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Chiral plasmonic nanomaterials have been widely utilized to study light‐matter interactions due to its capability to amplify chiroptic signals. Conventionally, chiro‐optic experiments have demonstrated interactions between circularly polarized light and materials. However, employing light with chiral phase, i.e., optical vortex, can generate a strong chiral response and holds the potential to unveil extensive material information owing to the infinite topological numbers. In this work, an array of 3D chiral nanoparticles is employed to demonstrate large helical dichroism (HD). Chiral gold nanoparticle arrays are illuminated by vortex beams of opposite helicity, which revealed the high HD value of 0.93. The chiral interaction is theoretically investigated, and enantioselective interaction can be explained by multipole analysis. It is determined that the strong HD is attributed to the interaction of higher‐order multipole moments such as electric quadrupole and magnetic quadrupole moments. This study provides deeper insight into understanding of the interaction between optical vortex and chiral plasmonic nanostructures and paves the way for next‐generation chiroptical applications ranging from ultrasensitive chiral spectroscopy to chiral quantum optics. [ABSTRACT FROM AUTHOR]

The development of straightforward and effective methods to determine the topological charge of phase singular beams is crucial for broadening the applications of optical vortices. Here, a straightforward and elegant method for determining the topological charge of an optical vortex using an innovative switchable achromatic nematic liquid crystal Fresnel lens is proposed. The approach allows for the unambiguous determination of both the absolute value and the sign of the topological charge of a singular beam across a wide range of the visible spectrum, as demonstrated both experimentally and theoretically. The research outcomes are promising for applications in optical information transmission systems, cryptography, and quantum computing. [ABSTRACT FROM AUTHOR]

We explore the dynamics of nonlinear parametric generation and light beam propagation in a Landau-quantized graphene structure with three energy levels interacting with two laser pulses, utilizing the Maxwell-Bloch equations. By applying a laser field to one transition of the graphene sample while keeping the second beam initially absent, the distinctive preparation of the graphene sample, coupled with its weak interaction with laser radiation, results in the parametric generation of a new laser beam in a different transition. We investigate the influence of diverse system parameters on both the efficiency of the generated beam and the propagation dynamics of both beams. Our findings reveal that manipulating these parameters can induce oscillations in the intensity of propagated beams, mitigate absorption losses during propagation allowing for earlier relaxation, and enhance the efficiency of energy transfer from the initial to the generated beam. Additionally, we demonstrate the transfer of optical vortices within the graphene ensemble by introducing an optical vortex to the initial beam. This scheme holds promise for applications in high-dimensional quantum information processing. [ABSTRACT FROM AUTHOR]

Abstract We explore the dynamics of nonlinear parametric generation and light beam propagation in a Landau-quantized graphene structure with three energy levels interacting with two laser pulses, utilizing the Maxwell-Bloch equations. By applying a laser field to one transition of the graphene sample while keeping the second beam initially absent, the distinctive preparation of the graphene sample, coupled with its weak interaction with laser radiation, results in the parametric generation of a new laser beam in a different transition. We investigate the influence of diverse system parameters on both the efficiency of the generated beam and the propagation dynamics of both beams. Our findings reveal that manipulating these parameters can induce oscillations in the intensity of propagated beams, mitigate absorption losses during propagation allowing for earlier relaxation, and enhance the efficiency of energy transfer from the initial to the generated beam. Additionally, we demonstrate the transfer of optical vortices within the graphene ensemble by introducing an optical vortex to the initial beam. This scheme holds promise for applications in high-dimensional quantum information processing.

It has been shown that the acousto-optic Raman-Nath diffraction on the acoustic wave, which bears an acoustic vortex, is accompanied by the appearance of the diffraction maxima that bear an optical vortex. The charge of the vortices that appears as a result of the diffraction corresponds to the order of diffraction if the incident optical beam is the Gaussian beam and the charge of the acoustic vortex is equal to unity. When the incident optical vortex beam takes part in this process, the charge of the diffracted optical vortices is shifted on the charge value of the incident optical beam. As a result of the analysis, we obtained the relation for the charge of vortices of diffraction maxima. It has been found that the described effect can be used for controlled demultiplexing. [ABSTRACT FROM AUTHOR]

Electrons in circular motion emit electromagnetic radiation and lose their energy and angular momentum, both of which are carried away by the radiation field. Electromagnetic radiation from such electrons is not only circularly polarized but also, in general, possessing helical phase structure, the former of which corresponds to spin angular momentum and the latter orbital angular momentum. Based on the classical electrodynamics, we show that the chiral topological property related to the orbital angular momentum arises from deformation of the electromagnetic field due to the relativistic effect. [ABSTRACT FROM AUTHOR]

Chiroptical response, demonstrating chiral interaction between optical vortex and chiral structure, plays an important role in variety of fields like optics and material science. However, the flexibility and efficiency of chiral structure fabrication are limited due to mask requirement and a point‐by‐point constructing strategy. In this paper, a novel chiral lithography method is proposed that utilizes optical vortex phase beam shaping to achieve chiral structure processing with high efficiency and flexibility. By programming topological charges of the vortex phase, chiral structures with adjustable appearance, rotation, and chirality can be produced using femtosecond laser single pulse exposure. Transmittance measurements of fabricated chiral structures array confirm a 66% helical dichroism that is predicted by simulation. Moreover, with the aid of convolutional neural networks (CNN), an accuracy of 98% in Orbital Angular Momentum (OAM) recognition can be achieved. This chiral lithography method provides an alternative for chiral structure fabrication and holds promise in the development of chiral optics, optical communications, and next‐generation optical devices. [ABSTRACT FROM AUTHOR]

