Journal of Optics

The Zernike polynomials are a complete set of continuous functions orthogonal over a unit circle. Since first developed by Zernike in 1934, they have been in widespread use in many fields ranging from optics, vision sciences, to image processing. However, due to the lack of a unified definition, many confusing indices have been used in the past decades and mathematical properties are scattered in the literature. This review provides a comprehensive account of Zernike circle polynomials and their noncircular derivatives, including history, definitions, mathematical properties, roles in wavefront fitting, relationships with optical aberrations, and connections with other polynomials. We also survey state-of-the-art applications of Zernike polynomials in a range of fields, including the diffraction theory of aberrations, optical design, optical testing, ophthalmic optics, adaptive optics, and image analysis. Owing to their elegant and rigorous mathematical properties, the range of scientific and industrial applications of Zernike polynomials is likely to expand. This review is expected to clear up the confusion of different indices, provide a self-contained reference guide for beginners as well as specialists, and facilitate further developments and applications of the Zernike polynomials.

Although a relatively new area of nanoscience, nonlinear plasmonics has become a fertile ground for the development and testing of new ideas pertaining to light–matter interaction under intense field conditions, ideas that have found a multitude of applications in surface science, active photonic nanodevices, near-field optical microscopy, and nonlinear integrated photonics. In this review, we survey the latest developments in nonlinear plasmonics in three-dimensional (metallic) and two-dimensional (graphene) nanostructures and offer an outlook on future developments in this field of research. In particular, we discuss the main theoretical concepts, experimental methods, and computational tools that are used together in modern nonlinear plasmonics to explore in an integrated manner nonlinear optical properties of metallic and graphene based nanostructures.

The Covid-19 pandemic showed forcefully the fundamental importance broadband data communication and the internet has in our society. Optical communications forms the undisputable backbone of this critical infrastructure, and it is supported by an interdisciplinary research community striving to improve and develop it further. Since the first ‘Roadmap of optical communications’ was published in 2016, the field has seen significant progress in all areas, and time is ripe for an update of the research status. The optical communications area has become increasingly diverse, covering research in fundamental physics and materials science, high-speed electronics and photonics, signal processing and coding, and communication systems and networks. This roadmap describes state-of-the-art and future outlooks in the optical communications field. The article is divided into 20 sections on selected areas, each written by a leading expert in that area. The sections are thematically grouped into four parts with 4–6 sections each, covering, respectively, hardware, algorithms, networks and systems. Each section describes the current status, the future challenges, and development needed to meet said challenges in their area. As a whole, this roadmap provides a comprehensive and unprecedented overview of the contemporary optical communications research, and should be essential reading for researchers at any level active in this field.

In this perspective, the Editorial Board of the J. Opt. reflects on the past 25 years of the journal. The advances reported in journal have shaped the progress of diverse fields, from fundamental advances in optics to applications with optics as a key ingredient. The journal’s scope has seen it capture progress in several emergent fields, for instance, structured light covering orbital angular momentum, spatio-temporal solitons, topologies in light, singular optics and nonparaxial light. Reports include advances in optical devices, such as digital micromirror devices, metasurfaces and integrated photonics, as well as novel photonic materials based on nanophotonics. Application-based research includes super-resolution imaging, digital holography and nonlinear optics. We select key papers from across diverse disciplines to showcase the scope of the journal and the impact it has had on the wider community.

Metasurfaces are thin two-dimensional metamaterial layers that allow or inhibit the propagation of electromagnetic waves in desired directions. For example, metasurfaces have been demonstrated to produce unusual scattering properties of incident plane waves or to guide and modulate surface waves to obtain desired radiation properties. These properties have been employed, for example, to create innovative wireless receivers and transmitters. In addition, metasurfaces have recently been proposed to confine electromagnetic waves, thereby avoiding undesired leakage of energy and increasing the overall efficiency of electromagnetic instruments and devices. The main advantages of metasurfaces with respect to the existing conventional technology include their low cost, low level of absorption in comparison with bulky metamaterials, and easy integration due to their thin profile. Due to these advantages, they are promising candidates for real-world solutions to overcome the challenges posed by the next generation of transmitters and receivers of future high-rate communication systems that require highly precise and efficient antennas, sensors, active components, filters, and integrated technologies. This Roadmap is aimed at binding together the experiences of prominent researchers in the field of metasurfaces, from which explanations for the physics behind the extraordinary properties of these structures shall be provided from viewpoints of diverse theoretical backgrounds. Other goals of this endeavour are to underline the advantages and limitations of metasurfaces, as well as to lay out guidelines for their use in present and future electromagnetic devices.

