprehensive overview and summary of the manipulating mechanisms of spin angular momentum and discuss the underlying relationship between the Abraham-Poynting momentum density, Minkowski canonical momentum density, Belinfante's spin momentum density, spin angular momentum density, and orbital angular momentum density in classical optical theory. Subsequently, starting from the longitudinal spin in the paraxial beams, we introduce the spin angular momentum in different optical fields, including transverse spin in evanescent fields and transverse spin in interference fields. Finally, to address the difficulty in simply defining transverse and longitudinal spins in structured light fields, we present a set of spin momentum equations, analogous to Maxwell's equations, to describe the dynamical properties of spin angular momentum density and momentum density. Furthermore, these spin-momentum equations extend the properties of optical spin-momentum locking from evanescent plane waves to general evanescent fields. We also comprehensively overview the measurement techniques for spin angular momentum in confined fields and free space, including scanning near-field optical microscopy, nano-particle-film structures, photoemission electron microscopy, and nonlinear optical effects. By utilizing these techniques, it is possible to effectively extract different electromagnetic field components to obtain the information of spin angular momentum carried by the optical field. The current application scenarios of spin angular momentum are also comprehensively summarized, including weak effect measurements, optical differentials, optical lateral forces, precision sensing, and magnetic domain detection.Conclusions and ProspectsAs a novel degree of freedom in the field of optics in addition to intensity, phase, and polarization, the spin angular momentum carried by the structured light can be applied in communication, imaging, precision detection, and other fields. In this paper, we introduce the concept, definition, classification, and physical origin of spin angular momentum and review the characterization methods of spin angular momentum developed in recent years, as well as its applications in weak effect detection, optical differentials, optical lateral forces, precision sensing, and magnetic domain detection. On the one hand, spin angular momentum is a fundamental dynamical physical quantity of basic particles such as photons and atoms, providing new perspectives for the interaction of small-scale light with matter. On the other hand, as a novel optical degree of freedom, spin angular momentum can provide new solutions for large-scale light field control, optical imaging, optical communication, and optical detection applications. In turn, it further serves to explore new mechanisms and phenomena in the interaction between light and matter, expanding the applications of spin photonics.

SignificanceThe two-dimensional photonic crystal slab (PhCS) is a structure characterized by the spatial periodicity of the dielectric constant within the plane. In contrast to traditional metamaterial surfaces, the two-dimensional PhCS enables light field manipulation in momentum space based on the Fourier principle, thus achieving complex and diverse functionalities. Since modes above the light cone can radiate to the far field and possess definite polarization states, polarization is matched with wave vectors, defining polarization fields in momentum space. Various polarization singularities exist within the polarization field, such as V points and C points. Previous studies generally focus on information such as frequency and momentum, while the polarization field can reflect the topological information of the bands and provide a new dimension for light field manipulation. For example, by controlling the evolution of polarization singularities, researchers have obtained bound states in the continuum (BICs) with robust characteristic and unidirectional guided resonances (UGRs). By utilizing these characteristics, researchers have designed high-performance lasers and realized complex light field manipulation and such functionalities as optical information processing. Compared to traditional structures, the two-dimensional PhCS exhibits non-local characteristics and has significant advantages in miniaturization and integration. Thus, it holds promising prospects for device applications. Studying the evolution of the polarization field helps guide the structural design of photonic crystal slabs, which expands the applications in communication, sensing, and other fields, and provides a deeper understanding of how topological photonics is manifested in optical systems.ProgressWe start by introducing the definition of the polarization field in the momentum space of the two-dimensional PhCS and introduce the concept of polarization singularities (Fig. 1). Subsequently, an analysis is conducted from the perspective of symmetry, with the relationship between the topological charge of polarization singularities and the in-plane point group symmetry examined (Fig. 2 and Table 2). Additionally, we outline the description of the polarization field using the temporal coupled mode theory (TCMT). Furthermore, the conservation law followed by the topological charges during their evolution is discussed (Fig. 3) to detail the research on the evolution of polarization singularities based on whether the band is non-degenerate or degenerate. It is observed that non-degenerate V points correspond to BICs and are split into more fundamental C points during symmetry change (Fig. 4). The evolution of these polarization singularities is controlled by structural parameters and symmetry (Fig. 5). Degenerate V points typically correspond to band degeneracy points and are also influenced by structural parameters and symmetry (Fig. 6). Based on the evolution patterns of polarization singularities, researchers have designed robust merging BICs and utilized the topological charge to generate vortex beams and beam shifts (Fig. 7), providing significant guidance for laser design. Furthermore, by altering the out-of-plane symmetry, UGR can be achieved (Fig. 8). Additionally, appropriately designed PhCS can achieve full coverage on the Poincaré sphere and perform complex image processing tasks such as edge detection (Fig. 9).Conclusions and ProspectsGenerally, the investigation of the polarization field characteristics of PhCS guides the design of appropriate structures and can help achieve complex and rich functionalities. Despite the presence of numerous unresolved physical issues currently, the application potential of the polarization field remains largely untapped. However, these unknowns are expected to stimulate enthusiasm for exploration and boost progress in related fields.

SignificanceLight is an indispensable carrier of energy and information in humans' daily life. The main information of light fields can be described by a few attributes such as amplitude, phase, frequency, and polarization. How to flexibly and effectively manipulate these light field dimensions has been a key research focus in optics and photonics. Meanwhile, with the development of technology, “Moore's Law” is gradually losing its effectiveness, and traditional electronic chips are facing increasing performance improvement challenges. Compared with electrons, photons have fast transmission velocity, high information-carrying capacity, and unique parallel processing capability. Therefore, replacing electronic components partially or completely with optical components is expected to solve many problems facing traditional electronic chips. However, traditional optical components are generally large in size and heavy. Therefore, the miniaturization and integration of multiple optical components into the same chip is an important trend in the future development of photonic chips.Optical artificial microstructure (also called“metaatom”) is a kind of artificial structure with subwavelength size in one or more dimensions, which can resonate with light fields to achieve functions beyond traditional natural materials. A metasurface can be formed by ordering optical artificial microstructures on a two-dimensional surface. It provides not only practical and effective solutions for the miniaturization and integration of traditional optical components but also more diverse means of controlling light fields and richer light-matter interactions. However, most current metasurfaces are focused on the manipulation of free-space light fields, and a metasurface can only achieve a single or a few functions. To further achieve more compact and versatile photonic chips, researchers have begun to integrate optical artificial microstructures with on-chip optical waveguides or optical microcavities in recent years. The research on on-chip integrated artificial microstructures injects new vitality into light field manipulation and nano-photonics devices. Thanks to their subwavelength sizes and unique resonance characteristics, artificial microstructures can serve as a bridge connecting free-space light fields with on-chip waveguide modes, thus opening up new opportunities for fully manipulating light in integrated optical systems and free space. Even though various novel optical devices have been proposed based on on-chip integrated artificial microstructures in the past few years, they still face a series of challenges in large-scale ultra-compact integration and performance improvement. Therefore, a review of light field manipulation based on on-chip integrated artificial microstructures is necessary to provide helpful guidance for researchers to design novel on-chip optical devices.ProgressBased on different types of light fields manipulated by on-chip integrated artificial microstructures, we categorize them into three classes for discussions (Fig. 1). The first category involves “meta-couplers” that can couple free-space optical modes into waveguides or microcavities and convert them into specific guided modes. The artificial microstructure-based meta-couplers can achieve more diverse and complex functions than traditional grating couplers, such as wavelength- and polarization-demultiplexing, or the excitation of specific guided modes (Fig. 2). The second category involves “in-plane modulators” that enable on-chip manipulation of confined light fields within the chip plane. Artificial microstructures can be either partially- or fully-etched aperture antennas, or they can be directly integrated onto the waveguide surface. By adopting the refractive index perturbation or phase gradient provided by the microstructures, in-plane focusing of waveguide modes, filters, mode conversions between different guided modes, and on-chip nonlinear harmonic generations can be achieved (Figs. 3 and 4). Additionally, on-chip integrated artificial microstructures can be combined with dynamic control schemes such as electro-optic modulators to further optimize the modulator's footprint and bandwidth performance. The third category involves “guided wave-driven metasurfaces” that can convert guided waves into free-space waves. By employing one-dimensional (Fig. 5) and multi-dimensional (Figs. 6 and 7) manipulation of far-field radiation, guided wave-driven metasurfaces can achieve various applications, such as holographic imaging, vortex beam generation, beam focusing, and beam deflection. Theoretically, the polarization, amplitude, phase, and orbital angular momentum of the emitted light field can be manipulated arbitrarily to provide new solutions for applications such as virtual reality, augmented reality, and information encryption and multiplexing.Conclusions and ProspectsWe systematically introduce the research progress of on-chip integrated artificial microstructures in the areas of free-space light coupling, in-plane manipulation of guided modes, and the manipulation of off-chip radiated fields. Additionally, we provide an outlook on some emerging directions in this field. By cascading multiple optical metasurfaces on waveguides, on-chip optical components can be more compact, and multifunctional devices beyond traditional metasurfaces can be realized. Some novel physical effects such as bound states in the continuum, parity-time symmetry, and exceptional points can provide a richer range of physical processes for on-chip integrated artificial microstructures. The introduction of new materials such as two-dimensional materials and laser gain materials can provide a new platform for studying excitons, valley spin, nonlinear effects, on-chip lasing, and other phenomena. The utilization of inverse design methods such as deep learning and topological optimization can serve as powerful tools for designing on-chip integrated artificial microstructures. In summary, with the advancement of technology, the application scope of on-chip integrated artificial microstructures will become more widespread. The operating wavelength range can expand from visible and near-infrared light to terahertz, microwave, and ultraviolet wavebands. Additionally, numerous miniaturized and integrated on-chip photonic devices will continue to emerge with the help of artificial microstructures.