This work theoretically tested the possibility of expanding the spectrum of vortex charges generated using multi-cascade optical systems based on LiNbO3 crystals twisted around their optical axis. As a result, analytical expressions for the electric field parameters of the output optical wave were obtained for the four main types of elementary cascades that allow the generation of vortices with charges +1 and –1 and also provide the matching of adjacent cascades in the multi-cascade optical system. At the same time, it was shown that when using the appropriate number of sequentially located cascades, each of which belongs to a certain type from the above, it is possible to generate a vortex beam with arbitrary integer vortex charges, including zero. Using the proposed cascade system, one can operate the outgoing beam parameters. This system can be used at the vortex beam multiplexing for information transfer. [ABSTRACT FROM AUTHOR]

Vortex beams with orbital angular momentum play a crucial role in increasing the information capacity in optical communications. The magnitude of orbital angular momentum determines the ability of information encoding. In practice, a vortex beam can encounter random objects or turbulence during free-space propagation, resulting in information damage. Therefore, accurately measuring the orbital angular momentum of a randomly fluctuated and obstructed vortex beam is a considerable challenge. Herein, we propose a single-shot method for the phase retrieval of a randomly fluctuated and obstructed vortex beam by combining the phase-shift theorem and self-reference holography. Experimental results reveal that the sign and magnitude of the initial orbital angular momentum can be simultaneously determined based on their quantitative relation with the number of coherence singularities on the observation plane, thus addressing the effects of random occlusion and atmospheric turbulence. The proposed method considerably improved the accurate decoding of orbital angular momentum information in nonideal freespace optical communications. [ABSTRACT FROM AUTHOR]

In this paper, tight focusing of a superposition of a vortex laser beam with topological charge n with linear polarization and a plane wave with the same linear polarization directed along the horizontal axis is considered. Using the Richards–Wolf formalism, analytical expressions are obtained for the intensity distribution and longitudinal projection of the spin angular momentum in the focal plane. It is shown that for even and odd numbers n, the intensity and the spin angular momentum have different symmetries: for even n they are symmetric about both Cartesian axes, and for odd n they are symmetric only about the vertical axis. The intensity distribution has n local maxima at the focus, and it is nonzero on the optical axis for any n. The distribution of the longitudinal spin angular momentum (spin density) in the focal plane has (n + 2) subwavelength regions with a positive spin angular momentum and (n + 2) regions with a negative spin angular momentum, the centers of which alternately lie on a circle of a certain radius with a center on the optical axis. This spin distribution with different signs demonstrates the spin Hall effect at the focus. Negative and positive spins are mutually compensated, and the total spin is equal to zero at the focus. We have shown that by changing the topological charge of the optical vortex, it is possible to control the spin Hall effect at the focus, that is, to change the number of regions with spins of different signs. [ABSTRACT FROM AUTHOR]

In this paper, we present a picosecond pulsed, synchronously pumped optical parametric oscillator producing vortex beam output with tunable wavelengths in the near- to mid-infrared range. The system utilizes a Nd:YVO4 picosecond pulsed solid-state laser emitting at a wavelength of 1.064 µm to pump a Z-shaped, singly resonant OPO which contains a MgO:PPLN crystal with a fan-shaped grating. The wavelength tuning characteristics of the OPO output are examined both as a function of the MgO:PPLN grating period and crystal temperature. The orbital angular momentum of the pump field can be selectively transferred to either the signal or idler fields by appropriately adjusting the location of the MgO:PPLN crystal within the OPO cavity. The maximum output power of the signal and idler vortex fields are 5.12 W and 3.46 W, respectively, for an incident pump power of 19 W. [ABSTRACT FROM AUTHOR]

Hybridly polarized (HP) vector vortex Raman lasers dramatically extend their applications on optical microscopy, optical communication, and quantum information. Spatial light modulators and waveplates are widely used for generating HP vector vortex lasers, however, the performance and beam quality of HP vector vortex lasers are restricted by diffraction loss and low damage threshold of these optical elements. Here, HP vector vortex Raman microchip lasers constructed with Yb3+:Y3Al5O12 (Yb:YAG) and vanadate (YVO4) crystals is demonstrated. The states of polarization (SoP) of HP vector vortex lasers are combination of radial and anti‐radial polarizations (RP‐ARP), azimuthal and anti‐azimuthal polarizations (AP‐AAP). The SoP of HP vector vortex lasers can be controlled by adjusting the length of YVO4 crystal and applying pump power. Maximum output powers are 456 and 586 mW with optical efficiency of 7.1% and 9.2% for HP vector vortex lasers with SoP of RP‐ARP and AP‐AAP. The HP vector vortex Raman lasers with SoP of RP‐ARP and AP‐AAP oscillate ≈1076 nm with bandwidths of 11.4 and 10.8 nm. High beam quality is achieved for HP vector vortex lasers with measured M2 nearly equal to theoretical value. The broadband HP vector vortex Raman lasers with high beam quality extend applications on optical trapping, and quantum information processing. [ABSTRACT FROM AUTHOR]