This Roadmap is divided into five sections:

1. Metasurface based antennas. In the last few years, metasurfaces have shown possibilities for advanced manipulations of electromagnetic waves, opening new frontiers in the design of antennas. In this section, the authors explain how metasurfaces can be employed to tailor the radiation properties of antennas, their remarkable advantages in comparison with conventional antennas, and the future challenges to be solved.

2. Optical metasurfaces. Although many of the present demonstrators operate in the microwave regime, due either to the reduced cost of manufacturing and testing or to satisfy the interest of the communications or aerospace industries, part of the potential use of metasurfaces is found in the optical regime. In this section, the authors summarize the classical applications and explain new possibilities for optical metasurfaces, such as the generation of superoscillatory fields and energy harvesters.

3. Reconfigurable and active metasurfaces. Dynamic metasurfaces are promising new platforms for 5G communications, remote sensing and radar applications. By the insertion of active elements, metasurfaces can break the fundamental limitations of passive and static systems. In this section, we have contributions that describe the challenges and potential uses of active components in metasurfaces, including new studies on non-Foster, parity-time symmetric, and non-reciprocal metasurfaces.

4. Metasurfaces with higher symmetries. Recent studies have demonstrated that the properties of metasurfaces are influenced by the symmetries of their constituent elements. Therefore, by controlling the properties of these constitutive elements and their arrangement, one can control the way in which the waves interact with the metasurface. In this section, the authors analyze the possibilities of combining more than one layer of metasurface, creating a higher symmetry, increasing the operational bandwidth of flat lenses, or producing cost-effective electromagnetic bandgaps.

5. Numerical and analytical modelling of metasurfaces. In most occasions, metasurfaces are electrically large objects, which cannot be simulated with conventional software. Modelling tools that allow the engineering of the metasurface properties to get the desired response are essential in the design of practical electromagnetic devices. This section includes the recent advances and future challenges in three groups of techniques that are broadly used to analyze and synthesize metasurfaces: circuit models, analytical solutions and computational methods.

Spatiotemporal sculpturing of light pulse with ultimately sophisticated structures represents a major goal of the everlasting pursue of ultra-fast information transmission and processing as well as ultra-intense energy concentration and extraction. It also holds the key to unlock new extraordinary fundamental physical effects. Traditionally, spatiotemporal light pulses are always treated as spatiotemporally separable wave packet as solution of the Maxwell’s equations. In the past decade, however, more generalized forms of spatiotemporally nonseparable solution started to emerge with growing importance for their striking physical effects. This roadmap intends to highlight the recent advances in the creation and control of increasingly complex spatiotemporally sculptured pulses, from spatiotemporally separable to complex nonseparable states, with diverse geometric and topological structures, presenting a bird’s eye viewpoint on the zoology of spatiotemporal light fields and the outlook of future trends and open challenges.

Structured light beams, in contrast to conventional Gaussian beams, typically possess unique characteristics such as orbital angular momentum, exotic wavefronts and Stokes phase singularities in polarization textures. These characteristics have led to the use of structured light in applications including optical trapping and manipulation, free space optical and quantum communications, nano and microfabrication, environmental optics, and astrophysics. Furthermore, new classes of structured light fields, such as topological states of light (optical quasiparticles), and geometrical modes with particle-like and wave-like duality, are being applied across numerous scientific and practical applications. We review recent progress on the development of structured light laser sources based on solid-state laser technologies; in particular, we focus on the nonlinear optical processes which are used to expand their wavelength diversity.

