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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 (...

An analytical expression of the rotating elliptical chirped Gaussian (RECG) beam in uniaxial crystals orthogonal to the optical axis has been derived. The uniaxial crystals considered here are the ...

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.

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.

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.

In this paper, we use the rotating elliptical Gaussian beams (REGBs) to impinge the surfaces coated with cross-anisotropic metasurfaces (CMs) to investigate the Goos–Hanchen (GH) and Imbert–Fedorov (IF) shifts. The effect of the CM coating on the reflection coefficient in this system is considered. In particular, we will show that the angle of incidence and the relative permittivity of the weakly absorbing medium have an influence on the GH and the IF shifts. A comparison with the case of surfaces without the CM is also discussed.

Mixed transition-metal oxides have witnessed increasing attention in catalysts and electrocatalysts. Herein, reduced graphene oxide-wrapped ZnMn2O4 microspheres (ZnMn2O4@rGO) were facilely synthesized through the solvothermal technique. The microstructure and morphology of ZnMn2O4@rGO microspheres were analyzed under Raman, X-ray photoelectron, X-ray diffraction, and energy-dispersive spectroscopies and scanning electron microscopy. The synthesized ZnMn2O4@rGO was employed as an excellent electrocatalyst for the reduction of hydrogen peroxide (H2O2). The ZnMn2O4@rGO-modified glassy carbon electrode (ZnMn2O4@rGO/GCE) exhibited a linear detection to H2O2 in a wide concentration range of 0.03-6000 μM with a detection limit of 0.012 μM. The biosensor was evaluated to determine H2O2 secreted by human breast cancer cells (MCF-7), indicating its promising applications in physiology and diagnosis.

With a facile solvothermal technique, ZnMn2O4 microspheres were synthesized in this work, which were used as enzyme mimics for the electrocatalytic reduction of H2O2. The morphology, crystal phase and structure of the ZnMn2O4 microspheres underwent characterization under X-ray diffraction spectroscopy, Raman spectroscopy, energy-dispersive spectroscopy, and scanning electron microscopy. The synthesized ZnMn2O4 microspheres showed an average diameter of 2 μm with great crystallinity, and exhibited excellent catalytical activity towards H2O2 electroreduction in alkaline media. The glassy carbon electrode modified by ZnMn2O4 microspheres showed a linear amperometric response for H2O2 in a wide concentration range of 0.02 ˜ 15 mM with detection limit of 0.13 μM under the optimized conditions. Besides, the sensor proposed here was successfully used to determine H2O2 in milk, suggesting that ZnMn2O4 microspheres can be used for non-enzymatic electrochemical sensor applications.

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.

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.

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.

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.

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 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.

In this Letter, we introduce a new kind of radially polarized beam called the radially polarized symmetric Airy beam (RPSAB). Compared to the linearly polarized symmetric Airy beam (SAB), the hollow focus spot of RPSAB enables it to trap a microparticle whose refractive index is lower than that of the surrounding medium, and the focus intensity of RPSAB is nearly three times higher than that of SAB under the same conditions. Also, we present the on-axis and off-axis radially polarized symmetric Airy vortex beam (RPSAVB). In the on-axis case, we find the maximum intensity of RPSAVB is about two times higher than that of RPSAB. For the off-axis case, we prove that slight misalignment of the vortex and RPSAB enables guiding the vortex into one of the self-accelerating channels, the same as the symmetric Airy vortex beam. Our results may expand the applications of RPSAB in laser cutting, metal processing, nanofocusing, and three-dimensional trapping of metallic Rayleigh particles.

Three-dimensional chirped Airy Complex-variable-function Gaussian vortex (CACGV) wave packets in a strongly nonlocal nonlinear medium (SNNM) are studied. By varying the distribution parameter, CACGV wave packets can rotate stably in a SNNM in different forms, including dipoles, elliptic vortices, and doughnuts. Numerical simulation results for the CACGV wave packets agree well with theoretical analysis results under zero perturbation. The Poynting vector related to the physics of the rotation phenomenon and the angular momentum as a torque corresponding to the force are also presented. Finally, the radiation forces of CACGV wave packets acting on a nanoparticle in a SNNM are discussed.