We propose a method for creating parallel Bessel-like vortical optical needles with an arbitrary axial intensity distribution via the superposition of different cone-angle Bessel vortices. We analyzed the interplay between the separation of individual optical vortical needles and their respective lengths and introduce a super-Gaussian function as their axial profile. We also analyzed the physical limitations to observe well-separated optical needles, as they are influenced by the mutual interference of the individual beams. To verify our theoretical and numerical results, we generated controllable spatial arrays of individual Bessel beams with various numbers and spatial separations by altering the spectrum of the incoming laser beam via the spatial light modulator. We demonstrate experimentally how to implement such beams using a diffractive mask. The presented method facilitates the creation of diverse spatial intensity distributions in three dimensions, potentially finding applications in specific microfabrication tasks or other contexts. These beams may have benefits in laser material processing applications such as nanochannel machining, glass via production, modification of glass refractive indices, and glass dicing. [ABSTRACT FROM AUTHOR]

Aiming at the propagation of asymmetric vortex beam, we investigate the spreading and wander characteristics of asymmetric Bessel-Gaussian beam in oceanic turbulence. Based on the cross-spectral density and Wigner distribution function of beam field, the theoretical expressions of spreading factor and beam center displacement are established to evaluate spreading and wander. The anisotropic turbulent condition is adopted to analyze turbulence impacts with more generality. The turbulence dominated by salinity fluctuation with lower anisotropy, larger temperature dissipation and smaller kinetic energy dissipation induces more beam spreading and wander. As for asymmetric Bessel-Gaussian beam, the increment of asymmetry can improve beam directionality. Besides, smaller beam scale but larger Gaussian waist radius, vortex order and beam wavelength also mitigate spreading and wander. The investigations are instructive for the underwater applications of asymmetric vortex beams.

Optical information and communication technologies are essentially based on the ability to shape the light field, either at the transmission or at the reception of the optical signal. Nowadays, wavelength and polarization state are already implemented in current telecom architectures and adding the spatial structuring of the light field as a novel degree of freedom to enhance data rate is desirable. In this context, the development of optical devices to shape optical modes belonging to orthogonal basis remains challenging. Here, in the context of singular optics, this work reports on the design, fabrication, and characterization of modal optical vortex beam shaping of paraxial light in the visible domain, in the framework of the Laguerre–Gauss basis. Both the azimuthal and radial degrees of freedom are univocally shaped via optical spin‐orbit interaction mediated by dielectric metasurfaces by combining the spatial modulation of amplitude, geometric phase, and dynamic phase. These results not only demonstrate the realization of new optical components, but also highlight how metasurface‐based technologies can contribute to optical information processing in the classical or quantum regime. [ABSTRACT FROM AUTHOR]

Vortex beams are unique in that they have annular spatial profiles and carry orbital angular momentum. This has led to their use in applications including laser processing, microparticle manipulation and signal transmission. Off-axis vortex beams, which may be considered a subset of vortex beams, display a broader spectrum of physical characteristics in comparison with their conventional (integer-order) counterparts. In this work, we derive the equations which describe the intensity distribution of off-axis vortex beams and use these to theoretically model their spatial profile. These models are supported by experimental generation of both integer and off-axis vortex beams, and the presence of orbital angular momentum is investigated through the use of the cylindrical lens transformation method. [ABSTRACT FROM AUTHOR]

The paper briefly presents some essential concepts and features of light fields with strong spatial inhomogeneity of amplitude, phase, polarization, and other parameters. It contains a characterization of optical vortices, speckle fields, polarization singularities. A special attention is paid to the field dynamical characteristics (energy, momentum, angular momentum, and their derivatives), which are considered not only as mechanical attributes of the field but also as its meaningful and application-oriented descriptive parameters. Peculiar features of the light dynamical characteristics in inhomogeneous and dispersive media are discussed. The dynamical properties of paraxial beams and evanescent waves (including surface plasmon -- polaritons) are analyzed in more detail; in particular, a general treatment of the extraordinary spin and momentum, orthogonal to the main propagation direction, is outlined. Applications of structured light fields for optical manipulation, metrology, probing, and data processing are described. [ABSTRACT FROM AUTHOR]

We study numerically the statistics of the formation of local intensity maxima in the focal plane of a collecting lens after a Gaussian beam passes through a spiral phase transparency in the presence of amplitude‒phase noise in the beam. It is shown that when the amplitude of field fluctuations is about 15%, two hot spots are most likely to be formed on the annular profile of an optical vortex with a topological charge m = 1. Moreover, in more than half of the implementations, these hot spots are located diametrically opposite to the phase dislocation region. In an elliptical beam, regions of increased intensity in the cross section of the optical vortex are located predominantly along the shorter axis. [ABSTRACT FROM AUTHOR]