Optical parametric amplifiers (OPAs) exploit second-order nonlinearity to transfer energy from a fixed frequency pump pulse to a variable frequency signal pulse, and represent an easy way of tuning over a broad range the frequency of an otherwise fixed femtosecond laser system. OPAs can also act as broadband amplifiers, transferring energy from a narrowband pump to a broadband signal and thus considerably shortening the duration of the pump pulse. Due to these unique properties, OPAs are nowadays ubiquitous in ultrafast laser laboratories, and are employed by many users, such as solid state physicists, atomic/molecular physicists, chemists and biologists, who are not experts in ultrafast optics. This tutorial paper aims at providing the non-specialist reader with a self-consistent guide to the physical foundations of OPAs, deriving the main equations describing their performance and discussing how they can be used to understand their most important working parameters (frequency tunability, bandwidth, pulse energy/repetition rate scalability, control over the carrier-envelope phase of the generated pulses). Based on this analysis, we derive practical design criteria for OPAs, showing how their performance depends on the type of the nonlinear interaction (crystal type, phase-matching configuration, crystal length), on the characteristics of the pump pulse (frequency, duration, energy, repetition rate) and on the OPA architecture.

Laser beams carrying orbital angular momentum (OAM), so-called vortex beams, are highly topical forms of light, having found a myriad of applications across diverse fields. The usual approach to their creation, either internal or external to lasers, imbues them with a size that scales with the topological charge, for an ever larger ring of light. Here we show that this need not be the case, demonstrating arbitrary topologically controlled beam sizes, from maintaining an OAM-independent size to exotic functional dependence. We use the opportunity to highlight inconsistencies in prior studies where OAM and size have been conflated for erroneous conclusions, and provide a framework for overcoming this.

Perfect optical vortex (POV) beams exhibit unique spatial characteristics, including a topological charge (TC)-independent ring radius and an annular intensity distribution. We investigate the propagation of POV beams in a chiral medium. Within the paraxial limit, an analytical expression for the complex amplitude of a POV beam propagating in a chiral medium is derived based on the Huygens–Fresnel integral and the ABCD matrix formalism. Our results show that the beams split into left-circularly polarized POV (LCPPOV) and right-circularly polarized POV (RCPPOV) beams, each following distinct propagation trajectories and exhibiting different longitudinal intensity distributions in the chiral medium. We numerically study the influence of various beam and medium parameters-such as the TC, the ratio of the ring radius to the half-ring width, the chiral parameter, and the refractive index-on the longitudinal intensity distributions of LCPPOV, RCPPOV, and total POV beams. We find that both non-diffracting and self-focusing effects occur at different propagation distances for LCPPOV, RCPPOV, and total POV beams. The self-focusing effect gradually diminishes as the ratio of the ring radius to the half-ring width decreases. Additionally, while the TC has no impact on intensity distributions during the non-diffracting stage, noticeable effects emerge in the self-focusing stage, including the expansion of the dark core with increasing TC and the appearance of multiple rings in the intensity distributions. Furthermore, the chiral parameter and refractive index influence the intensity distributions of LCPPOV, RCPPOV, and total POV beams in distinct ways. Our findings may be useful for applications of POV beams in optical micromanipulation.

Accurate measurement of the spatial coherence function is critical for applications ranging from imaging to communication. However, accurate measurement of arbitrary complex spatial coherence function still remains a significant challenge. In this work, we present a phase-shifting wavefront-inversion and shearing interferometric technique which enables direct, noise-insensitive measurement of the complex cross-spectral density function for a very broad class of fields, which includes all spatially stationary fields and the physically most relevant class of spatially non-stationary fields. By integrating the phase-shifting technique with wavefront inversion interferometry, we implement an intensity difference protocol that eliminates all phase-insensitive noise, significantly enhancing measurement fidelity. Experimental results validate the method’s robustness and accuracy, demonstrating its applicability to both stationary and non-stationary fields, and extending its utility to single-photon-level measurements. This technique represents a promising tool for all coherence-driven applications.