We introduce the circle Pearcey Gaussian vortex (CPGV) beams in a harmonic potential for the first time and investigate their abruptly autofocusing properties by theoretical analysis and numerical simulations in this paper. By varying the spatial distribution factors, one can effectively control the propagating dynamics of the beams, including the position of the focus, the radius of the focal light spot and the intensity contrast. Meanwhile, the magnitude of topological charges and the position of the vortex can alter the focal pattern and the intensity contrast. Furthermore, the position of the focus can be flexibly controlled in a tiny range by adjusting the scaled parameter of the incident beam properly.

Based on the extended Huygens–Fresnel integral, the analytical formulas for the average intensity of the rotating elliptical chirped Gaussian vortex beam (RECGVB) in the oceanic turbulence are derived in this paper. Meanwhile, the evolutions of the intensity, the effective beam widths in the x - and y -directions and the dynamic center of gravity for the RECGVB propagating through the oceanic turbulence are explored by numerical examples. Results show that the intensity pattern of the RECGVB which presents two light spots at the beginning deforms and spins within a certain propagation range. Moreover, the position of the dynamic center of gravity can be modulated by the first-order chirped parameters while the profile of the intensity pattern can be affected by the second-order chirped parameters. In addition, the effects of the oceanic turbulence parameters and the initial beam width on the normalized intensity and the effective beam width of the RECGVB are discussed in detail.

The self-accelerating Airy Ince–Gaussian (AiIG) and Airy helical Ince–Gaussian (AihIG) wave packets in strongly nonlocal nonlinear media (SNNM) are obtained by solving the strongly nonlocal nonlinear Schrödinger equation. For the first time, the propagation properties of three dimensional localized AiIG and AihIG breathers and solitons in the SNNM are demonstrated, these spatiotemporal wave packets maintain the self-accelerating and approximately non-dispersion properties in temporal dimension, periodically oscillating (breather state) or steady (soliton state) in spatial dimension. In particular, their numerical experiments of spatial intensity distribution, numerical simulations of spatiotemporal distribution, as well as the transverse energy flow and the angular momentum in SNNM are presented. Typical examples of the obtained solutions are based on the ratio between the input power and the critical power, the ellipticity and the strong nonlocality parameter. The comparisons of analytical solutions with numerical simulations and numerical experiments of the AiIG and AihIG optical solitons show that the numerical results agree well with the analytical solutions in the case of strong nonlocality.

As one of the spatial dimensions, orbital angular momentum (OAM) expands the channel capacity of underwater wireless optical communication (UWOC) system. However, the performance of the OAM-UWOC system is degraded due to the distortion of the OAM by oceanic turbulence. In this paper, we present a 7-layer convolutional neural network (CNN) and validate its ability to identify OAM patterns carried by Bessel Gaussian (BG) beams in oceanic turbulence channels. The trained CNN performs the task of recognizing OAM patterns with an accuracy of over 99% under weak-to-moderate oceanic turbulence at 100 m. Furthermore, in order to demonstrate the performance and robustness of the designed CNN, the effects of training sample number, epoch, turbulence intensity, balance parameter, transmission distance, type of training dataset, and coding method on the recognition ability of CNN are fully investigated. We hope that the method devised in our work will contribute to UWOC and facilitate its further development.

We address the propagation of vortex beams with the circular Airy–Gaussian shape in a ( 2 + 1 )-dimensional optical waveguide modeled by the fractional nonlinear Schrödinger equation. Systematic analysis of autofocusing of the beams reveals a strongly non-monotonous dependence of peak intensity in the focal plane on the corresponding Lévy index α , with a strong maximum at α ∼ 1.4 . Effects of the nonlinearity strength, the ratio of widths of the Airy and Gaussian factors in the input, as well as the beams’ vorticity on the autofocusing dynamics are explored. In particular, multiple autofocusing events occur if the nonlinearity is strong enough. Under the action of azimuthal modulational instability, an axisymmetric beam may split into a set of separating bright spots. In the case of strong fractality (for α close to one), the nonlinear beams self-trap, after the first instance of autofocusing, into a breathing vortical quasi-soliton. Radiation forces induced by the beams’ field are considered too, and a capture position for a probe nanoparticle is thus identified.