SignificanceThe significance of optical skyrmions and the research around them cannot be overstated. Optical skyrmions which are topologically protected spin textures have attracted considerable attention due to their unique properties and potential applications in various fields. The skyrmion is a unified model of nucleons initially proposed by British particle physicist Tony Skyrme in 1962 and behaves like a nano-scale magnetic vortex with intricate textures. Meanwhile, it occupies significant positions in quantum field theory, solid-state physics, and magnetic materials. Skyrmions are widely regarded as efficient information carriers thanks to their unique topological stability, high speed, high density, and low energy consumption. However, generating optically controlled skyrmions remains a significant challenge. Breaking the limitation of topological control for skyrmions will unlock infinite possibilities for the next-generation information revolution, including applications in optical communication, information encryption, and topological phase transitions. This will present new opportunities for the expansion and practical application of advanced fundamental theories of photonics. Optical skyrmions exhibit nontrivial topological structures, robustness against external perturbations, and ultra-fast motion dynamics, serving as promising candidates for the development of novel information storage and processing technologies. Studying optical skyrmions is essential for several reasons. First, optical skyrmions provide a new paradigm for information storage with high-density and low-energy requirements. Their topological nature ensures stability against thermal fluctuations and material defects, which makes them highly reliable for long-term data retention. This property is particularly valuable in the era of big data and cloud computing, where efficient and durable information storage solutions are in high demand. Second, the unique properties of optical skyrmions make them ideal for spintronic applications. Spintronics, which utilizes the spin of electrons for information processing, has emerged as a promising field for the development of next-generation electronic devices. Optical skyrmions provide a means of manipulating and controlling spin currents, thus enabling the design of novel spin-based devices, such as spin transistors, logic gates, and memory elements, with enhanced functionality and reduced power consumption. Furthermore, the study of optical skyrmions can shed light on fundamental physics principles and contribute to our understanding of condensed matter physics. The complex interplay between spin, magnetism, and topology in optical skyrmions poses intriguing scientific challenges and opens up new avenues for exploring new phenomena. Additionally, investigating the formation, dynamics, and interactions of optical skyrmions can provide valuable insights into the fundamental laws governing quantum systems and promote the development of advanced theoretical frameworks. Meanwhile, optical skyrmions hold promise for applications in photonics and optoelectronics. The ability to control and manipulate light at the nanoscale is of significance in fields such as telecommunications, data transmission, and sensing. Optical skyrmions provide a new approach to achieving efficient light modulation, waveguiding, and information encoding, thereby enabling the development of compact and high-speed photonic devices with improved performance. In summary, the study of optical skyrmions is of paramount significance due to their potential applications in information storage, spintronics, fundamental physics research, and photonics. By unraveling the unique properties and behavior of optical skyrmions, researchers can pave the way for innovative technologies that can revolutionize various domains. Continuous exploration of this field will undoubtedly lead to exciting discoveries and transformative advancements in science and technology. In recent years, there has been a continuous emergence of optical skyrmions with different topological structures and vector configurations, including transient field skyrmions, structured medium skyrmions, free-space skyrmions, spacetime skyrmions, and momentum space skyrmions. In particular, spin skyrmions in transient fields and Stokes skyrmions in free space provide valuable references for skyrmion applications. However, the practical applications of optical skyrmions still face a series of challenges. Therefore, it is important and necessary to summarize the existing research achievements and provide more rational guidance for the future development of this field's applications.ProgressWe review the current research progress of optical skyrmions, and discuss in detail the topological structure classification of optical skyrmions, the generation and manipulation of optical skyrmions with different vector configurations, and the potential applications of optical skyrmions in micro-displacement measurement and optical communication encoding and encryption. As a result, references are provided for further development in this field. With the flourishing topological optics, the existence of optical skyrmions has been confirmed by the scientific community. In 2018, the research team led by Tsesses first realized Néel-type electric field vector optical skyrmions via surface plasmon interference excited by metal surface hexagonal grating structures [Fig. 4(a)]. Meanwhile, the research team led by Yuan realized Néel-type spin vector optical skyrmions via surface plasmon interference excited by tightly focused vector structured light fields on a metal surface [Fig. 6(a)]. Additionally, they further developed a sub-nanometer optical displacement sensing system by controlling the spin distribution of optical skyrmions on a skyrmion pair (Fig. 13), opening up the path for practical applications of optical skyrmions. In 2023, the research team led by Shen proposed a high-capacity optical communication and secure encryption scheme based on optical topological quasi-particles, with the reliance on Stokes vector optical skyrmions (Fig. 14). Currently, optical skyrmions with different topological structures and vector configurations continue to emerge, providing new ideas and methods for the study of spatio-temporal characteristics of topological structured light fields.Conclusions and ProspectsOptical skyrmions have become a major focus in the research on topological optics. Skyrmions can be formed and controlled within optical fields, and the development of high-dimensional structured light provides possibilities for constructing complex topological structures of high-dimensional skyrmions. In conclusion, if the topological limitations of skyrmions can be overcome to achieve freely controllable topological states, infinite possibilities will be posed to the next-generation information revolution. Applications such as optical communication, information encryption, spin-orbit interactions, and topological phase transitions will benefit from the expansion and practical applications of advanced photonics fundamentals.