Exact analytical expressions for the density of the longitudinal projection of the orbital angular momentum (OAM) vector in the sharp focus plane are obtained in this work. We derive expressions of four light fields with uniform and non-uniform polarizations: an optical vortex with elliptical polarization, a superposition of a cylindrical vector beam and a beam with linear polarization, an optical vortex with cylindrical polarization, and a beam with non-uniform elliptical polarization. All OAM densities for these four fields depend on the polarization state of the initial light field. For two light fields with hybrid polarization, the OAM density at the focus changes sign with a change in both the azimuthal and radial coordinates. It is known that in the case of paraxial optical vortices with elliptical polarization, the OAM density does not depend on the polarization state, and is completely determined by the optical vortex topological charge. Therefore, in the paraxial case, the azimuthal orbital energy flux always rotates in one direction, determined by the sign of the optical vortex topological charge. However, in the case of non-paraxial light fields, the OAM density at the focus is shown in this work to depend on the polarization state. The energy flow can rotate in different directions at different distances from the optical axis.

Over the past decades, there has been significant progress in imaging technology based on metasurfaces. The amount of optical information that can be stored on metasurface has increased continuously, evolving from static imaging to dynamic imaging. In this article, a three-channel dynamic switching imaging metasurface based on the phase-change material ${\text{Sb}}_2 \text{S}_3$ has been proposed, where three images are captured at the interface of the metasurface, the near field (Fresnel region), and the far field (Fraunhofer region), respectively. Thanks to the significant differences in their optical properties between the crystalline and amorphous states of the ${\text{Sb}}_2 \text{S}_3$ material, dynamic imaging and hiding capabilities have been demonstrated by temperature-controlled switching of the material state. By employing the Adam optimization algorithm to systematically tune the parameters of ${\text{Sb}}_2 \text{S}_3$ meta-atom, coupled with rigorous validation through finite-difference time-domain simulations, we successfully demonstrate tri-channel dynamic imaging with low crosstalk, high resolution, and exceptional contrast ratio. This design provides an efficient platform for dynamic optical display, information encryption, and multifunctional integration with promising prospects in image display, information security, and optical storage fields.

We propose and numerically demonstrate a novel high-speed physical layer secure optical communication system based on a dual-path mutual feedback phase encryption scheme, which comprises two coupled electro-optic phase modulation feedback branches. The proposed scheme is able to randomly scramble the phase of a confidential message without any additional encryption signal and eliminate the time delay signature (TDS) that exists in a conventional electro-optic phase feedback loop. The TDS concealment is accomplished by the nonlinear transformation produced by the dual-path mutual feedback optical phase encryptor. As a proof-of-principle demonstration, a 32 Gbps differential phase shift keying signal is encrypted and secretly transmitted over a span of 330 km standard single-mode fiber with a bit error rate lower than the hard-decision forward-error correction threshold. Both the sensitive delay time and dispersion values in the feedback loop are employed as hardware keys to guarantee system security. It is envisioned that the proposed scheme may provide an attractive approach for future hardware encryption based high-speed secure optical communication.

The non-intuitive spatiotemporal modal content of space-time optical vortices (STOVs) is calculated in a graded-index fiber supporting a large number of propagating modes. We discuss how a fiber supporting many modes allows to truly couple higher-order STOVs, the number of modes necessary to support a STOV of a certain order, and conversely the truncation effect in a few-mode fiber. Based on the excited modes and their temporal profiles, we show numerical results for the linear and nonlinear propagation of STOVs in multimode fibers, specifically the linear space-time beating at short propagation distances, and the nonlinear trapping effect between modes producing stable states on long propagation distances. Our results underline how STOVs present a rich platform for multimode nonlinear optics and technology.