In this article, we present a new kind of autofocusing surface plasmonic wave: the Pearcey plasmon. The result shows that the Pearcey plasmon evolves at the silver-air interface in the form of two-dimensional Pearcey plasmon function. And the Pearcey plasmon can be decomposed into two Airy-like plasmons bending in the opposite direction after autofocusing, which leads to dual self-bending behavior of a Pearcey plasmon. We demonstrate the interference patterns of two Airy-like plasmons and find that the self-focusing focus position during propagation is controllable. Also, we find that when a single variable is controlled, both the long wavelength and the large truncation coefficient will reduce the maximum intensity as well as the focal length of the Pearcey plasmon. Furthermore, taking the intensity reduced to 50% of the maximum intensity as a reference, we find that the divergence distance of a Pearcey plasmon is approximately 65 times longer than that of a Gaussian plasmon, which means that under the same intensity, a Pearcey plasmon propagates much farther than a Gaussian plasmon.

We analyze the propagation dynamics of radially polarized symmetric Airy beams (R-SABs) in a (2+1)-dimensional optical system with fractional diffraction, modeled by the fractional Schrodinger equation (FSE) characterized by the Levy index, α. The autofocusing effect featured by such beams becomes stronger, while the focal length becomes shorter, with the increase of α. The effect of the intrinsic vorticity on the autofocusing dynamics of the beams is considered too. Then, the ability of R-SABs to capture nano-particles by means of radiation forces is explored, and multiple capture positions emerging in the course of the propagation are identified. Finally, we find that the propagation of the vortical R-SABs with an off-axis shift leads to rupture of the ring-shaped pattern of the power-density distribution.

We analytically and numerically investigate the dynamic propagation of the quadratically chirped Airy beams in right-handed material (RHM) and left-handed material (LHM) slabs. Based on the analytical expressions and numerical calculations, we find that through choosing the appropriate value of the quadratic chirp, one can modify the diffraction, the intensity distribution, the propagation path, and acceleration and deceleration of the quadratically chirped Airy beams to meet the actual usage accordingly. In addition, we also demonstrate the effect of the quadratic chirp on the Poynting vector and the angular momentum of the quadratically chirped Airy beams, respectively. Furthermore, we explore the gradient and scattering forces on a Rayleigh dielectric particles induced by the quadratically chirped Airy beams.

The evolution of the chirped ring Pearcey Gaussian vortex (CRPGV) beams in free space is numerically investigated. The optical bottle beam and two-consecutive optical bottle beam can be directly generated from a ring Pearcey Gaussian beam with central vortices and the second-order chirp in free space. In particular, the focusing intensity will decrease when the vortices’ locations are far away from the center of the beam or the topological charges are smaller. Our results show that the beam shapes, the normalized focusing intensity, and the focal length of the CRPGV beams can be controlled by choosing different beam parameters.

By solving the Schrodinger equation in spatial and temporal coordinates, the exact solution of the chirped Airy-Gaussian (CAiG) wave packets in a gradient-index medium is obtained. Based on that, we conduct a theoretical analysis about the properties of CAiG wave packets and discover that the chirp factor, the distribution factor, the initial velocity, as well as the propagation distance have an effect on the wave packets in both the propagation process and the spatiotemporal profiles. Among these, the Gaussian distribution factor, which is first added to the initial pulses, also alters the peculiarities of the Airy-Gaussian beams in the temporal domain and spatial domain. In addition, the investigation about the radiation force illuminates certain evolution properties of the CAiG wave packets well.