Vortex beams carrying orbital angular momentum (OAM) have gained much interest in optical communications because they can be used to expand the number of multiplexing channels and greatly improve the transmission capacity. However, the number of states used for OAM-based communication is generally limited by the imperfect OAM generation, transmission, and demultiplexing methods. In this work, we proposed a dense space-division multiplexing (DSDM) scheme to further increase the transmission capacity and transmission capacity density of free space optical communications with a small range of OAM modes exploiting a multi-ring perfect vortex (MRPV). The proposed MRPV is generated using a pixel checkerboard complex amplitude modulation method that simultaneously encodes amplitude and phase information in a phase-only hologram. The four rings of the MRPV are mutually independent channels that transmit OAM beams under the condition of occupying only one spatial position, and the OAM mode transmitted in these spatial channels can be efficiently demodulated using a multilayer annular aperture. The effect of atmospheric turbulence on the MRPV was also analyzed, and the results showed that the four channels of the MRPV can be effectively separated under weak turbulence conditions. Under the condition of limited available space and OAM states, the proposed DSDM strategy exploiting MRPV might inspire wide optical communication applications exploiting the space dimension of light beams. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for generating structured light using a diffractive beam‐shaping element that can generate multiple beams with distinct spatial structures in the focal plane. The element is constructed by restructuring a spiral zone plate with fork gratings, providing a tunable and controllable means for generating structured light. The element can create linear and 2D arrays of various structured beams, including vortices with adjustable charge and vorticity, petallike beams, and ring‐lattice structures. To control the generation of these beams, it introduces several parameters of the fork gratings, enabling tailoring of the beam properties to specific applications. The proposed approach involves significant mathematical analysis, including the derivation of complex equations and expressions to understand the behavior of the proposed element and its impact on the generated beams. It conducts simulations and experiments to validate the mathematical analysis and demonstrate the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

Theoretical, numerical, and experimental means are used to study the propagation of three-Airy beams with and without an optical vortex in free space. These light fields are objects of interest for use in modern photonics, due to strong localization of the transverse intensity of the field upon propagation, self-healing, autofocusing, and a change in the intensity structure. This is useful for various applications. [ABSTRACT FROM AUTHOR]

Optical vortices (OVs) have rapidly varying spatial phase and optical energy that circulates around points or lines of zero optical intensity. Manipulation of OVs offers innovative approaches for various fields, such as optical sensing, communication, and imaging. In this work, we demonstrate the correlation between OVs and absorption enhancement in two types of structures. First, we introduce a simple planar one-dimensional (1D) structure that manipulates OVs using two coherent light sources. The structure shows a maximum of 6.05-fold absorption gap depending on the presence of OVs. Even a slight difference in the incidence angle can influence the generation/annihilation of OVs, which implies the high sensitivity of angular light detection. Second, we apply inverse design to optimize two-dimensional (2D) perfect ultrathin absorbers. The optimized free-form structure achieves 99.90 % absorptance, and the fabricable grating structure achieves 97.85 % at 775 nm wavelength. To evaluate OV fields and their contribution to achieving absorption enhancement, we introduce a new parameter, OV circularity. The optimized structures generate numerous OVs with a maximum circularity of 95.37 % (free-form) and 96.14 % (grating), superior to our 1D structure. Our study reveals the role of high-circularity localized OVs in optimizing nano-structured absorbers and devices for optical sensing, optical communication, and many other applications.

Hall effect of light is a result of symmetry breaking in spin and/or orbital angular momentum (OAM) possessing optical system and is caused by e.g. refractive index gradient/interface between media or focusing of a spatially asymmetrical beam, similar to the electric field breaking the symmetry in spin Hall effect for electrons. The angular momentum (AM) conservation law in the ensuing asymmetric system dictates redistribution of spin and orbital angular momentum, and is manifested in spin-orbit, orbit-orbit, and orbit-spin conversions and reorganization, i.e. spin-orbit and orbit-orbit interaction. This AM restructuring in turn requires shifts of the barycenter of the electric field of light. In the present study we show, both analytically and by numerical simulation, how different electric field components are displaced upon tight focusing of an asymmetric light beam having OAM and spin. The relation between field components shifts and the AM components shifts/redistribution is presented too. Moreover, we experimentally demonstrate, for the first time, to the best of our knowledge, the spin-orbit Hall effect of light upon tight focusing in free space. This is achieved using azopolymers as a media detecting longitudinal or z component of the electrical field of light. These findings elucidate the Hall effect of light and may broaden the spectrum of its applications.

Topological spin textures are field arrangements that cannot be continuously deformed to a fully polarized state. In particular, merons are topological textures characterized by half-integer topological charge ±1/2 and vortex-like swirling patterns at large distances. Merons have been studied previously in the context of cosmology, fluid dynamics, condensed matter physics and plasmonics. Here, we visualized optical spin angular momentum of phonon polaritons that resembles nanoscale meron spin textures. Phonon polaritons, hybrids of infrared photons and phonons in hexagonal boron nitride, were excited by circularly polarized light incident on a ring-shaped antenna and imaged using infrared near-field techniques. The polariton field reveals a half-integer topological charge determined by the handedness of the incident beam. Our phonon polaritonic platform opens up new pathways to create, control, and visualize topological textures.

It is shown that a squared Laguerre-Gaussian (LG) vortex beam is Fourier-invariant and retains its structure at the focus of a spherical lens. In the Fresnel diffraction zone, such a beam is transformed into superposition of conventional LG beams, the number of which is equal to the number of rings in the squared LG beam. If there is only one ring, then the beam is structurally stable. A more general beam, which is a “product” of two LG beams, is also considered. Such a beam will be Fourier-invariant if the number of rings in two LG beams in the “product” is the same. The considered beams complement the well-known family of LG beams, which are intensively studied as they remain stable during their propagation in turbulent media.

