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We introduce the effects of the multi-order and off-axis vortex on the propagation of Pearcey Gaussian vortex beams (PGVBs) in a chiral medium. The effects of vortex positions, topological charges ...

Based on the extended Huygens–Fresnel integral, the analytical expressions for the average intensity of a partially coherent radially polarized rotating elliptical cosine-Gaussian optical lattice (...

The evolution dynamic properties of self-accelerating Hermite complex-variable-function Gaussian (SHCG) wave packets in highly nonlocal nonlinear media are investigated. Analytical results from a $$(3+1)$$ -dimensional Snyder–Mitchell model show that various SHCG wave packets carrying multi-order vortices rotate smoothly. Increasing the distribution factor will cause the intensity layout to cluster more closely around the center, while the vortices will be farther away. The SHCG wave packets can reverse the positions of their temporal side lobes. The role of the power ratio in determining the rotation period and the angular velocity is also discussed. Furthermore, numerical results of the nonlocal nonlinear Schrodinger equation are simulated to illustrate the effects of different nonlocalities and initial perturbations. The SHCG wave packets show interesting features during propagation, which can provide new ideas for the regulation of the multi-dimensional optical field.

We investigate the propagation of the first-order chirped Airy vortex (FCAiV) beams in a quadratic index media analytically by applying the Huygen-Fresnel integral. The intensity, the phase, the en...

The atmospheric turbulence (AT) causes distortion of phase fronts of orbital angular momentum (OAM) beams, which hinders the recognition of OAM modes. Convolutional neural network (CNN), a deep learning (DL) technique, can be utilized to realize the effective recognition of OAM modes. In this article, we propose a properly designed six-layer CNN model that can achieve high recognition accuracy (RA) of OAM modes at a reasonable computing complexity. We used intensity images of Laguerre-Gaussian (LG) beams to train our CNN model and explored the relationship between the RA for different single OAM modes and many factors including the number of training epochs, AT intensity, transmission distance, and the number of single OAM modes. Our CNN model can obtain an RA of 97.1% under moderate turbulence and 80% under strong turbulence, which are better than some CNN models proposed previously. Compared with these previous CNN models, our CNN model can also reduce the time consumption for at most 70%. Our research could contribute in achieving higher data capacity in OAM-based free space optical (FSO) communication systems.

Optical vortex is a structured beam with a spiral phase wavefront. Different orbital angular momentums (OAM) are orthogonal to each other and multiplexed together without crosstalk. Vortex optical communication (VOC) can obtain good bandwidth and channel number. In this paper, we creatively exchanged the order of the spatial light modulator (SLM) and the optical switch, the communication link from “Vortex after Modulation (VAM)” to “Vortex Modulation (VM)”, which constitutes a new link structure. Compared with the VAM communication link, the VM link has the advantages of higher transmission rate, better signal quality, lower signal error rate and so on. The results show that the VM link is 0.126 Gbit/s faster than the VAM on a single channel link, and 15.5 Gbit/s faster in 16-QAM 8 OAM beams multiplexing. The error rate of the received signal under the same conditions at the transmitting end has an improvement of 2~4 orders of magnitude. The method is simple, convenient to implement, and has a significant improvement in transmission rate. It can provide a wide range of applications in vortex high-capacity communication.

In this paper, a class of one-dimensional (1D) Fibonacci quasi-periodic multilayers composed of two parity-time-symmetric ( PT -symmetric) elements are designed. Their scattering spectra, transparencies, invisibilities, and other singular optical properties are investigated in detail. It is found that three types of new systematic phases, ten types of new unidirectional transparencies, two types of new bidirectional transparencies and one type of new bidirectional invisibility are created by this class of interesting systems, which possess more types compared with the PT -symmetric periodic multilayers and the Thue–Morse multilayers composed of PT -symmetric elements. It can be seen that although the order degree of the Fibonacci multilayers is lower than that of the other two systems, their types of systematic phases, transparencies, and invisibilities are obtained, their types of systematic phases, transparencies, and invisibilities are more abundant. This proves that, as the order degree of the PT -symmetric system decreases, its types of singular optical properties become more abundant. This work sheds some light on the PT -symmetric optical structures and Fibonacci sequence, offering the possibility to widen their application field. Moreover, it provides a theoretical basis to design new optical devices.