We introduce the propagation properties of the circular Pearcey Gaussian (CPG) waves in Kerr medium for the first time. The breathers-like structure and breathers-like groups structure (filamentions) of CPG waves will form due to the interaction between the linear waves and the nonlinear medium. The focusing characteristics in Kerr medium can be adjusted by the deviation factor and the initial input power of the CPG waves. By choosing appropriate input power, the imaginary part of the CPG waves can split into some wavelets during the propagation. It is worth noting that the distinctive stepwise focusing of the imaginary part of the CPG waves which can be applied to wave modulation. Furthermore, the numerical experiment results show good agreement with the numerical simulation results.

In this Letter, we introduce a new class of abruptly autofocued and rotated circular chirp Pearcey Gaussian vortex beams (AARCCPGVBs) which tend to abruptly autofocused circular chirp Pearcey vortex beams or chirp Gaussian vortex beams by adjusting the spatial distribution factors. Different from other rotated beams [Opt. Lett.31, 694 (2006) OPLEDP0146-959210.1364/OL.31.000694 and Opt. Lett.31, 2199 (2006)OPLEDP0146-959210.1364/OL.31.002199], the AARCCPGVBs are autofocused abruptly, maintain a low rotating speed before the focal point, and rotate abruptly and quickly in the focal point. Further, the position of the focal point in the propagating direction can also be controlled by adjusting the chirp factor.

The Goos-Hanchen (GH) shift of a Gaussian beam reflected from surfaces coated with a cross-anisotropic metasurface (CM) is theoretically investigated. It is revealed that, the CM coating has influence on the spatial GH shift as well as the angular one, only at the total internal reflection condition, where the incident angle θ is above critical angle θ c . Moreover, near θ c , a positive or negative larger peak spatial GH shift occurs while a pair of positive and negative peaks angular GH shifts appear, compared to the case of no coating, which are induced by the CM coating. Therefore, our results may provide a feasible method to obtain a larger GH shift, and open new possibilities for applications of the CMs.

In our study, an analytical expression of the second order chirped Pearcey Gaussian vortex beam (CPGVB) in a medium with a parabolic refractive index is derived. We demonstrate its propagation behaviors as well as the effects of the parameters on the propagation properties. Expectedly, the CPGVB performs periodically automatic Fourier transform in the specific positions, but unexpectedly the off-axis autofocusing position can be generated and controlled without changing the laser incident angle. Furthermore, we investigate the radiation forces of the CPGVB, and thus notice that trapping positions form in the beam-propagation direction.

We study the abruptly autofocusing and autodefocusing properties of the circular Airy Gaussian vortex (CAiGV) beams in strongly nonlocal nonlinear medium for the first time through numerical simulations. The magnitude of topological charges and the position of the vortex could change not only the light spot pattern but also the intensity contrast. Meanwhile, we can change the position of the autofocusing and autodefocusing planes by changing the parameter of the incident beam. Furthermore, we can control the peak intensity contrast through choosing properly the truncation factor. As for the radiation force, we study the gradient and the scattering forces of CAiGV beams on Rayleigh dielectric sphere. Our analyses demonstrate that the radiation force can be enhanced by choosing proper parameters of CAiGV beams.

The construction of metal-oxide heterojunction architecture has greatly widened applications in the fields of optoelectronics, energy conversions and electrochemical sensors. In this study, olive-like hetero-structured MnO-Mn3O4 microparticles wrapped by reduced graphene oxide (MnO-Mn3O4@rGO) were synthesized through a facile solvothermal-calcination treatment. The morphology and structure of MnO-Mn3O4@rGO were characterized by scanning electron microscopy, transmission electron microscopy, X-ray photoelectron spectroscopy, Raman spectroscopy, and X-ray diffraction. The as-synthesized MnO-Mn3O4@rGO exhibited prominent catalyzing effect on the electroreduction of H2O2, due to the combination of good electrical conductivity of rGO and the synergistic effect of MnO and Mn3O4. The MnO-Mn3O4@rGO modified glassy carbon electrode provided a wide linear response from 0.004 to 17 mM, a low detection limit of 0.1 μM, and high sensitivity of 274.15 μA mM−1 cm−2. The proposed sensor displayed noticeable selectivity and long-term stability. In addition, the biosensor has been successfully applied for detecting H2O2 in tomato sauce with good recovery, revealing its promising potential applications for practical electrochemical sensors.