In this paper, we considered design of the complex metalens with high numerical aperture. It proposed to be manufactured in a thin film of silicon nitride. The element represents two slanted sectored metalenses, every sector of which is binary sub-wavelength gratings set. The diameter of the proposed lens is 14 µm. Numerical modelling by applying the finite difference time-domain method demonstrated that the proposed element was able to detect laser vortex beams with different topological charges –2 and –1. Moreover, it can operate over the whole visible range of light. The proposed metalens is able to discern beams with different wavelengths since they are focused in different focal planes. The change of wavelength in a 1 nm produces the shift of focal spot in about 4 nm. In the case of a Gaussian incident beam with left circular polarizing, this metalens simultaneously forms two vortex beams with topological charges one and two at the focal length of 6 μm. [ABSTRACT FROM AUTHOR]

Recently, a variety of mechanisms have been discovered that extend the range of optical techniques for identifying and characterizing molecular chirality, beyond those associated with optical polarization. It is now evident that beams of light with a twisted wavefront, known as optical vortices, can also interact with chiral matter with a specificity determined by relative handedness. Exploring this chiral sensitivity of vortex light in its interactions with matter requires careful consideration of the symmetry properties that engage in such processes. Most of the familiar measures of chirality are directly applicable to either matter, or to light itself—but only to one or the other. To elicit the principles that determine the viability of distinctly optical vortex‐based forms of chiral discrimination invites a more universal approach to symmetry analysis, as is afforded by the common, fundamental physics of CPT symmetry. Taking this approach supports a comprehensive and straightforward analysis to identify the mechanistic origins of vortex chiroptical interactions. Careful inspection of selection rules for absorption also elicits the principles governing any identifiable engagement with vortex structures, providing a reliable basis to ascertain the viability of other forms of enantioselective vortex interaction. [ABSTRACT FROM AUTHOR]

In this work, we have achieved an advancement by integrating wide-angle capacity into vortex beams with an impressive topological charge (TC) of 12. This accomplishment was realized through the meticulous engineering of a propagation-phase-designed metasurface. Comprising gallium nitride (GaN), meta-structures characterized by their high-aspect ratio, this metasurface exhibits an average co-polarization transmission efficiency, reaching a remarkable simulated value of up to 97%. The intricate spiral patterns, along with their respective quantification, have been meticulously investigated through tilt-view scanning electron microscopy (SEM) and were further analyzed through the Mach–Zehnder interferometer. A captivating revelation emerged, a distinctive petal-like interference pattern manifests prior to the metasurface's designed focal distance. The occurrence of this petal-like pattern at a specific z-axis position prompts a deliberate manipulation of the helicity of the spiral branches. This strategic helicity alteration is intrinsically tied to the achievement of a minimized donut diameter at the designed focal length. In regard to the angular capability of the device, the captured images continuously showcase prominent attributes within incident angles spanning up to 30 degrees. However, as incident angles surpass the 30-degree threshold, the measured values diverge from their corresponding theoretical projections, resulting in a progressive reduction in the completeness of the donut-shaped structure. [ABSTRACT FROM AUTHOR]

Along with broad applications of the linear Doppler effect, the rotational Doppler effect (RDE) of a structured light source carrying orbital angular momentum (OAM) has attracted significant attention for applications ranging from optical sensors to Doppler cooling. However, the high‐purity structured source's low energy efficiency and unknown optimal OAM parameters have significantly degraded the RDE's performance in previous work. Here, instead of utilizing an optical vortex source, the Doppler features are analyzed in scattered twisted photons carrying OAM with a common light source, and it is demonstrated that the RDE induced by a typical rotator can be extracted using a spiral phase spatial filter (SPSF) at the receiver. This model reveals that a rotating rough surface scatters abundant twisted photons carrying varied OAM values, and the OAM spectrum distribution is modulated by its angular coherence of spatial signature. Furthermore, common surfaces with different autocorrelation structures on received signals using the SPSF method are analyzed theoretically and experimentally. Such a scheme facilitates rotator detection with a generalized nonvortex simple source and dozen–fold improved efficiency with robustness against noncoaxial problems. These demonstrations open a path for studying and applying scattered twisted photons during light detection. [ABSTRACT FROM AUTHOR]

We have shown how the spin Hall effect is formed in a tight focus for two light fields with initial linear polarization. We have demonstrated that an even number of local subwavelength regions appear in which the sign of the longitudinal projection of the spin angular momentum (the third Stokes component) alternates. When an optical vortex with topological charge n and linear polarization passes through an ideal spherical lens, additional optical vortices with topological charges n + 2, n − 2, n + 1, and n − 1 with different amplitudes are formed in the converged beam. The first two of these vortices have left and right circular polarizations and the last two vortices have linear polarization. Since circularly polarized vortices have different amplitudes, their superposition will have elliptical polarization. The sign of this elliptical polarization (left or right) will change over the beam cross section with the change in the sign of the difference in the amplitudes of optical vortices with circular polarization. We also have shown that optical vortices with topological charges n + 2, n − 2 propagate in the opposite direction near the focal plane, and together with optical vortices with charges n + 1, n − 1, they form an azimuthal energy flow at the focus. [ABSTRACT FROM AUTHOR]