Based on the angular spectrum of rotating elliptical Gaussian vortex beams (REGVBs), the Imbert Fedorov (IF) shift of REGVBs with the topological charge m = 1 is calculated analytically and numerically. The effects of the topological charge and the vortex position on the IF shift of REGVBs are discussed. By comparing the IF shifts of Gaussian beams, Airy beams with finite energy and REGVBs, we find that REGVBs have unique advantages in the control of the IF shift, that is, the IF shift of REGVBs is similar to the odd symmetry near the Brewster angle, and the rotation parameters can specially control the magnitude and the direction of the IF shift at the same time. Our discovery breaks the previous thinking barrier, that is, most of the control of the IF shift direction is based on materials, and provides a new perspective for controlling the IF shift based on the properties of beams.

We introduce the propagation of Pearcey Gaussian (PG) beams in a strongly nonlocal nonlinear medium (SNNM) analytically. Our results show that PG beams propagating in the SNNM have two different focusing positions. The intensity peak appears at different focusing positions depending on the selection of the nonlinear parameters. In addition, the effects of the nonlinear parameters and the scaling factor on the trajectory, the position of the intensity focusing, the intensity evolution between focus locations, and the radiation force are studied.

To study the effect of structural symmetry on both the quantity and quality of singular optical properties, a one-dimensional parity-time-symmetric (PT-symmetric) Thue–Morse (TM) optical-waveguide networks family is built and investigated. It is shown that this type of optical waveguide networks can produce 15 types of singular optical properties that have not yet been reported. These include 3 types of new systematic phases, 6 types of new unidirectional transparencies and 6 types of new bidirectional transparencies. Compared with a PT-symmetric periodic photonic crystal (structure 1), PT-symmetric periodic optical waveguide networks (structure 2) and PT-symmetric TM optical multilayers (structure 3), this type of optical system has lower symmetry. However, the number of singular optical properties for this system is higher. This strongly suggests that for an optical system, which contains a PT-symmetric substructure, with decreasing symmetry of the PT-symmetric optical system, the quantity and quality of systematic phase, transparency, and invisibility for the system tends to increase. This work deepens not only the understanding of the TM sequence and singular optical properties of PT-symmetric optical systems but also that of the influence of structural symmetry on the singular optical properties of PT-symmetric systems is clarified. In addition, the structure also allows the occurrence of previously-unreported bidirectional invisibility, which has potential applications for the manufacturing of invisibility-generating devices.

In this paper, the circle Bessel Gaussian vortex beams (CBGVBs) are introduced in a harmonic potential for the first time, whose autofocusing properties are explored by theoretical analysis as well as numerical simulation. According to the dimensionless linear (2+1)D Schrödinger equation, we numerically simulate the transmission trajectories of different topological charges of the off-axis vortices and the positions, the intensity and the phase distributions, the maximum transmission intensity, the center of mass, the energy flow, and the angular momentum. The simulation results show that the periodically autofocusing CBGVBs can flexibly adjust the position, the intensity, and the focus points by controlling the parameters. By increasing the number of off-axis vortices and adjusting the position of off-axis vortices, the transmission trajectory and the intensity of the CBGVBs can be controlled. Furthermore, we notice that the larger the slope of the curve where the combined force of the scattering force and the gradient force is 0, the particles are more likely to be trapped.

Light-field shaping technology plays an important role in optics and nanophotonics. For instance, the spatially structured light field, which exhibits characteristic features in complex phases, light intensity, and polarization, is crucial to understanding new physical phenomena and exploring practical applications. Herein, we propose and demonstrate a new class of tunable circular Pearcey beams (TCPBs) by imposing the annular spiral-zone phase (ASZP). Through experiments, we used a spatial light modulator to generate TCPBs based on their spiral phase distribution, and numerically analyzed the generation and control of the beams with unusual autofocusing and self-rotating dynamics. ASZP is a general term for complex phases composed of the spiral phase, equiphase, and radial phase. TCPB typically exhibits dynamical properties, including abrupt autofocusing, automatic generation of optical bottles, and self-rotation of the beam pattern, during propagation. Besides, the number of generated optical bottles can be modulated by the superposition mode of ASZP and the number of subphases. We found that an inappropriate superposition mode leads to distortion, and we analyzed the underlying mechanism. Potential applications of TCPBs in optical manipulation are also discussed, presenting an exemplary role desired for light-field manipulation.