In this paper, the propagation of a Pearcey Gaussian vortex (PeGV) beam in a harmonic potential is studied analytically and numerically from different perspectives, such as the intensity, the angular momentum, and radiation forces. The results show that the PeGV beam is in a periodical deformation with respect to the period and there exist two times auto-focusing and inverse processes within a period. With the decrease of the period, the adjacent auto-focusing planes are closer and the overall energy of the PeGV beam is enhanced. It is peculiar that the maximum intensity deflects the auto-focusing plane because of the modulations of the Gaussian and the vortex factors. We can adjust the intensity distribution, especially the auto-focusing and the inversion positions, the overall energy and the radiation forces distributions of the PeGV beam by choosing an appropriate period to meet the actual usage accordingly.

We introduce axisymmetric Airy-Gaussian vortex beams in a model of an optical system based on the (2+1)-dimensional fractional Schrodinger equation (FSE), characterized by its Levy index (LI), 1 α ⩽ 2 . By means of numerical methods, we explore propagation dynamics of the beams with vorticities from 0 to 4. The propagation leads to abrupt autofocusing, followed by its reversal (rebound from the center). It is shown that LI, the relative width of the Airy and Gaussian factors, and the vorticity determine properties of the autofocusing dynamics, including the focusing distance, radius of the focal light spot, and peak intensity at the focus. A maximum of the peak intensity is attained at intermediate values of LI, close to α = 1.4 . Dynamics of the abrupt autofocusing of Airy-Gaussian beams carrying vortex pairs (split double vortices) is considered too.

We introduce a sufficient condition under which the Lorentz beam convolution with other beams constitutes valid cross-spectral densities. Two examples are given to show how the Lorentz related beam can be used for generation of a far field being a modulated version of another one. The far-field intensity patterns in the Cartesian symmetries by the convolution operation of the Lorentz beams with multi-sinc beams, and the convolution operation of the Lorentz beams with multi-sinc Gaussian beams, are shown respectively. We find that different beam order can result distinct far field changes.

We study the interaction of the Airy–Gaussian (AiG) beams by using the numerical simulations with the split-step Fourier method. The results show that the single breathers and breather pairs can be formed in the condition with interaction. The breathers can be formed with the enough intensity of interactive beams. By adjusting the parameters of amplitude, interval, phase and χ 0 , we find that the interaction of the two beams is the strongest with in-phase and out-of-phase cases, especially in the shorter distance. Moreover, both the interaction intensity and the location, the interaction happens, can be changed by adjusting the distribution factor χ 0 of the beams. It is notable that the various propagation directions of the beams can be obtained by changing the phase, at the same situation, when the interval of the two beams becomes narrower, the phase plays an important role of controlling the direction of the accelerated spot.

In this work, we report the synthesis of MnO2/RGO (reduced graphene oxide)/P25 nanocomposites for a non-enzymatic hydrogen peroxide sensor. MnO2/RGO/P25 nanocomposites were synthesized with a photo-reduction approach and characterized by field emission scanning electron microscopy, X-ray photoelectron spectroscopy, Fourier transform infrared spectroscopy and Raman spectroscopy. A non-enzymatic hydrogen peroxide sensor was fabricated by dropping MnO2/RGO/P25 nanocomposites on the surface of a glassy carbon electrode. Electrochemical measurements of the MnO2/RGO/P25 modified electrode were carried out on an electrochemical workstation. The as-prepared sensor exhibited high electrocatalytic activity, selectivity and stability towards the oxidation of H2O2. Under optimum conditions, the calibration curve for H2O2 determination was linear in the range from 1.0 × 10−6 to 4.0 × 10−3 M (R2 = 0.999) with a detection limit of 3 × 10−7 M (S/N = 3).

By investigating the cross-spectral density of partially coherent multi-rotating elliptical Gaussian beams (REGBs) that propagate through a focusing optical system, we obtain the radiation force on a Rayleigh particle. The radiation force distribution is studied under different beam indexes, coherence widths, and elliptical ratios of the partially coherent multi REGBs. The transverse and the longitudinal trapping ranges can increase at the focal plane by increasing the beam index or decreasing the coherence width. The range of the trapped particle radii increases as the elliptical ratio increases. Furthermore, we analyze the trapping stability.