Structured light beams, in contrast to conventional Gaussian beams, typically possess unique characteristics such as orbital angular momentum, exotic wavefronts and Stokes phase singularities in polarization textures. These characteristics have led to the use of structured light in applications including optical trapping and manipulation, free space optical and quantum communications, nano and microfabrication, environmental optics, and astrophysics. Furthermore, new classes of structured light fields, such as topological states of light (optical quasiparticles), and geometrical modes with particle-like and wave-like duality, are being applied across numerous scientific and practical applications. We review recent progress on the development of structured light laser sources based on solid-state laser technologies; in particular, we focus on the nonlinear optical processes which are used to expand their wavelength diversity.

We review holography techniques related to imaging and sensing. Holography has been actively researched as three-dimensional (3D) imaging and 3D display techniques. Because of the successive evolutions of electronic and optical devices, digital holographic and quantitative 3D measurements with high accuracy and realistic 3D motion-picture image display without glasses have been realized. Moreover, holography has led to breakthroughs in various applications in the fields of measurement and processing through the development of holographic light-wave modulation techniques. We briefly introduce various applications of holography and then review imaging and sensing techniques with holography, focusing on quantitative phase imaging with daily-use light, spatially incoherent digital holography, holographic display, and microscopy with holographic light modulation.

Optically transparent microwave absorbers based on metamaterials demonstrate exceptional microwave absorption performance while maintaining high optical transmittance, showcasing significant potential for applications in modern communication, defense, and architectural fields. Transparency in the visible light spectrum is primarily achieved through material selection and structural optimization. The artificially designed metamaterials based on transparent resistive films can be used to achieve devices with excellent wave absorption characteristics in the microwave frequency band. In this paper, we systematically review the research progress in the domain of optically transparent microwave metamaterial absorbers. We first introduce the implementation principles of optically transparent microwave metamaterial absorbers from the perspectives of transparency and wave absorption, laying the foundation for the in-depth discussions in subsequent sections. Subsequently, we focus on the research progress of optically transparent microwave metamaterial absorbers. In this paper, microwave metamaterial absorbers are classified into three types: passive absorbers, tunable absorbers and adaptive absorbers. Passive and tunable absorbers are further discussed based on their structural classifications. This paper summarizes the current research status and technical bottlenecks of optically transparent microwave absorbers while envisioning their extensive applications in stealth technology, wireless communication, and multifunctional devices. While challenges persist in balancing thickness, bandwidth and transmittance, future advancements in novel material, innovative structural designs, and manufacturing processes are expected to enable the realization of efficient, intelligent, multifunctional absorbers.

This review focuses on novel phenomena that emerge when optical pulses propagate through a spatiotemporal dispersive medium whose refractive index is modulated, both in space and time, in a traveling-wave fashion. Using optical fibers as an example of a dispersive medium, we first derive an equation governing the evolution of short pulses in such a medium. This equation is used to discuss the phenomena such as temporal reflection and refraction, total internal reflection, and waveguiding from a moving boundary with different refractive indices on its two sides. The use of solitons, forming through the Kerr effect, shows how such effects can be observed with silica fibers by employing a pump-probe configuration. A pair of solitons provide the temporal analog of a waveguide or a Fabry–Perot resonator. A new kind of grating, called a spatiotemporal Bragg grating, is formed when a train of pump pulses creates periodic high-index regions inside an optical fiber moving at the speed of pump pulses. The interaction of probe pulses with such a Bragg grating is studied both within and outside of momentum gaps. It is also shown that a photonic analog of Anderson localization is possible when disorder is introduced into a spatiotemporal Bragg grating.

Skyrmions are topologically protected quasi-particles that have aroused substantial interest in nuclear physics and condensed matter physics. For instance, magnetic skyrmions are regarded as having potential applications in high-density information storage due to their ultracompact size, topologically protected stability, and low driven current. Recently, optical analogs have been discovered in light field, known as optical skyrmions. With similar intriguing properties, research on optical skyrmions has grown dramatically. Several types of optical skyrmions defined by various optical parameters have been uncovered. Along with the fundamental physics studies, methods for generating, modifying, and detecting optical skyrmions have also been developed, which in turn enriches the toolkit for light field modulation and detection. It has shown promising applications in high-precision positioning, information storage, and optical communication. In this paper, we begin with the fundamental theory and then introduce generalized classes of optical skyrmions, with a particular emphasis on optical spin skyrmions. We discuss their generation, modulation, and detection methods. Additionally, we highlight the emerging applications of optical skyrmions, showcasing the potential of these unique properties for future advancements.