SignificanceLight waves will propagate without distortion in a uniform medium according to its wave equation and are widely employed for energy and information transmission. However, absolutely uniform media do not exist in the real world, and there are various defects and impurities in various media, especially in completely disordered media. Small particles within the scattering medium can make light waves deviate from their original propagation direction, which results in a disordered light field, forms speckles, and thus hinders energy and information transmission. Since in the early stages scattering was believed to be irreversible, most conventional methods relied on extracting ballistic photons from the scattering photons to address scattering-induced aberrations. As the ballistic photons decay exponentially with the increasing propagation distance, and it is difficult to extract ballistic photons from scattering photons after a certain depth, scattering correction based on ballistic photons is only applicable to weakly scattering media.With the rapid development of spatial modulation devices such as spatial light modulators and digital micromirrors, it has become possible to realize the spatial light modulation with high accuracy. In 2007, Vellekoop and Mosk proposed a landmark new technique based on spatial light modulators that can compensate for the strong scattering effect, which is the wavefront shaping method to pre-compensate for the wavefront aberrations due to scattering by iteratively optimizing the wavefront of the input light. Meanwhile, the scattering light field manipulation has become possible. Additionally, light propagation in complex media is characterized by the transmission matrix. In just over a decade, scattering light field manipulation based on the wavefront shaping method has been widely adopted in many fields. For example, wavefront shaping methods can be employed to achieve light focusing beyond the diffraction limit by strongly scattering media and compensate for light scattering effects, further enabling high-resolution imaging at high transmission depths. In addition to the imaging field, scattering light field manipulation can transform the inherently harmful scattering medium into a variety of optical elements such as beam splitters, angular momentum generators and converters, and polarization controllers. In the field of communication, the scattering light field manipulation can increase the scattering light intensity received by an optical receiver and realize high-speed non-line-of-sight communication with lower power consumption. Additionally, mode selection of the outgoing field of a multi-mode fiber can be performed by scattering light field manipulation and the spectrum modulation of a nonlinear output field.ProgressWe focus on scattering light field manipulation, introduce the research progress in related fields and highlight the new applications of scattering light field manipulation in various research fields. Meanwhile, we first introduce the light field scattering characteristics, followed by the introduction of scattering and its light field modulation methods based on transmission matrix, feedback-based wavefront shaping, optical phase conjugation, and artificial intelligence-assisted wavefront shaping. Subsequently, the studies of the modulation methods of multiple degrees of freedom of the scattering light field, such as spatial (Figs. 1-3), polarization (Figs. 4-5), spectral (Figs. 6-8), energy (Fig. 9), and orbital angular momentum (Fig. 10) are presented. Finally, the existing applications in various fields of scattering light field manipulation are introduced. For example, the fluorescence-based transmission matrix is employed to achieve non-invasive imaging of biological tissues (Fig. 12). Orbital angular momentum communications in a complex environment are realized by exploiting the transmission matrix method (Fig. 18). Manipulation of nonlinear scattering optical field is achieved by adopting the transmission matrix method (Fig. 22). Scattering compensation of entangled photon pairs is performed by optimizing the pump wavefront (Fig. 24). Discrete Fourier transform can be achieved by utilizing the transmission matrix method (Fig. 27).Conclusions and ProspectsIn summary, we introduce in detail the manipulation methods of each degree of freedom of the scattering light field, and the latest progress of the scattering light field manipulation in various fields, such as imaging, optical communication, nonlinear optics, quantum optics, optical sensing, integrated optics, and optical computing. Although scattering light field manipulation has made great progress, there are still some limitations to be broken through. 1) The energy utilization of scattering light is low with only part of the fully modulated scattering field. 2) The modulation speed is slow, and real-time scattering light field manipulation should be realized under dynamic scenarios. 3) It is difficult to modulate multiple physical quantities simultaneously, and most of the scattered light modulation can only realize the manipulation of a single physical quantity. With the further development of optimization algorithms, artificial intelligence, and modulation devices, scattering light field manipulation will move towards more precision, higher resolution, and deeper detection depth. The high degree of freedom brought by the combination of scattering light field manipulation and strong scattering media will also provide new solutions for the development of new optical components in the future. We believe that the further development of scattering light field manipulation will lead to many new applications.

SignificanceCoherence and polarization are two intrinsic properties of optical fields. The investigation of optical coherence has boosted the development of partially coherent optics, while the study of polarization properties has led to the discovery and application of optical structured vector fields. For a long time, the coherence and polarization properties of optical fields were generally treated as independent degrees of freedom and often studied separately. Since the 1990s, researchers have gradually realized the inherent correlation between the coherence and polarization properties of optical fields. It has been recognized that coherence and polarization properties can interact during light beam propagation or in the interaction of light with complex media. The joint control of coherence and polarization has driven the study of partially coherent vector optical fields. However, previous research mainly focuses on electromagnetic Gaussian Schell-model beams, whose coherence structure follows a Gaussian distribution. Recently, with the emerging research on light field manipulation and structured light, and the development of theories and technologies for controlling the coherence structure of optical fields, the research focus on partially coherent vector beams has gradually shifted toward those with special spatial coherence structures. Due to the control of vectorial coherence structures, these beams exhibit characteristics during propagation that are completely different from traditional electromagnetic Gaussian Schell-model beams. They have potential applications in far-field polarization shaping and optical super-resolution imaging. Furthermore, with the rapid development of nano-optics, research on three-dimensional optical fields has emerged. Studies have indicated that due to the modulation of coherence, partially coherent vector fields exhibit rich three-dimensional polarization characteristics. We review the research progress on the joint control of coherence and polarization in optical fields, with a focus on the characterization and synthesis of two-dimensional partially coherent vector optical beams with special spatial coherence structures, and their robust transmission properties in complex environments. By combining developments in nanophotonics, we present the extension of two-dimensional partially coherent vector beams to three-dimensional partially coherent vector fields.ProgressWe start by reviewing the characterization, synthesis, measurement, and propagation of two-dimensional partially coherent optical beams. In the characterization of two-dimensional partially coherent vector beams, the utilization of two-dimensional coherence and polarization matrices is common. Various polarization characteristics of the beams and construction of polarization Stokes parameters and Poincaré sphere are obtained by the two-dimensional polarization matrix. Although the coherence Stokes parameters similar to the polarization Stokes parameters can be constructed using the two-dimensional coherence matrix, the lack of Hermitian symmetry in the coherence matrix prevents the direct construction of a coherence Poincaré sphere. To this end, Set?l? et al. from the University of Eastern Finland proposed a method using the Gram matrix to construct a coherence Poincaré sphere as shown in Fig. 1. This sphere can fully describe the coherence and polarization characteristics of a partially coherent vector optical beam between points r1 and r2 using the coherence Poincaré sphere vectors q12 and q21. Concerning the construction and synthesis of partially coherent vector optical beams, we primarily review methods for synthesizing partially coherent vector optical beams with novel coherence structures. This includes the scheme based on the generalized van Cittert-Zernike theorem (Fig. 2) and the method based on vector-mode superposition (Fig. 3). The former method based on the generalized van Cittert-Zernike theorem is suitable only for synthesizing vector optical beams with spatially uniform coherence structures and has low optical efficiency due to the utilization of rotating ground glass to synthesize spatially incoherent light. The latter method based on vector-mode superposition solves the low efficiency and the inability to synthesize spatially non-uniform coherence structures, providing a significant advantage in synthesizing high-power spatially non-uniform coherence structures. In terms of measuring partially coherent vector optical beams, traditional methods based on Young's double-slit interference have low spatial resolution and measurement speeds. While the Hanbury Brown-Twiss (HBT) experiment based on intensity correlation resolves the limitations of Young's double-slit interference, it only allows for the absolute value measurement of coherence structures. To this end, Chen et al. proposed a generalized Hanbury Brown-Twiss experimental scheme (Fig. 4), which introduces a vector fully coherent reference light to achieve simultaneous and rapid measurement of the real and imaginary parts of the coherence structures of partially coherent vector optical beams. Regarding the propagation of partially coherent vector optical beams, studies indicate that due to the modulation of vectorial coherence structures, these beams exhibit completely different propagation characteristics compared to traditional electromagnetic Gaussian Schell-model beams. The former shows a gradual increase in polarization degree during propagation, while the latter exhibits a gradual decrease in polarization degree during propagation (Fig. 5). Meanwhile, it is demonstrated that vector optical beams with special coherence structures exhibit robust propagation characteristics in complex media (Fig. 6) to present potential applications in far-field polarization shaping. Additionally, we review the research on three-dimensional partially coherent vector optical fields. In the characterization of three-dimensional partially coherent vector fields, three-dimensional coherence and polarization matrices are employed. Unlike fully coherent vector optical fields, partially coherent vector fields exhibit rich three-dimensional polarization characteristics due to the coherence modulation, with polarization dimensions exceeding 2 (Fig. 7). In contrast, fully coherent vector optical fields localized in a plane at a determined spatial position only exhibit two-dimensional polarization characteristics. Furthermore, for clearer presentation of three-dimensional polarization structures in partially coherent vector optical fields, characteristic decomposition is utilized to decompose the three-dimensional polarization matrix into fully polarized state, middle-component polarization state, and three-dimensional unpolarized state (Fig. 8). The middle-component state is