The non‐trivial polarization topology of bound states in the continuum (BICs) provides new strategies in nanophotonics. The polarization topology depends on the geometric parameters and energy‐momentum dispersion of the system and can be engineered to add specific functionalities for light molding. Herein, such a possibility is investigated by studying the topology of the polarization states associated with the optical field radiated by BICs when Dirac‐cone‐degeneracy is lifted. The opening of a pseudogap in the Dirac cone dispersion of square‐lattice dielectric photonic crystal slabs is achieved by tuning the slab thickness. First, the emergence of half‐integer topological charges without the requirement of BIC annihilation is theoretically shown, which instead occurs when in‐plane inversion symmetry is broken. Then, using spin‐to‐orbital angular momentum conversion, the theory of half‐integer topological charges mediated by BICs is demonstrated and experimentally proved. The same device is able to give rise to vortices with different orbital angular momentum depending on the way it is illuminated, thus improving the potential of optical multiplexing. In addition, the additive character of the topology‐induced phase‐vortex generation is finally demonstrated for both integer and half‐integer charges using also vortex states as input beams, which is of relevance for information delivery. [ABSTRACT FROM AUTHOR]

A combined high-aperture metalens in a thin silicon nitride film, which consists of two inclined sector metalens, is considered. Each sector metalens consists of a set of binary subwavelength gratings. The diameter of the lens is 14 μm. It has been shown using time-domain finite difference method that the metalens can simultaneously detect optical vortices with two topological charges –1 and –2, in almost the entire visible wavelength range. The metalens can distinguish several wavelengths that are focused at different points in the focal plane: a 1 nm change in wavelength results in a focal spot shift of about 4 nm. When the metalens is illuminated by a Gaussian beam with left-handed circular polarization, two optical vortices with topological charges 1 and 2 are simultaneously formed at 6 nm between each other at focal distance equals 6 nm. This metalens can be used to increase information in transmission channel in wireless telecommunication systems by selecting the space-time modes of laser radiation with different topological charges and different wavelengths. The considered microlens is an example of a compact demultiplexer.

An optical microsensor of the laser light polarization state based on a metalens is proposed. Well-known polarization sensors based on metasurfaces usually transmit different types of polarization at different angles to the optical axis. The polarization sensor proposed in this work forms different patterns for different polarization types at the metalens focus. Specifically, the left-handed circular polarization at the focus forms a ring-shaped spot, the right-handed circular polarization - a round focal spot, and linear polarization forms an elliptical spot with two side lobes. Moreover, the angle of inclination of the elliptical focal spot corresponds to the angle of inclination of the initial E-vector of the linearly polarized beam. The simulation is consistent with theoretical predictions. A 30-μm metalens with a low aspect ratio, high numerical aperture, and short focal length equal to the incident wavelength 633 nm in a 120-nm thick thin film of amorphous silicon is designed, fabricated and characterized.

In this paper, tight focusing of a superposition of a vortex laser beam with topological charge n with linear polarization and a plane wave with the same linear polarization directed along the horizontal axis is considered. Using the Richards–Wolf formalism, analytical expressions are obtained for the intensity distribution and longitudinal projection of the spin angular momentum in the focal plane. It is shown that for even and odd numbers n, the intensity and the spin angular momentum have different symmetries: for even n they are symmetric about both Cartesian axes, and for odd n they are symmetric only about the vertical axis. The intensity distribution has n local maxima at the focus, and it is nonzero on the optical axis for any n. The distribution of the longitudinal spin angular momentum (spin density) in the focal plane has (n + 2) subwavelength regions with a positive spin angular momentum and (n + 2) regions with a negative spin angular momentum, the centers of which alternately lie on a circle of a certain radius with a center on the optical axis. This spin distribution with different signs demonstrates the spin Hall effect at the focus. Negative and positive spins are mutually compensated, and the total spin is equal to zero at the focus. We have shown that by changing the topological charge of the optical vortex, it is possible to control the spin Hall effect at the focus, that is, to change the number of regions with spins of different signs.

In this paper, we present a picosecond pulsed, synchronously pumped optical parametric oscillator producing vortex beam output with tunable wavelengths in the near- to mid-infrared range. The system utilizes a Nd:YVO4 picosecond pulsed solid-state laser emitting at a wavelength of 1.064 µm to pump a Z-shaped, singly resonant OPO which contains a MgO:PPLN crystal with a fan-shaped grating. The wavelength tuning characteristics of the OPO output are examined both as a function of the MgO:PPLN grating period and crystal temperature. The orbital angular momentum of the pump field can be selectively transferred to either the signal or idler fields by appropriately adjusting the location of the MgO:PPLN crystal within the OPO cavity. The maximum output power of the signal and idler vortex fields are 5.12 W and 3.46 W, respectively, for an incident pump power of 19 W.