Spin Hall effect (SHE) of Laguerre-Gaussian (LG) beams reflected and transmitted in parity-time (PT) symmetric metamaterials are investigated near the coherent-perfect-absorption (CPA)-laser point and exceptional points (EPs). The numerical results show that large transverse shifts occur at the CPA-laser point regardless of the incident direction. But at EPs, the SHE increases at one side and disappears at the other side, thus achieving the intense SHE of the reflected light beams at the specified side incidence. In addition, it is found that Bragg oscillation can be generated by increasing the period number of PT symmetric metamaterial layers, thus increasing the number of formants in transverse displacement. In particular, the transverse shift peaks of the transmitted beams merge into a positive peak when the incident angle is close to 90 ∘ and does not change basically with the increasing of Im(ɛ), which can also be considered as a strong tolerance to the variation of Im(ɛ). This feature is expected to realize a new type of optoelectronic devices with anti-interference performance. These results provide a feasible path for the modulation of spin Hall effect of light (SHEL) and provide the possibility for the development of new nanophotonic devices.

Obtaining the analytical expression of focusing off-axis hollow vortex Gaussian (HVG) beams by solving the (2 + 1) dimensionless linear Schrodinger-like equation, we perform the propagation path, the intensity and phase distributions, the center of mass, the peak intensity and the beam width with different potential widths α , different hollow orders n , different topological charges m , different off-axis coordinates ( X 0 , Y 0 ). In general, the off-axis HVG beams are swirled counterclockwise and periodically focus during the propagation. The topological charge m separates the focusing center but the hollow order n concentrates the focusing area. Moreover, the off-axis coordinate ( X 0 , Y 0 ) significantly increases the focusing intensity and the potential width α can also increase the focusing frequency during the propagation. Interestingly, the influences of the hollow order n , the topological charge m and off-axis coordinate ( X 0 , Y 0 ) are the same on the peak intensity, which are different with the beam width. Furthermore, we also discuss the Poynting vector, angular momentum and radiation forces. In terms of the radiation forces, we can easily explore the position trapping particles stably regardless of the off-axis coordinate ( X 0 , Y 0 ) selection.

We investigate nonparaxial propagation properties of the radially polarized Airy-Gaussian (RPAiG) beams with different initial launch angles in uniaxial crystal orthogonal to the optical axis. The influences of both the ratio of the extraordinary refractive index ( n e ) to the ordinary refractive index ( n o ), distribution factor χ 0 and a parameter related to the initial launch angle β on the intensity evolution, the gradient force and the scattering force of the nonparaxial RPAiG beams are analyzed and described in detail. Our results indicate that the re-focusing effect of nonparaxial RPAiG beams is more obvious with the increasing of the parameter related to the initial launch angle β and the ratio of n e to n o . Furthermore, as the propagation distance increases, the intensity of the side lobes continues to flow into the main lobe until the intensity distribution of main lobes reaches the maximum, finally that of the main lobe will move into the side lobes and the intensity pattern of the main lobe will gently divide into two Airy-like patterns. One can see that the RPAiG beams tend to radially polarized Airy (RPAi) beams when χ 0 is smaller, the RPAiG beams tend to the radially polarized Gaussian (RPG) beams when χ 0 is larger. Meanwhile, the position of side lobes and the evolution speed of the radiation force can be modulated by the ratio of n e to n o and the parameter β in the observation plane. The investigation of the nonparaxial propagation characteristics of the RPAiG beams may have potential applications in the particles trapping and optical tweezers.

The self-accelerating Airy–Hermite–Gaussian (AiHG) and Airy–helical–Hermite–Gaussian (AiHHG) wave packets in strongly nonlocal nonlinear media (SNNM) are obtained analytically and numerically. The complex amplitudes of the AiHG and AiHHG wave packets are obtained by multiplying the self-accelerating Airy functions, the Hermite Polynomials and Gaussian functions. Furthermore, the different 3D spatiotemporal profiles and the photoelasticity can be obtained by selecting different values of the mode number, the chirp factor, the initial velocity, and the degree of the nonlocality.