generally considered as the two-dimensional unpolarized state, but under complex polarization matrix of the middle-component state, it exhibits three-dimensional polarization properties, which can be characterized by the concept of the degree of nonregularity.It is shown that rich three-dimensional polarization structures are presented in partially coherent tightly focused fields. In studying the three-dimensional polarization characteristics of partially coherent tightly focused fields, the first challenge is the rapid calculation of the tightly focused fields. Traditional methods using the Richard-Wolf vector diffraction integral formula for direct integration typically take hundreds of hours. To enhance computational efficiency, Tong et al. proposed a method based on random-mode expansion in 2020 to achieve rapid computation of partially coherent tightly focused fields. Subsequently, researchers from Spain (Carnicer et al.) and China (Chen et al.) separately put forward convolution algorithms to fast calculate the tight focusing properties of partially coherent vector optical beams with a Schell-model correlation function. Compared to random mode expansion algorithms, the advantage of convolution algorithms is that the computation time is independent of the coherence length of the incident partially coherent vector beams, providing a significant advantage in computing the tightly focused characteristics of low-coherence optical fields. However, the four-dimensional convolution algorithm can only compute the tightly focused characteristics of partially coherent optical fields with Schell-model correlations. The random mode expansion algorithm is still required to improve computational efficiency and thus compute the tightly focused characteristics of partially coherent fields with spatially non-uniform correlations. Additionally, the four-dimensional convolution algorithm can only rapidly compute the polarization characteristics of tightly focused fields. The mode superposition algorithm is still required to compute the coherence characteristics between two or more points in the tightly focused field. By adopting fast algorithms, it is discovered that coherence structures play a critical role in shaping tightly focused fields. Research indicates that the transverse and longitudinal intensities of the tightly focused field can be controlled by the coherence structure of the incident light (Fig. 9). Furthermore, fast algorithms help discovered that in the tightly focused field of a radially polarized Gaussian Schell-model beam, three-dimensional polarization states with polarization dimension greater than 2 and three-dimensional degree of polarization less than 0.5 can be observed. By controlling the coherence length of the incident beam, the polarization dimension and three-dimensional degree of polarization of the focused field can be controlled (Fig. 10). Additionally, by introducing coherence structure control, three-dimensional unpolarized lattice and channels with specific spatial distributions can be designed near the focus (Fig. 11). Due to the rich three-dimensional polarization structures in partially coherent tightly focused fields, the spin angular momentum vector of the field can be decomposed into contributions from the fully polarized state and middle-component state. Under the nonregular middle-component state, the spin angular momentum will be carried. Research indicates that for the classical Gaussian Schell-model beams, the focused field exhibits three-dimensional nonregular polarization characteristics under moderate coherence length. Therefore, the spin angular momentum is contributed by both the fully polarized state and the nonregular middle-component state. Since the coherence structures and radial polarization of the optical field exhibit rotational symmetry, the generated spin angular momentum in the focused field has a vortex distribution with rotational symmetry as well. When the coherence structure or polarization state exhibits spatial asymmetry, it is found that the directions for spin vectors of the fully polarized state and middle-component state can be completely different (Fig. 12).Conclusions and ProspectsWe review partially coherent vector optical fields, including two-dimensional partially coherent vector beams and three-dimensional partially coherent vector fields. Meanwhile, we emphasize the basic principles and experimental techniques for controlling and measuring the two-dimensional coherence structure of partially coherent vector beams and analyze the propagation characteristics of beams with novel vectorial coherence structures. Results show that partially coherent vector optical beams controlled by coherence structures can maintain robust propagation characteristics in complex environments and have potential applications in far-field optical polarization shaping. Additionally, in conjunction with the development of nanophotonics, we discuss the extension of two-dimensional partially coherent beams to three-dimensional partially coherent fields. Specifically, we introduce the three-dimensional polarization structure, three-dimensional nonregular polarization state, and spin angular momentum structure caused by optical coherence in vector optical fields. Genuine three-dimensional polarization structures are discovered in partially coherent tightly focused fields, with the influence of coherence on polarization dimensions, three-dimensional degree of polarization, degree of nonregularity, and spin angular momentum structure analyzed. Optical coherence as a novel degree of freedom plays a crucial role in the control and application expansion of vector optical fields. With the development of temporal and spatio-temporal joint control techniques in the optical field, temporal or spatio-temporal structured optical fields play a significant role in fields such as ultra-fast optics, quantum optics, and nonlinear optics. Currently, the spatial coherence structure control of vector optical fields has been widely studied, but research on their temporal or even spatio-temporal joint control is limited. Optical coherence as an intrinsic property of the optical field is expected to provide a novel degree of freedom for spatio-temporal structured optical fields and thus expand the application range of such fields. Additionally, we specifically review the joint control of coherence and polarization parameters. Optical coherence plays a crucial role in the joint control of more parameters. Research suggests that coherence plays an important role in the spin (polarization)-orbital angular momentum (phase) coupling of light. In the case of three-dimensional partially coherent vector optical fields, coherence not only induces three-dimensional polarization structures in tightly focused fields but also plays a significant role in controlling the evanescent waves and surface plasmon polaritons. Finally, this has led to the research on physical properties and potential applications of partially coherent surface waves.

SignificanceMultifunctional integrated devices have become the mainstream of nanophononics research in recent years as optical devices continue to evolve towards high capacity, multichannel, low loss and integration. Additionally, the arbitrary manipulation of circularly polarized (CP) electromagnetic (EM) waves is significant for a wide range of applications such as chiral molecule manipulation, imaging, and optical communication. However, conventional optical devices composed of natural materials cannot realize multiplexing with only one optical device because they rely on the body properties to change the propagation phase so as to modulate electromagnetic waves. As a result, conventional optical devices are not conducive to the diversification, integration, miniaturization, and efficiency improvement of optical devices due to the single function, system complexity, large size, and low efficiency.ProgressIn recent years, metasurfaces consisting of a series of ultra-thin subwavelength artificial atoms arranged in a specific manner in the plane have demonstrated powerful modulation of electromagnetic waves, providing a good platform for realizing multifunctional integration. Researchers have discovered a series of exotic physical phenomena and powerful planar optical devices by exploiting the advantages of metasurfaces, such as lightness and thinness, large degree of modulation freedom, low loss, and easy conformality and integration. The mechanisms for modulating the phase of EM waves based on metasurfaces can be classified into three main types including resonant phase, geometric phase, and propagation phase. The resonant phase modulation mechanism is usually achieved by changing the geometry of the constituent artificial atoms to shift their resonant frequencies under arbitrarily polarized incident light. The propagation phase is realized by accumulating the phase of an EM wave as it propagates within the artificial atoms of the medium. The geometric phase is achieved by rotating the artificial atoms to change the phase of the outgoing light, while the polarization state of the outgoing light is opposite to the circular polarization state of the incident light. Among them, the resonance phase and the propagation phase do not depend on the polarization state of the incident light, while the geometric phase relies on the CP light. Typically, the three types of metasurfaces realize a single function, and it is vital to extend the integration of device functions as the application and device integration requirements continue to increase. By changing the geometry of the two orthogonal directions of the artificial atoms and employing the resonance phase or propagation phase to design the resonance frequency of the artificial atoms, researchers can realize multifunctional integration of different lines of polarized incident light under irradiation from the device, which can be completely different in free space. This type of device is complicated by the fact that the two main axes of artificial atoms are not completely independent, resulting in crosstalk and complex design. Due to the strong controllability of CP waves, geometric phase metasurfaces have caught enormous research interest. However, these meta-devices exhibit locked functionalities under illuminations of CP light with different chirality. Meanwhile, such metasurfaces for modulating CP light are also employed to achieve multifunctional integration. This is yielded by combining several sets of geometric phases with different functions in the same device, and thus several different functions are formed in free space under irradiation from the same CP light, which is referred to as a “merge phase metasurface”. However, as it does not fully decouple different chirality of light, there is still function binding and low efficiency. More recently, researchers have found that the combination of the spin-dependent geometric phase with the resonance or propagation phase can unlock the fixed function. Such metasurfaces often referred to as composite phase metasurfaces have been adopted to further improve device performance and integration in response to the growing demand for integrated optics applications. Starting from the three different phase mechanisms for electromagnetic wave manipulation by metasurfaces, we present a brief overview of resonant phase metasurfaces, geometric phase metasurfaces, propagation phase metasurfaces, and composite phase metasurfaces, with their operating principles, design strategies, and experimental implementations included, and recent research advances in this field briefly discussed.Conclusions and ProspectsFinally, we study spin-decoupled composite phase metasurfaces. Today’s multifunctional devices are still at the laboratory stage, but in the future, they can be integrated with research in other fields to solve some bottlenecks, such as directing incident light of different chirality to different regions on a chip for biomonitoring. Additionally, most polarization multiplexing devices to date can only perform passive and static functions. Therefore, the study of multifunctional devices with active tunable operation of incident waves of different polarization states will play a vital role in future practical applications. We hope that this brief review will help readers deepen their understanding of geometric phase metasurfaces and composite phase metasurfaces, and provide guidance for designing their components in the future.