Recently discovered reactive optical forces have nule time-average of their instantaneous values on monochromatic illumination, so that their detection suggests the use of ultrafast optics, specially in the femto and attosecond domain. We report a theoretical study of the time variations of reactive forces versus active real ones on small dipolar particles by using illumination with subcycle pulses; and show their corresponding pushing or pulling effects. Future developments and experiments based on the proposed model should increase the insight and operation of the ultrafast dynamics of nanostructures.

Surface Plasmon Resonance (SPR)-based sensors have emerged as powerful tools for label-free detection of minute refractive index (RI) changes in biological and chemical samples. However, conventional PCF-SPR sensors face challenges related to fabrication complexity, poor coupling efficiency, and limited sensitivity. To address these limitations, this work proposes a side-polished D-shaped PCF-SPR sensor with simplified design and enhanced sensitivity, making it suitable for biomedical applications. A 0.1 µm gold layer is deposited on the polished surface to excite surface plasmon resonance (SPR), thereby enhancing biomolecule detection. Numerical simulations are performed using the finite element method (FEM). After optimizing the structural parameters, the sensor's performance is evaluated for various bio-analytes by varying the refractive index from 1.32 to 1.36, achieving a maximum sensitivity of approximately 30,000 nm/RIU. The proposed sensor offers a cost-effective and efficient solution for real-time, point-of-care (POC) biomedical diagnostics and drug development.

Topological light fields represent a cutting-edge frontier at the intersection of modern optics and condensed matter physics, offering new dimensions for light field control and functional expansion through their distinctive topological structures. This review traces the progression from singular optics to optical skyrmions, providing an overview of representative real-space topological features, including phase singularities, polarization singularities, optical knots, and Möbius strips. It focuses on the generation mechanisms and characterization techniques of various types of optical skyrmions in parameter space, and reviews key studies that have shaped the development of the field. With ongoing advances in nano-optics and light-field manipulation, topological light fields exhibit strong potential in high-dimensional optical communication, massive data storage, all-optical computing, and precision metrology. This review aims to offer a coherent framework for researchers in topological optics and to support the further exploration of topological structures in optical devices and photonic information technologies.

Free-space optical (FSO) communication faces significant challenges owing to atmospheric turbulence, which can severely degrade the system performance. This paper presents a comprehensive performance analysis of various dual-polarization (DP) modulation schemes, including DP-differential phase shift keying (DP-DPSK), DP-differential quadrature phase shift keying (DP-DQPSK), DP-quadrature amplitude modulation with orthogonal frequency division multiplexing (DP-QAM-OFDM), and DP-PSK with OFDM (DP-PSK-OFDM), under turbulent FSO link conditions. Utilizing the OptiSystem simulation Software and the Gamma-Gamma turbulence model, the study evaluates the bit error rate (BER) performance of these schemes across varying link distances and turbulence intensities. The findings demonstrate a clear trade-off between spectral efficiency and robustness. DP-DPSK emerges as the most suitable option for long-range links, particularly under weak turbulence conditions, while DP-DQPSK demonstrates better performance in shorter-range scenarios with higher turbulence levels. Furthermore, higher-order DP-QAM-OFDM modulation exhibits increased sensitivity to turbulence, leading to significant performance degradation over extended distances. Conversely, lower-order DP-PSK-OFDM modulation displays superior robustness, maintaining lower BERs even at longer ranges at the cost of reduced spectral efficiency. These findings provide critical guidance for selecting optimal modulation schemes in turbulence-affected FSO systems, highlighting the importance of balancing three key factors—turbulence resilience, spectral efficiency demands, and implementation complexity—to ensure reliable and high-performance optical links.