The polarization state is described by a quantum mechanical two-level system, which is known as special unitary group of degree 2 [SU(2)]. Polarization is attributed to an internal spin degree of freedom inherent to photons, while photons also possess an orbital degree of freedom. A fundamental understanding of the nature of spin and orbital angular momentum of photons is significant to utilize the degrees of freedom for various applications in optical communications, computations, sensing, and laser-patterning. Here, we show that the orbital angular momentum of coherent photons emitted from a laser diode can be incremented using a vortex lens, and the magnitude of orbital angular momentum increases with an increase in the topological charge inside the mode. The superposition state of the left and right vortices is described by the SU(2) state, similar to polarization; however, the radius of the corresponding Poincaré sphere depends on the topological charge. Consequently, we expect a nested SU(2) structure to describe various states with different magnitudes in orbital angular momentum. We have experimentally developed a simple system to realize an arbitrary SU(2) state of orbital angular momentum by controlling both amplitudes and phases of the left and right vortices using a spin degree of freedom, whose interplays were confirmed by expected far-field images of dipoles and quadruples.

Twisted photons with finite orbital angular momentum have a distinct mode profile with topological charge at the center of the mode while propagating in a certain direction. Each mode with different topological charges of m is orthogonal, in the sense that the overlap integral vanishes among modes with different values of m. Here, we theoretically consider a superposition state among three different modes with left and right vortices and a Gaussian mode without a vortex. These three states are considered to be assigned to different quantum states; thus, we employed the su(3) Lie algebra and the associated SU(3) Lie group to classify the photonic states. We calculated expectation values of eight generators of the su(3) Lie algebra, which should be observable, since the generators are Hermite matrices. We proposed to call these parameters Gell-Mann parameters, named after the theoretical physicist Murray Gell-Mann, who established quantum chromodynamics (QCD) for quarks. The Gell-Mann parameters are represented on the eight-dimensional hypersphere with its radius fixed due to the conservation law of the Casimir operator. Thus, we discussed a possibility of exploring photonic QCD in experiments and classified SU(3) states to embed the parameters in SO(6) and SO(5).

If a vortex propagation-invariant beam is given by all its intensity nulls, then its topological charge (TC) can be defined easily: its TC is equal to the sum of topological charges of all optical vortices in these intensity nulls. If, however, a propagation-invariant beam is given as a superposition of several light fields, then determining its TC is a complicated task. Here, we derive the topological charges of four different types of propagation-invariant beams, represented as axial superpositions of Hermite–Gaussian beams with different amplitudes and different phase delays. In particular, topological charges are obtained for such beam families as the Hermite–Laguerre–Gaussian (HLG) beams and two-parametric vortex Hermite beams. We show that the TC is a quantity resistant to changing certain beam parameters. For instance, when the parameters θ and α of the HLG beams are altered, the beam intensity also changes significantly, but the TC remains unchanged. [ABSTRACT FROM AUTHOR]

We consider sharp focusing of an axial superposition of two optical vortices with identical topological charges, but different amplitudes and circular polarizations of different signs. The ratio of the amplitudes of the two beams is a parameter. When this parameter changes, the polarization state of the superposition changes from linear polarization to right-hand circular polarization. Based on the Richards–Wolf theory, exact expressions are obtained for the longitudinal components of the spin angular momentum (SAM) density and orbital angular momentum (OAM) density at the focus of the considered superposition. It follows from these expressions that the sum of the total longitudinal components of the SAM and OAM is conserved upon focusing, and also that, due to the spin-orbit conversion, the total longitudinal component of the SAM decreases during focusing, while the total longitudinal component of the OAM increases by the same amount. By changing the ratio of the amplitudes of the constituent beams from 1 to 0, one can change the value of the spin-orbit conversion from zero (for linear polarization) to a maximum (for circular polarization). Also, by changing this parameter, one can control the spin Hall effect at the focus, which takes place at the focus of the considered beam. This study can be applied for controlling the rotation velocity of microparticles trapped in the focus. [ABSTRACT FROM AUTHOR]

The dynamics of the topological charge of a vortex optical beam propagating in turbulent air while accounting for the cubic nonlinearity is theoretically considered. In a number of examples, we show that the optical beam, self-focusing, manifests itself ambiguously depending on the optical wave power. At near-critical values of beam power, self-focusing leads to enhanced spatial localization of optical vortices and substantial suppression of vortex walk-off relative to the beam axis caused by air turbulence. However, with increasing optical intensity, the modulation instability imposed by cubic nonlinearity becomes significant and contributes jointly with medium turbulence and leads to faster divergence of vortex beams. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the study of the negative energy flow in the tight focusing of a radially polarized vortex beam. We know that, because of the coupling of the polarization state and the vortex charge, the on-axis energy flow in the focal region can be well modulated by changing the polarization order and the vortex charge of the incident vector beam. This shows that when the polarization order and the vortex charge satisfy the specific relation, the on-axis negative energy flow can be obtained in the focal region. Moreover, the initial phases of two polarization unit vectors also affect the evolution of the on-axis negative energy flow in the tight focusing of the radially polarized beam. The phase difference modulation of the two polarization unit vectors indicates two different modulations of the polarization state. Our work provides a more flexible modulation method for focal shaping and optical modulation. [ABSTRACT FROM AUTHOR]

Here, we investigate coaxial superpositions of Gaussian optical vortices that can be described by a geometric sequence. For all superpositions analyzed, a topological charge (TC) is derived. In the initial plane, the TC can be either integer or half-integer, acquiring an integer value upon free-space propagation of the light field. Generally, the geometric sequence of optical vortices (GSOV) has three integer parameters and one real parameter. Values of these four parameters define the TC of the GSOV. Upon free-space propagation, the intensity pattern of the GSOV is not conserved, but can have intensity petals whose number is equal to one of the four beam parameters. If the GSOV has a unit real parameter, all constituent angular harmonics in the superposition have the same weight. In this case, the TC of the superposition is equal to the average index of the constituent angular harmonics. For instance, if the TC of the first and of the last angular harmonics, respectively, equals k and n, then the total TC of the superposition in the initial plane will be (n + k) /2, becoming equal to n upon free-space propagation.