SignificanceThe light-matter interaction at the nanoscale is crucial for the development of miniaturized optoelectronic devices. These devices often encounter energy leakage and loss, stimulating researchers to explore non-Hermitian photonics. An exceptional point, a specific optical degenerate state with identical momentum and energy has emerged as a research hotspot in this field. In recent years, the research on physical mechanisms of phenomena like parity-time symmetry, geometric phase, asymmetric scattering, and bound states in the continuum (BICs) has all revolved around exceptional points. These unique physical mechanisms are expected to inject new energy into the advancement of fields such as quantum computing, advanced materials, and low-power optoelectronic devices. We primarily focus on the chiral phenomena associated with the BIC mode, a concept originating from quantum mechanics and first proposed by von Neumann and Wigner in 1929. They identified a unique solution to the Schr?dinger equation: a spatially localized electronic state with zero linewidth and positive energy, despite existing within the continuum spectrum of the radiation. Theoretically, BICs are non-radiating solutions to the wave equation and can manifest in various systems such as acoustics and fluids. However, it was not until 2008 that this concept was introduced into optics by Borisov et al. Subsequently, Plotnik et al. utilized a single-mode optical waveguide array to achieve an initial experimental observation of BICs. In 2013, researchers from MIT detected optical BICs in periodic photonic crystal slabs, boosting further exploration of BIC modes in planar artificial nanostructures. Optical BICs not only squeeze light fields and enhance resonance Q-factors in real space but also exhibit diverse polarization topological properties in momentum space. By adjusting the interaction between BIC modes, individuals can precisely manipulate the distribution, polarization, and emission of the light fields. Over the past decade, owing to the easily fabricated metasurface platform with numerous degrees of freedom, optical BICs have rapidly evolved as a novel approach for controlling light fields in nanophotonics. Additionally, artificial nanostructures can offer chiroptical responses surpassing those of natural materials, with the involved intricate physical mechanisms catching significant attention. The momentum space characteristics of optical BICs provide fresh theoretical insights and design strategies for enhancing the chiroptical response of chiral metasurfaces. The ideal BIC mode is completely decoupled from the free space. By breaking the symmetry of the system, the topology charge of the ideal BIC in momentum space splits into two circularly polarized states, which enables precise control of the radiation process to maximize the chiroptical response. In approximately 2020, research teams from the Russian Academy of Science and the City University of New York independently verified that high-Q quasi-BIC resonances can manipulate the wavefront of circularly polarized light and optimize the chiroptical response of metasurfaces. Both studies utilized periodic chiral metasurfaces with dual tuning parameters, and it was easy to break the symmetry within and out of the structural plane by simultaneously controlling the two parameters. This transformation converted the ideal BIC (with an infinite Q-factor) into chiral quasi-BIC. This highlights that the often-disregarded longitudinal dimension of metasurfaces, particularly symmetry, plays a crucial role in their interaction with circularly polarized light. However, the experimental validation was hindered until 2022 due to constraints in fabricating multi-layer metasurfaces. Our team overcame this obstacle by employing a tilted etching scheme to break the out-of-plane symmetry and observe chiral quasi-BIC in the visible spectrum. Over the last decade, BICs have been identified in different photonic structures, particularly in the metasurfaces platform, which leads to numerous fascinating phenomena. By thoroughly investigating the properties of BICs in both real and momentum spaces, it is possible to reveal clearer physical mechanisms behind various intricate chiroptical phenomena.ProgressThe concept of BIC has been around for almost a century, with well-established basic theories and various property studies. We begin by briefly outlining the concept and characteristics of BIC (Fig. 1), and then discuss the topic of chiral quasi-BIC (Fig. 2). Subsequently, we explore the applications of chiral BIC and other chiroptical phenomena related to BIC. In Fig. 3, we summarize the methods for creating chiral BIC by breaking the structural symmetry. Figure. 4 illustrates instances of chiral BIC resulting from the disruption of the individual dimension symmetry of nanostructures (including the breaking of in-plane or out-of-plane symmetry), while Fig. 5 presents research on intrinsic chirality induced by slant-perturbation metasurfaces that completely break both in-plane and out-of-plane symmetries. In addition to the tilted etching method, out-of-plane symmetry can also be disrupted by grayscale electron beam lithography and multi-step nanofabrication methods (Fig. 6). We have included Table 1 to compare the specific features of chiral BIC nanodevices currently yielded in the laboratory. Furthermore, we present examples of other chiroptical phenomena related to BICs in Figs. 7-9, corresponding to nonlinear circular dichroism, vortex beam generation, superchiral field enhancement, and the optical spin Hall effect, respectively. Finally, we address the current challenges and potential applications in this field.Conclusions and ProspectsIn photonics, BIC initially caught attention for its exceptional high-Q resonance and later was extensively studied due to its unique momentum space polarization characteristics. The high-Q BIC can significantly enhance the performance of applications that rely on strong light-matter interaction, with lowered laser thresholds and improved nonlinear conversion efficiency. Meanwhile, the polarization characteristics of BICs in momentum space have greatly expanded the application fields, thus achieving polarization conversion and enhancing chiral light-matter interaction. Furthermore, more attention is paid to exploring new applications and mechanisms of BIC in combination with novel materials or special photonic structural systems. Although research on BICs in nanostructures has rapidly developed from theory to experimental stages, it still faces many challenges. In terms of sample design, there is an urgent need to explore rapid design schemes using artificial intelligence or inverse design methods. In sample fabrication, tasks such as improving the fabrication precision, implementing double-layer metasurfaces, and incorporating active semiconductor materials are very difficult. In terms of sample characterization, the extreme high-Q resonances make it difficult to measure the physical properties of BICs. Generally, although the biggest challenge in this field is from sample fabrication, combining sophisticated fabrication steps with reasonable sample design can accelerate the development of BIC-assisted photonic devices.