Based on the ABCD matrix and Huygens diffraction integral, the expressions for the quadratically chirped Airy vortex (QCAiV) beams with vortex’s arbitrary position and vortex’s topological charge propagating in the right-handed (RHMs) and left-handed materials (LHMs) slabs are deduced. The effects of the position and the topological charge m of the vortex on the intensity distribution, the intensity concentration, the peak intensity, diffraction range and radiation forces are deeply investigated in the paper. It is shown that the acceleration of the optical vortex is always bigger than that of the corresponding QCAiV beams in both RHMs and LHMs slabs. Therefore, with suitable position of the vortex, plurality of intersections of the vortex and the QCAiV beams can be achieved and the intensity concentration can be controlled during propagation. The range of the diffraction can be controlled by the off-axis vortex and it depends on the relative distance from vortex to the origin. At last, we demonstrate the effect of the vortex on the maximum scattering force and gradient force distribution on the Rayleigh dielectric particles respectively.

In this paper, the bit error rate (BER) performance and outage probability of quadrature amplitude modulation free space optical (QAM/FSO) communications with spatial diversity in turbulent environ...

Based on the analytic expression of the chirped Airy hollow Gaussian (CAiHG) wave packets derived from the ( 3 + 1 )-dimensional ( ( 3 + 1 ) D) Schrodinger equation, their propagation properties are investigated in detail for the first time. The results show that a focusing of the chirped Airy Gaussian pulses is found, which leads to the same focusing of the propagation trajectory and the maximum scattering force. The distribution factor α can modulate the convergence of the side wave rings at Z = 0 . During the propagation process, with the increase of the β , when the β is negative, the side wave rings rise along the main wave axis but their moving is opposite when the β is positive. When the beam order n = 1 , the intensity, the angular momentum and the gradient force gradually tend to the center but they move radially when n = 2 . The direction of the peripheral gradient force points to the center but the direction is opposite in the center. The beam orders only affect the magnitude of the normalized maximum scattering force but have little effects on their distribution.

Tunable transmission characteristics of electromagnetic waves in periodically layered metamaterials (PLMMs), constructed by alternating dielectric layer and gyromagnetic layer such as yttrium-iron-garnet (YIG), are investigated through an external magnetic field. Based on transfer matrix method (TMM) and effective medium theory (EMT), we compare the dispersion curves of TE waves propagating in the PLMMs, and obtain the effective permeability and permittivity tensors of the homogenized gyromagnetic PLMMs by expanding the exact dispersion relation in long-wavelength limit. Then, we calculate some propagating parameters when TE waves incident on the PLMMs by EMT in detail. Numerical results show that the refraction state of TE waves in the PLMMs can be dynamically changed between positive refraction state and cutoff state by controlling the external magnetic field. These exotic properties of gyromagnetic PLMMs may have wide potential applications in many fields such as sub-wavelength all-optical switches and wave cutoff devices.

Based on the analytical expression obtained by solving the ( 3 + 1 ) D Schrodinger-like equation, the spatiotemporal propagation properties of the chirped Airy hollow Gaussian (CAiHG) wave packets in harmonic potential are described and discussed in detail. Results show that the folds on the isosurfaces of the CAiHG wave packets deepen with the temporal chirp parameter β increasing. The wave rings of the CAiHG wave packets can be eliminated as the distribution factor increases, which lead to the stretch of the intensity distribution along the T axis. Moreover, in HGB-like condition, with the increase of the potential width parameter, the Poynting vector and the angular momentum increase and distribute more evenly while their distributions gradually become hollow as the propagation distance increases. Besides, the quantity of the main peaks of the gradient force is exactly proportional to the potential width parameter. As the beam orders increase, the secondary peaks gradually increase while the main peaks are opposite. When β ≤ 0 , the gradient force rapidly decreases while the gradient force decreases first and then increases when β > 0 .

Here we investigate the propagation properties of spatiotemporal autofocused chirped Pearcey Pearcey Gaussian (PePeG) wavepackets by solving (3 + 1) D Schr o ¨ dinger equation in a quadratic index medium. When the spatial distribution factor p and the temporal distribution factor f are the same, PePeG wavepackets can simultaneously autofocus in spatial and temporal domain and the peak intensity at the focus is more 28 times than that at the initial plane. With the increase of distribution factor p, the scope of the radius of trapped particles decreases.