A fiber optic sensor for detecting gas precipitation in 18650 battery is proposed and demonstrated experimentally. A theoretical model for the co-measurement of temperature and pressure based on an open Fabry-Perot interferometer (FPI) cascaded with a Fiber Bragg Grating (FBG) is established, and the measurement mechanism of gas precipitation is analyzed in detail. According to the complex environment inside the battery, a scheme for measuring the gas state inside the lithium-ion battery is designed, and experiments are carried out. The experimental results show that the pressure sensitivity of the sensor is 4.1108 nm/MPa, the temperature sensitivity is -1.8 pm/℃, and the sensitivity of the battery's internal pressure increase due to the rise in temperature is 2.3 pm/℃. When the discharge rate is 1 C, the pressure change caused by gas precipitation in the battery is 10.71 kPa, which leads the FP red-shift of 44.3 pm, when the discharge rate is 2 C, the pressure change in the battery caused by gas precipitation is 52.87 kPa, and the FP red-shift of 217.3 pm. The scheme can effectively analyze the internal gas precipitation of 18650 battery under different discharge rates, which provides a new idea for battery health monitoring and discharge level evaluation.

Recently discovered reactive optical forces have nule time-average of their instantaneous values on monochromatic illumination, so that their detection suggests the use of ultrafast optics, specially in the femto and attosecond domain. We report a theoretical study of the time variations of reactive forces versus active real ones on small dipolar particles by using illumination with subcycle pulses; and show their corresponding pushing or pulling effects. Future developments and experiments based on the proposed model should increase the insight and operation of the ultrafast dynamics of nanostructures.

Laser beams carrying orbital angular momentum (OAM), so-called vortex beams, are highly topical forms of light, having found a myriad of applications across diverse fields. The usual approach to their creation, either internal or external to lasers, imbues them with a size that scales with the topological charge, for an ever larger ring of light. Here we show that this need not be the case, demonstrating arbitrary topologically controlled beam sizes, from maintaining an OAM-independent size to exotic functional dependence. We use the opportunity to highlight inconsistencies in prior studies where OAM and size have been conflated for erroneous conclusions, and provide a framework for overcoming this.

Light, or electromagnetic radiation, is well known to possess momentum, and the exchange of this momentum with a reflecting surface leads to radiation pressure. More often than not, it is the radiation pressure generated by a plane wave incident on a flat mirror that is considered. The last few decades have seen the emergence of structured light beams that may possess a complex phase and amplitude structure in both their transverse and longitudinal directions. This paper provides a historical overview of radiation pressure, tracing its discovery and experimental validation, and examines the influence on it transitioning to structured light from a plane wave. In particular, we elucidate the difference in radiation pressure force for structured light fields and how this differs from that of a plane wave at an identical frequency. In particular, the well-known Gouy phase is shown to contribute to a reduction in the radiation pressure force exerted on a flat mirror in comparison to a plane wave for both HG and LG modes. As an illustrative example, we compute that the radiation pressure force for LG modes differs from that of a plane wave by approximately 20 fN W⁻¹ for each unit of orbital angular momentum. A detailed experimental proposal to quantify this variance in radiation pressure is described, and we demonstrate that this measurement is within the realm of current metrological techniques.

Perfect optical vortex (POV) beams exhibit unique spatial characteristics, including a topological charge (TC)-independent ring radius and an annular intensity distribution. We investigate the propagation of POV beams in a chiral medium. Within the paraxial limit, an analytical expression for the complex amplitude of a POV beam propagating in a chiral medium is derived based on the Huygens–Fresnel integral and the ABCD matrix formalism. Our results show that the beams split into left-circularly polarized POV (LCPPOV) and right-circularly polarized POV (RCPPOV) beams, each following distinct propagation trajectories and exhibiting different longitudinal intensity distributions in the chiral medium. We numerically study the influence of various beam and medium parameters-such as the TC, the ratio of the ring radius to the half-ring width, the chiral parameter, and the refractive index-on the longitudinal intensity distributions of LCPPOV, RCPPOV, and total POV beams. We find that both non-diffracting and self-focusing effects occur at different propagation distances for LCPPOV, RCPPOV, and total POV beams. The self-focusing effect gradually diminishes as the ratio of the ring radius to the half-ring width decreases. Additionally, while the TC has no impact on intensity distributions during the non-diffracting stage, noticeable effects emerge in the self-focusing stage, including the expansion of the dark core with increasing TC and the appearance of multiple rings in the intensity distributions. Furthermore, the chiral parameter and refractive index influence the intensity distributions of LCPPOV, RCPPOV, and total POV beams in distinct ways. Our findings may be useful for applications of POV beams in optical micromanipulation.