SignificanceScattering medium is a substance commonly found in nature such as turbid atmosphere, smoke, and biological tissues. Coherent light beams propagating through scattering media will be disrupted due to random scattering effects. The wavefront will be destroyed, and the transmission direction will deviate from the original input direction and becomes chaotic. Random scattered light interference will form a particle-like intensity pattern, known as an “optical speckle”. In multi-mode fibers, due to mode dispersion and inter-modal interference, a similar scattering distribution will be formed. Thus, multi-mode fibers are also regarded as a special class of scattering medium.Due to the scattering phenomenon, it is difficult to maintain the original spatial distribution of the light beam, and the energy is exponentially attenuated with the increasing penetration depth, which greatly limits the applications of advanced technologies such as optical tweezers, optical communications, and biomedicine in a strong scattering environment. However, in 1990, Freund proposed that light scattering in static scattering media is a deterministic linear process, a property that reveals the possibility of reutilizing the energy of the scattered light field. Due to the existence of a deterministic response relationship between incident and scattered lights, suitable input conditions can lead to the formation of the desired distribution of the output light field after passing through the scattering medium. In 2007, Vellekoop and Mosk put forward the concept of optical wavefront shaping whereby optimizing the distribution of the incident light wavefront leads to an in-phase coherent superposition of the light field at the target point, which thus achieves a focused light field that reaches the diffraction limit after the scattering medium. The focusing spot that reaches the diffraction limit is realized after the scattering medium. The emergence of wavefront shaping technology makes it possible to effectively employ the scattered light, thereby overcoming the limitations of the scattering problem for the above optical applications.With the development of modulation devices and computer technology in recent years, increasingly more wavefront shaping methods have been applied to scattering medium focusing, mainly including iterative optimization methods, transmission matrix methods, and phase conjugate methods. The focusing quality and speed have been continuously improved, and exciting progress has been made in the applications based on this. By adopting wavefront shaping techniques, precise light manipulation through strong scattering media has become possible. The intensity of fluorescence excitation in deep biological tissues can be greatly enhanced to expand the penetration depth of fluorescence imaging. Additionally, even the scattering media can be adopted to improve the numerical aperture of the focusing objective lens and thus achieve focusing beyond the diffraction limit. Thanks to the wavefront shaping technology, the scattering medium has become a new type of optical device with the ultra-high degree of freedom of operation, which can realize some special applications that cannot be accomplished by ballistic light, such as functional modules in optical computing, super-resolution imaging, and directional energy delivery. Therefore, it is necessary to sort out the representative studies of wavefront shaping-based optical focusing technology for scattering media in recent years and the outlook on the future development direction.ProgressFocusing through turbid medium based on wavefront shaping technique is mainly divided into three technical routes of the iterative optimization method, transmission matrix method, and phase conjugate method, with the basic principles shown in Fig. 1. Among them, the iterative optimization method relies on the set feedback physical quantities, improves the evaluation value by changing the input conditions, and finally realizes the light focusing at the target position. Meanwhile, this method plays an important role in complex optimization scenarios and dynamic scattering media. Currently, the most employed ones are intelligent optimization algorithms (Fig. 3) and neural network algorithms (Fig. 4). Diverse feedback signals further broaden the applications of this method (Fig. 7). On the other hand, the transmission matrix method relies on the measurement of the transmission matrix to establish a correlation between the input optimized wavefront and the scattered light field on the target focusing plane. Additionally, it employs the operation of time inversion to calculate the optimized wavefront for achieving focusing, which provides a powerful theoretical research tool for studying the mechanism of light transmission and focusing in scattering media (Fig. 8). By depending on the physical quantities of interest, various types of transport matrices have been developed (Figs. 9-11) and adopted in a variety of fields such as energy transport, optical communication, and particle manipulation (Figs. 12-13). The phase conjugate method relies on the light source placed at the target focusing position and utilizes the reversibility principle of the optical path to solve the phase of the received scattering light field. The utilization of the conjugate phase as the input condition can achieve focusing, which requires the fewest number of calculations and is currently applied to internal focusing of dynamic scattering media (Figs. 15-16).Conclusions and ProspectsTill now, scattering medium focusing based on wavefront shaping has successfully realized dynamic focusing inside or through the scattering medium, providing powerful technical support for applications including optical manipulation, long-distance communication, and deep biological tissue imaging. In future development, researchers should further improve the optical field transport mechanism inside the scattering medium, build a more refined physical model, and explore more dimensions of controllable physical quantities. Finally, broader scattering focusing and optical field modulation can be achieved, with the application scope of wavefront shaping technology in optics expanded. Additionally, combined with emerging optical computing, artificial intelligence, and other technologies, it is expected to achieve more compact optical path structure and faster and more efficient optimization. In conclusion, under the traction of cutting-edge exploration and the impetus of technological innovation, the scattering medium focusing technology based on wavefront shaping will continue to break through the limitations of traditional optical scattering and provide brand-new possibilities for optical applications in strong scattering environments.

ObjectiveThe optical orbital angular momentum (OAM) can exist either as longitudinal OAM in the spatial vortex beam or transverse OAM in the spatiotemporal optical vortices. In contrast to the amount of research focused on longitudinal OAM, very few pay attention to optical fields with transverse OAM. Unlike longitudinal OAM which is only affected by diffraction, transverse OAM can be affected by both diffractive effect and dispersive effect. One of the biggest challenges in utilizing optical fields carrying transverse OAM is to overcome diffraction and dispersion as the optical field propagates. Diffraction and dispersion will cause the fields to spread in space and time, which limits the applications of the optical field with OAM. We introduce a class of three-dimensional (3D) spatiotemporal localized wave packets with transverse optical OAM. The combination of the transverse OAM and the localized waves enables it to be immune to both dispersion and diffraction as the wave packet propagates. 3D spatiotemporal localized wave packets carrying transverse OAM provide a new opportunity for the utilization of transverse OAM and are expected to be applied in optical communication, quantum optics, and other fields in the future.MethodsIn previous studies, the vortex phase is placed in the spatial x-y plane and the resulting localized wave packet carries longitudinal OAM. In this study, we rotate the polar axis by 90°, so that it is now aligned in the y-direction. Therefore, the vortex phase term eim? locates in the x-t plane. Two spatiotemporal localized wave packets carrying two types of OAM: longitudinal OAM and transverse OAM are plotted (Fig. 1). Then, the theoretical derivation [Eqs. (4)-(6)] proves that the transverse OAM possessed by each photon is m?. In Fig. 2, 3D spatiotemporal localized wave packets described by Eq. (7) with different orders are presented. From the basic-order to higher-order 3D spatiotemporal localized wave packets with transverse OAM, a kind of 3D spatiotemporal localized wave packets in abnormal medium is proposed.Results and DiscussionsTo investigate the localized property, we choose one of the family of 3D localized wave packets and simulate its propagation in a virtual medium BK7 with negative material dispersion (β2=-25.26 fs2 mm-1) at the central wavelength of 1550 nm. As a comparison, we filter out the central lobe of the wave packet and propagate it in the same medium. Due to the condition that the effects of diffraction and dispersion are equalized, a proper pulse duration and beam size of the filtered wave packet is 112.25 fs and 0.30 mm at L=0 mm, respectively. Hence, we have diffractive length and dispersive length around Ldiff=Ldis=180 mm. As shown in Figs. 3 and 4, the spatiotemporal localized wave packet keeps its intensity shape without any distorts during propagation. It is noted that the central lobe wave packet experiences dramatic change and is magnified proportionally in intensity profile compared with the spatiotemporal localized wave packet. The propagation invariability of spatiotemporal localized wave packets has been presented. The ability of the wave packet to propagate free of diffraction/dispersion is only valid when the diffraction effect and the dispersion effect are balanced with each other. In other words, the wave packets propagate unstably in the unbalanced diffraction and dispersion. In addition, the localized capacity cannot be continued permanently due to finite energy in practice. However, the limited invariantly propagated length is longer than the length of the filtered wave packets. On the other side, self-healing is also often used to characterize non-spreading wave packets, leading to a wavefront reconstruction after an electromagnetic absorption obstacle. To verify the self-healing of the spatiotemporal localized waves, we numerically simulate that a rectangular plate (around widths of 600 μm) perfectly absorbing electromagnetic fields is placed in the central part of the spatiotemporal localized wave packet and propagate the blocked wave in BK7 (β2=-25.26 fs2 mm-1). 3D iso-intensity profile of the blocked wave packet in anomalous medium at different propagated lengths (0, 230, 320, and 500 mm) is shown in Fig. 5. We can see that the up blocked area and the down area are split into two rings and move towards to the central part in Fig. 5(d). In the end, the wave packets can be recovered to their original spatiotemporal localized wave packets. The linear momentum density and intensity distribution of the blocked wave packet at different propagated distances in y-t plane are shown in Figs. 5(e)-5(h). The direction of linear momentum density is labelled by arrows and points to the blocked areas visually indicating the reason why self-healing can happen in the spatiotemporal localized wave packets.ConclusionsIn summary, we present a new class of 3D spatiotemporal localized wave packets carrying transverse optical OAM. These wave packets exist in abnormal dispersion and can propagate invariantly when the diffractive effect and the dispersive effect are equal. To investigate the non-spreading nature of these wave packets, we simulate a wave packet (l,m)=(2,1) propagating in a proper and real medium BK7 glass. The results show that the wave packet propagates over several Rayleigh lengths while keeping its structure invariant. The wave packet can be recovered to its origin even when passing through a blocked obstacle. This kind of wave packets may provide new applications related to transverse OAM in the fields such as quantum optics and optical communications.