We study the autofocusing properties of the chirped circular Airy Gaussian vortex beams (CCAiGVBs) numerically. The evolutions of the intensity and the gradient force of the CCAiGVBs are investigated in this paper. Results show that the CCAiGVBs have two trapped areas where the gradient force vectors joint at the transverse planes. The chirps can greatly modulate the intensity distribution of the hollow portion aroused from the vortex at the focal plane. The focal position, the focal depth, the focal intensity and the focal light spot of the CCAiGVBs can be greatly affected by the chirped factors c 1 and c 2 , the distribution factor b and the topological charge m . We can adjust the intensity distribution and the gradient force distribution especially on the focal position of the CCAiGVBs through choosing an appropriate value of the chirped factors, the distribution factor and the topological charge to meet the actual usage accordingly.

We propose a new class of abruptly autofocusing beams, the chirped annular Bessel Gaussian beams (CABGBs), which are based on the radial Bessel profile. By using the Rayleigh–Sommerfeld diffraction formula, the nonparaxial propagation of the CABGBs is investigated. We find that the initial chirp with negative value tends to intensify the abruptly autofocusing property by shortening the focal length, shrinking the focal spot size, and increasing the peak intensity contrast. The optical trapping effect of the CABGBs acting on a Rayleigh particle is analyzed, and we find that the particle can be stably trapped in three dimensions if the parameters of the CABGBs are appropriate. If the absolute value of the negative chirp increases, the trapping position is shifted toward the input plane, and both the longitudinal and transverse trapping forces rise. A higher magnitude of the radiation forces can be reached if the incident power increases.

We introduce a new class of the chirped Airy–Gaussian vortex electron plasma (CAiGVEP) wave which constitutes the exact and continuous transition modes between the chirped Airy vortex and the chirped Gaussian vortex electron plasma wave. The intensity, the phase, and the angular momentum density flow of the CAiGVEP wave are discussed under different distribution factors and different chirp modes.

We have studied the propagation of the Pearcey Gaussian (PeG) beams in a medium with a parabolic refractive index. Compared to the Airy Gaussian beams and common Gaussian beams, there occur two kinds of focusing when the PeG beams propagate in a medium with a parabolic refractive index. One is the auto-focusing caused by the PeG beams and the other is the focusing effect for which the parabolic refractive index is responsible. In addition, we also have made a comparison of the focus-ability between these two kinds of focusing by analyzing the mean-squared beam width and the power in the bucket.

We show the tight-focusing properties of a linearly polarized circular Airy Gaussian vortex beam (CAiGVB) with a high-numerical-aperture objective lens; the light intensity distributions exhibit diversity with different positions of the vortex pairs (on-axis or off-axis vortex pairs). By choosing different optical distribution factors, the CAiGVB turns into a circular Airy vortex beam or Gaussian vortex beam, and the depth of focus can also be controlled. It is known that the vortex beam possesses both orbital and spin angular momentum. The spin density vector changes its direction in three-dimensional space during beam propagation, as long as it is not purely transverse or longitudinal, which would cause 3D polarization ellipse topologies. In contrast, the polarization topologies degenerate into 2D when the spin density vector is purely transverse or longitudinal. Furthermore, the direction of the spin density vector is closely related to the Gouy phase difference between longitudinal and transverse electric field components of the vectorial beam.

We simulate the propagation of the abruptly autofocusing chirped ring Pearcey Gaussian vortex (CRPGV) beams with caustics by modulating the phase of a circularly symmetric optical wavefront appropriately. The propagation characteristics of the CRPGV beams are explored in the Kerr medium. Different caustic surfaces of revolution which can be used as optical bottles are formed during the propagation. We also introduce the influence of the initial input power, the chirp factor and the stochastic type perturbations for the CRPGV beams during the propagation. Furthermore, the dynamics of the optical bottle and the breathers-like structures are explored in detail.