We calculate the topological charge (TC) of a coherent axial superposition of different-"color" Laguerre-Gaussian (LG) beams, each having a different wavelength and TC. It is found that the TC of such a superposition is equal to the TC of the longer-wavelength constituent LG beam regardless of the weight coefficient of this beam in the superposition and its corresponding TC. It is interesting that the instantaneous TC of such a superposition is conserved and the (time-averaged) intensity distribution of the "colored" optical vortex changes its light "gamut": whereas in the near field with increasing radius, colors of the light rings (rainbow) change according to their TC in the superposition from the smaller TC to the larger one, upon free-space propagation (to the far field), with increasing radius, the ring colors in the rainbow get arranged in the reverse order from the larger TC to the smaller one. It is also shown that choosing the wavelengths (blue, green, and red)in a special way in a three-color superposition of single-ringed LG beams allows obtaining a time-averaged white light ring at a certain distance.

Propagation of light beams in turbid media such as underwater environments, fog, clouds, or biological tissues finds increasingly important applications in science and technology, including bio-imaging, underwater communication, and free-space communication technologies. While many of these applications traditionally relied on conventional, linearly polarized Gaussian beams, light possesses many degrees of freedom that are still largely unexplored, such as spin angular momentum (SAM) and orbital angular momentum (OAM). Here, we present nonlinear light–matter interactions of such complex light beams with “rotational” degrees of freedom in engineered nonlinear colloidal media. By making use of both variational and perturbative approach, we consider non-cylindrical optical vortices, elliptical optical vortices, and higher-order Bessel beams integrated in time (HOBBIT) to predict the dynamics and stability of the evolution of these beams. These results may find applications in many scenarios involving light transmission in strongly scattering environments.

In this study, a four-level microwave-driven system is proposed for the transfer of the topological charge from an optical vortex light to a freshly created signal light. By adjusting the microwave field's intensity, we first investigated the exchange efficiency of the created light. We talked about the exchange efficiency versus the propagation distance and the probe detuning, respectively. We came to the conclusion that the microwave light's strong value makes it possible to achieve significant exchange efficiencies. Next, we talked about how the created light's absorption and dispersion spectra varied depending on azimuth. We discovered that altering the azimuthal angle of the vortex light allows the absorption curve to be transformed into the gain spectrum. Additionally, we demonstrated how altering the azimuthal angle might alter the dispersion's slope. Topological charge of the vortex light has also been used to explain the spatially dependent absorption spectrum of the generated light. We've discussed the spatial dependence of the intensity and phase distributions of the created light in the conclusion. We have established that the topological charge can be exchanged very effectively from optical vortex light to newly produced light. [ABSTRACT FROM AUTHOR]

We obtain a transform that relates the standard Bessel–Gaussian (BG) beams with BG beams described by the Bessel function of a half-integer order and quadratic radial dependence in the argument. We also study square vortex BG beams, described by the square of the Bessel function, and the products of two vortex BG beams (double-BG beams), described by a product of two different integer-order Bessel functions. To describe the propagation of these beams in free space, we derive expressions as series of products of three Bessel functions. In addition, a vortex-free power-function BG beam of the mth order is obtained, which upon propagation in free space becomes a finite superposition of similar vortex-free power-function BG beams of the orders from 0 to m. Extending the set of finite-energy vortex beams with an orbital angular momentum is useful in searching for stable light beams for probing the turbulent atmosphere and for wireless optical communications. Such beams can be used in micromachines for controlling the movements of particles simultaneously along several light rings. [ABSTRACT FROM AUTHOR]

Femtosecond light pulses carrying optical angular momentums (OAMs), possessing intriguing properties of helical phase fronts and ultrafast temporal profiles, enable many applications in nonlinear optics, strong-field physics, and laser micromachining. While generation of OAM-carrying ultrafast pulses and their interactions with matters are intensively studied in experiments, 3D characterization of ultrafast OAM-carrying light beams in spatiotemporal domain has, however, proved difficult to achieve. Conventional measurement schemes rely on the use of a reference pulsed light beam, which needs to be well characterized in its phase front and to have sufficient overlap and coherence with the beam under test, largely limiting practical applications of these schemes. Here a self-referencing set-up is demonstrated based on a tilted interferometer that can be used to measure complete spatiotemporal information of OAM-carrying femtosecond pulses with different topological charges. Through scanning one interferometer arm, the spectral phase over the pulse spatial profile can be obtained using the tilted interference signal, and the temporal envelope of the light field at one particular position around its phase singularity can be retrieved simultaneously, enabling 3D beam reconstruction. This self-referencing technique, capable of measuring spatiotemporal ultrafast optical-vortex beams, may find many applications in fields of nonlinear optics and light-matter interactions. [ABSTRACT FROM AUTHOR]