ObjectiveDue to the strong light-matter interactions, coupled plasmonic systems have broad applications in such areas as light manipulation, optical sensing, optical imaging, and optoelectronic devices. However, the inherent dissipation of materials and radiation dissipation of resonant structures limit the strength, service life, and propagation distance of coupled plasmonics, weakening the coupling signals and reducing the sensitivity and other performance of coupled plasmon devices. One possible solution is to add optical gain materials into the systems to compensate for the dissipation, but the utilization of gain materials is still limited because of the introduction of noise and instability. Another possibility is to employ complex frequency waves as light sources. It has been theoretically demonstrated that complex frequency waves with temporal attenuation can restore information losses. Unfortunately, producing complex frequency waves in real optical systems still faces significant challenges and has not been yielded experimentally. Currently, a novel method for synthesizing complex frequency waves has been proposed to be successfully applied to super-resolution imaging and highly sensitive biosensing. Therefore, we adopt this method to compensate for the dissipation of coupled plasmonic systems, thereby enhancing their resonance signals and avoiding experimental challenges. We hope that our study can benefit the development of coupled plasmonic systems for various potential applications.MethodsWe employ a periodic plasmonic structure composed of two perpendicular silver rods as an example to investigate the mechanism behind the attenuation of coupled resonance in coupled plasmonic systems. The structure is simulated by the finite-difference time-domain (FDTD) method using CST Studio Suite software. In the simulation, a plane wave with different polarization angles (45°, 90°, and 135°) is normally incident onto the structure with the periodic boundary to obtain the transmission coefficients, with the permittivity of silver described by the Drude model. Furthermore, we combine the Lorentz polarization model with temporal coupled-mode theory to analyze the interaction of plasmonic modes.Results and DiscussionsThe simulation results (Fig. 1) show that under an incident wave whose polarization angle equals 45° (135°) , the eigenmode of the plasmonic structure appears at 290 THz (310 THz) with no conversion of orthogonal polarization. Subsequently, a wave with 90° polarization can simultaneously excite the two eigenmodes and generate the coupled signal of the structure. Theoretical analysis shows that the strength of the coupled plasmonic signals depends on the frequency difference and the dissipation of the eigenmodes. Under the relatively small frequency difference and large dissipation, the two coupled new modes will have a large broadening and high overlap in the spectra, causing the coupled valley in the center to be weakened and shallowed. The Lorentz polarization model shows that complex frequency waves with temporal attenuation can enhance the weakened signals by reducing the dissipation of the eigenmodes. Based on Fourier transform analysis, the linear responses excited by complex frequency waves can be synthesized by the coherent combination of multiple real frequency responses. The calculation results (Fig. 3) show that synthesized complex frequency waves with different virtual gains can gradually enhance the coupled signals, where the coupled valley in the spectral line becomes increasingly deeper. Additionally, the synthesized complex frequency wave method is also effective for different coupling strengths (distance adjustment between silver rods). Even if the original signal is difficult to distinguish, this method can also restore it to the split state.ConclusionsWe study the dissipation in coupled plasmonic systems based on numerical simulations using CST Studio Suite software and theoretical analysis that incorporates the Lorentz polarization model and temporal coupled modes theory. Meanwhile, we explain the formation mechanism of coupled plasmonic signals and identify their limiting factors. Our findings suggest that under small coupling strength, larger dissipation of plasmonic systems will significantly hamper their coupled resonance. Then, we analyze the influence of complex frequency wave excitation on coupled plasmonic systems, and the results indicate that complex frequency waves with temporal attenuation can compensate for the dissipation of the system and restore the weak signal. To avoid the experimental difficulties of complex frequency waves in real optical systems, we employ a new method for synthesizing complex frequency responses via real frequency waves to calculate the transmission spectrum of the coupled plasmonic structure excited by complex frequency waves. Our results demonstrate that the proposed method can compensate for the dissipation of the coupled plasmonic structure in different conditions, significantly enhancing the coupled signals with almost no additional cost. The findings provide a practical and general method for solving the long-standing dissipation of coupled plasmonic systems, facilitating further applications of coupled plasmonic systems such as optical imaging, spectroscopy technology, and optical sensing.

ObjectiveTraditional imaging systems, due to their focal plane structure, exhibit significant optical gain but have a limited depth of focus. This creates a paradoxical scenario: achieving high image quality comes at the expense of weak laser protection capabilities. Established methods for laser protection in optoelectronic imaging systems encounter challenges including reliance on prior knowledge, bandwidth limitations, and degraded image quality. To address the conflict between image quality and laser protection, researchers utilize wavefront coding technology, leveraging its deep focus characteristics and light field regulation. This enables defocusing the image plane to enhance the system's laser protection capacity without compromising image quality. While wavefront coding can achieve a balance, previous studies have placed excessive focus on how defocus affects laser protection, overlooking its consequential impact on image quality and essentially ignoring how image quality can restrict laser protection. Therefore, investigating the balance between laser protection capability and image quality in wavefront coded imaging systems, as well as understanding the limits of the system's laser protection, is of utmost importance. We aim to examine this balance within the context of the arcsine wavefront coded imaging system and discern the limits of its laser protection capabilities.MethodsUsing the arcsine phase mask (ASPM) as an exemplar, we build imaging and laser transmission models for a defocused wavefront coding system. The trends are investigated in image quality and laser protection as the defocus parameters shift. By employing a decoupling approach, we take the system's image quality as a fundamental constraint. To ascertain the system's maximum permissible defocus parameters, we introduce quantitative evaluation metrics. Furthermore, our study assesses the system's laser protection capability based on these parameters, providing insights into the protection limits of wavefront coded imaging system.Results and DiscussionsNumerical simulations of the imaging model demonstrate that in conventional imaging system, increasing defocus parameters gradually blur the resulting image, leading to a significant deterioration in image quality. In the case of the ASPM wavefront coded imaging system, the coded image, modulated by the ASPM, also becomes blurred. However, by selecting an exploratory parameter K=4.25×10-4, the decoded image closely resembles the imaging effect of the conventional imaging system in its non-defocused state. This indicates that the ASPM wavefront coded imaging system achieves superior depth-of-focus extensions through joint hardware and software optimization (Fig. 5). To quantitatively evaluate the changes in image quality with defocus parameters, we employ peak signal-to-noise ratio and structural similarity metrics. Based on the Rayleigh criterion and using the peak signal-to-noise ratio and structural similarity values of the conventional imaging system as a threshold, we compute the defocus limit for the wavefront coded imaging system to be 9.70λ. The numerical simulation results of the laser propagation model reveal that as defocus parameters increase, the size of the light spot at the imaging plane of the conventional system grows rapidly. This leads to a sharp decline in light intensity and a significant reduction in the maximum single-pixel receiving power. However, the wavefront coded imaging system, with its defocus invariance, exhibits a more gradual decline in its maximum single-pixel receiving power (Fig. 6). Furthermore, both the conventional and wavefront coded systems show a decreasing trend in echo-detection receiving power (Fig. 7 and Fig. 8). At the same defocus parameters, the echo spot size of the wavefront coded imaging system is similar to that of the conventional imaging system, and their echo-detection receiving power are essentially the same. Therefore, the defocus limit of the imaging system determines the boundary of its laser protection capability.ConclusionsBy considering the image quality of the ASPM wavefront coded imaging system as a fundamental constraint, we establish that the maximum permissible defocus parameter for the wavefront coded imaging system is determined to be 9.70λ. When compared to the non-defocused state of the conventional imaging system, at this specific defocus parameter, the ASPM wavefront coded imaging system experiences a significant decline in the maximum single-pixel receiving power, reaching 96.37%. Additionally, the echo-detection receiving power drops to 0.217‰. These findings highlight the enhanced capabilities of the wavefront coded imaging system, with an improvement over one order of magnitude in anti-laser damage and three orders of magnitude in anti-laser active detection.