Structured light beams, in contrast to conventional Gaussian beams, typically possess unique characteristics such as orbital angular momentum, exotic wavefronts and Stokes phase singularities in polarization textures. These characteristics have led to the use of structured light in applications including optical trapping and manipulation, free space optical and quantum communications, nano and microfabrication, environmental optics, and astrophysics. Furthermore, new classes of structured light fields, such as topological states of light (optical quasiparticles), and geometrical modes with particle-like and wave-like duality, are being applied across numerous scientific and practical applications. We review recent progress on the development of structured light laser sources based on solid-state laser technologies; in particular, we focus on the nonlinear optical processes which are used to expand their wavelength diversity.

We present a detailed quantum field theory of single-photon states. The formalism we develop permits us to calculate the electric field of a single-photon light beam sent through a beam splitter (BS). This illustrates the nonlocal nature of quantum fields even when they are excited by discrete numbers of quanta. We find that the shape of the electromagnetic wave attached to a single photon entering the BS, determines the results of simultaneous measurements at two different locations behind the two ports of the BS. Therefore, our results confirm that a quantum field can be both local with respect to its discrete excitations, i.e. the photons, and nonlocal with respect to its continuous amplitude.

It is demonstrated that at a given cross-section and radius, a scalar, wide-sense stationary, beam-like optical field carrying orbital angular momentum (OAM) in L states can be uniquely characterized by the degree of orbitalization and the orbitalization ellipse pertaining to a plane in the L-dimensional functional space spanned by basis $\{\textrm{e}^{\textrm{i}l\phi}\}$, with $l$ and φ being the OAM index and the polar angle, respectively. This characterization bears similarities with that in polarization optics.

We demonstrate two-step phase-shifting interferometry (holography) of complex laser modes generated by a spatial light modulator (SLM), in which the amplitude and phase of the signal are determined directly from measurements of phase-shifted interferograms. The reference and signal beams are generated and phase-controlled with a single composite hologram on the SLM and propagated collinearly. This requires no additional optics and leads to measurements that are more accurate and less prone to noise, which we demonstrate with collinearly-referenced measurements of various Laguerre–Gaussian modes and structured images.

Tailoring the reactive helicity and momentum of electromagnetic fields has emerged as a unique way to control light-matter interaction. In this paper, we explore these reactive quantities in hybrid polarized vector beams (HPVBs) that are tightly focused through a high NA objective. By precisely controlling polarization parameter and topological charge, we are able to modulate the hybrid state of polarization for the focused HPVBs, which allows for controllable generation of the reactive helicity and momentum. Notably, we create a purely longitudinal reactive momentum which arises on the beam axis. We also generate a three-dimensional focused spot of the reactive helicity, the size of which can shrink beyond the diffraction limit imposed on light intensity spots. These findings provide new insights into the dynamic properties of structured light, and would have implications for optical manipulation techniques including particle trapping, pulling and rotation.

Direct writing systems equipped with a confocal micro-light-emitting diode array can employ active illumination for alignment purposes. Based on the principles of single-pixel imaging, structured illumination can be used to obtain position information via compressive sensing. The positions of markers with certain spectral signatures can be extracted from the recorded hyperspectral data through spectral filtering, spectral fitting, or principal component analysis. Its application to direct writing is demonstrated by creating individual photolithography patterns aligned with different types of fluorophores on the same substrate.