We derive analytical solutions that describe the one-dimensional displaced and chirped symmetric Pearcey Gaussian beam in a uniformly moving parabolic potential. The multiple effective manipulations of the beam, which are originated from the diverse configurations of the dynamic parabolic potential, are demonstrated. On the whole, the accelerating trajectory can transform into a linear superposition form of the oblique straight line and the simple harmonic motion. Meanwhile, we discuss the further modulation of the accelerating trajectory characteristics such as slope, amplitude and phase shift. Additionally, the extension into a two-dimensional scenario is also proposed. Our results theoretically improve the practical value of the Pearcey beam, and lead to potential applications in trajectory manipulation and particle manipulation.

In this Letter, a new, to the best of our knowledge, type of autofocusing and symmetric beam arisen from two quartic spectral phases is introduced in theory and experiment. The symmetric Pearcey Gaussian beam (SPGB), formed with a Gaussian term and two multiplying Pearcey integrals, processes a focusing intensity approximately 1.32 times stronger than the intensity of the symmetric Airy beam. Its four off-axis main lobes split into four bending trajectories symmetrically after focusing. The rectangular intensity distribution and the focal length of the SPGB can be adjusted by two kinds of distribution factors. Additionally, the vortex-guiding property of the beam is demonstrated by embedding an off-axis vortex into the SPGB, which can be applied in particle guiding.

Modulated by the spatial phase, Airy-like beams that possess the faster and better self-healing as well as the greater acceleration along the desired arbitrary trajectory are introduced. Airy-like beams have the strong spontaneous-focusing ability and the peak value of the focal plane is 5.4 times that of the initial plane when traveling along the quadratic function trajectory. Besides, the larger quadratic coefficient and the smaller constant term of the quadratic function can enhance the self-healing and the spontaneous-focusing of the beams. When the beams transmit along the snakelike trajectory, the original main lobe separates a new main lobe, and the energy will concentrate on the new main lobe. Airy-like beams, along a hyperbolic-secant trajectory, can remain non-diffraction over long distances. However, when traveling along a hyperbolic trajectory, the evolution process is very similar to that of Airy-Gaussian vortex beams. These excellent properties can be applied to the special beams’ modulation and optimization. Furthermore, it may provide a way for constructing beams along the special trajectory with the desired spontaneous-focusing and self-healing.

Based on the angular spectrum of high order off-axis Airy vortex beams (AiVBs), Goos-Hänchen (GH) shifts and Imbert-Fedorov (IF) shifts near the Brewster angle are numerically calculated. It is found that both GH and IF shifts increase with the increase of the vortex’s topological charge of AiVBs. The influences of the vortex’s positions on GH and IF shifts are studied for the case of the topological charge m = 1. The studies of the off-axis vortex show that the influences of the vortex’s position on shifts are inversely proportional to the distance between the vortex’s position and the origin point.

In this Letter, we introduce a new, to the best of our knowledge, structure of multioptical bottles formed by second-order chirped symmetric Airy vortex beams (CSAVBs). The numbers and the locations of the optical bottles embedded in the CSAVBs depend on the numbers and the locations of the vortices. Besides, the lengths and the sizes of the optical bottles could be adjusted by changing the chirp parameter and the topological charges of the vortices, respectively. We believe that our results can diversify the optical tweezers system for multiparticle manipulation.

In this study, a new, to the best of our knowledge, form of odd-Pearcey Gauss beams with peculiar characteristics is presented. Compared with the Pearcey beam, the odd-Pearcey Gauss beam is symmetrical about the origin. At the initial stages, the odd-Pearcey Gauss beam propagates with a main central lobe and some residual spots that autofocus to the center, and then splits into two off-axis parabolic lobes after the autofocus finishes. Furthermore, we also introduce the soft well function to investigate the propagation profiles of the odd-Pearcey Gauss beams passing through it with different calibers and discuss the influence of the Gaussian waist width towards the focal distance and the propagation form of the odd-Pearcey Gauss beam. We also enumerate some potential and possible applications based on its peculiar characteristics.