ObjectiveThe problem of low optical efficiency commonly exists on metasurfaces, which restricts their application and development. Although the efficiency of metasurfaces designed based on dielectric nanobricks structures is greatly improved compared to metal metasurfaces, the scattering and reflection losses of the unit structure are still relatively large. Metasurfaces are generally composed of high refractive index nanobricks to reduce their thickness and preparation process difficulty. Due to the high refractive index of the equivalent film layer on a high refractive index metasurfaces, it leads to significant interface reflection loss. In terms of improving the efficiency of metasurface devices, current research mainly focuses on improving the diffraction efficiency of metasurfaces and reducing scattering losses. However, there is no research focus on the reflection loss of metasurfaces currently, so it is necessary to study reducing the reflection loss of metasurfaces.MethodsWe propose an efficient design scheme for metasurfaces based on optical thin film theory to solve the problem of interface reflection loss caused by the mismatch between the equivalent refractive index of the metasurfaces and the substrate, as well as the mismatch between the equivalent optical thickness of the metasurfaces and the wavelength. First, we design the metasurface lens. Then, based on the equivalent medium theory, the metasurfaces are equivalent to a layer of dielectric thin films and serve as the outermost layer of the multi-layer antireflection coating system, with the equivalent layer thickness being the height of the metasurfaces. Finally, the optical thin film theory is adopted to design the antireflection coating that matches the substrate and incident medium.Results and DiscussionsWe simulate the near-infrared broadband silicon nanobrick metasurface lens on the quartz substrate and compare it with the metasurfaces designed with optical thin films. The transmittance of the antireflection coating designed by the equivalent medium theory is much higher than that of the equivalent film layer on the metasurfaces, with an average transmittance of 12.4% higher (Fig. 4). Comparison is made between the light field distribution patterns of a metasurface lens without optical thin films and with optical thin films (the antireflection coating structure of optical thin films combined with a metasurface) at different wavelengths (1460, 1530, 1600 nm). It can be seen that the focal spot size and focal length of the two types of structured metasurfaces at the same wavelength are basically the same. In the case of optical thin films, the light intensity at the focal point is significantly higher than that without optical thin films, whereas the focal point position is not affected by the antireflection coating and remains unchanged. This indicates that optical thin films only increase the transmittance of the metasurfaces and have little effect on their focusing performance (Figs. 5-7). The transmittance curves in the 1450-1600 nm wavelength range and the focusing efficiency at 1450, 1490, 1530, 1565, 1600 nm wavelengths are simulated and calculated. From the transmittance curves, it can be seen that in the 1450-1600 nm wavelength range, the transmittance of the metasurface lens designed with optical thin films remains around 94.0%, with the highest peak reaching 95.5%, which is much higher than that of metasurface without optical thin films, with an average increase of more than 10.5% (Fig. 8 and Fig. 9). The results of simulation calculations indicate that our proposed idea of combining optical thin films with metasurfaces is reasonable and has the potential to be applied to the actual production of metasurfaces.ConclusionsWe propose the concept of using optical thin films to improve the efficiency of metasurfaces. The characteristics of metasurface lens are studied in the near-infrared, and based on the properties of additional functional optical thin films on metasurfaces, the influence of the antireflection coating on the transmittance and focusing performance of metasurfaces are studied. Research has shown that combining the structure of optical thin films with the metasurfaces can significantly improve the optical efficiency of metasurfaces without affecting their optical properties. The idea of combining metasurfaces with the proposed optical thin films is expected to solve the problem of low efficiency of metasurfaces, bringing new ideas for the design of metasurface devices.

ObjectiveTo solve the problem that the traditional method can only produce spherical focused spots along the optical axis, we propose a method to generate spherical focused spots in any arbitrary spatial direction in a 4Pi focusing system, which consists of two opposing high numerical aperture objective lenses with the same focus. Spherical focused spots with equivalent three-dimensional spatial resolution have important applications in optical microscopy and metal particle capture. In particular, these spots can trap metal particles at resonant wavelengths, which is because the enhanced axial gradient force and the symmetry of the 4Pi focusing system can offset the axial scattering and absorption forces, making it possible to stabilize the trapping of resonant metal particles and precisely control the motion trajectory of metal particles. Spherical focused spots should be generated at any spatial position to capture resonant metal particles at arbitrary spatial positions. To our knowledge, this is the first time that controllable spherical focused spots can be obtained at an arbitrary spatial position. The proposed method features greater flexibility than traditional approaches, making it highly valuable for applications involving nanoparticle capture at arbitrary spatial locations.MethodsWe present a method to generate spherical focused spots with the specified spatial direction and spacing in a 4Pi focusing system using dipole antenna radiation fields generated by de-focusing. The method involves placing the spatial dipole antenna with predefined lengths and polarization direction at the focal point of the 4Pi focusing system and solving the inverse problem to determine the input field on the objective pupil plane that generates spherical focused spots. By utilizing the field on the pupil plane and selecting the appropriate length of the dipole antenna, spatial spherical focused spots can be obtained.Results and DiscussionsFirstly, the number of generated spatial spherical focused spots is related to odd or even multiple of half wavelength (Fig. 2). When the length of the dipole antenna L is an odd multiple of half wavelength, two same intensity spherical spots symmetrical at the center of the focus are formed in the set spatial direction. When L is an even multiple of half wavelength, three spherical focused spots with the equal size are formed, with one high-intensity spot at the focus and two lower-intensity spots symmetrically arranged. Since the distance between spatial spherical focused spots is calculated to be equal to L, the distance of spatial spherical focused spots can be easily adjusted by changing the parameter L. Meanwhile, arbitrary spatial directions of spherical focused spots are created to demonstrate the flexibility of the proposed method (Figs. 4 and 5). It is observed that the direction of the spherical focused spots is consistent with the polarization direction of the dipole antenna. Finally, we investigate the normalized input field Eiρ,φ required to create the spatial spherical focused spots (Figs. 6 and 7). It is evident that the polarization direction of the input field is determined by the dipole antenna parameter φ0, and the dipole antenna parameter θ0 determines the spatial rotation angle of the input field.ConclusionsWe present a simple and flexible method for generating spherical focused spots of prescribed length and controllable spatial orientation. By focusing the electromagnetic field radiated by a virtual dipole antenna in reverse at the focal point of a 4Pi focusing system, spherical focused spots with specified characteristics can be conveniently obtained. The simulation results show that the number of spherical focused spots is related to odd or even multiple of half a wavelength, and the distance between spherical focused spots is adjustable and only depends on the antenna length L, while the spatial direction of spherical focused spots is controllable and depends on the antenna parameters θ0,φ0. Furthermore, all spherical focused spots generated by the optical antennas are of the same size, with a full width at half maximum (FWHM) of 0.459λ. The generated spatial spherical focused spots have potential applications in precise multi-point trapping of spatial nanoparticles with full degrees of freedom, showing broad prospect in optical micro-manipulation.