Parametric characterization of Mathieu-Gauss beams

Structured light beams with distinct spatial inhomogeneity of amplitude, phase, and polarization have garnered tremendous attention in recent years. A better understanding of the vectorial structure of such beams is helpful to reveal their important and interesting features for further applications. In this paper, explicit analytical expressions for the electric field components of typical spatial-structured light beams, including fundamental Gaussian beams, Hermite-Gaussian beams, Laguerre-Gaussian beams, Bessel/Bessel-Gaussian beams, and Airy beams, beyond the paraxial approximation are derived on the basis of the vectorial Rayleigh-Sommerfeld diffraction integrals. Compared with the existing expressions in the literature, the expressions given in this paper are very concise. Using the derived analytical expressions, distributions of the electric field components of these typical structured light beams are displayed and analyzed.

The propagation properties and kurtosis parametric characteristics of Hermite-cosh-Gaussian beams passing through fractional Fourier transformation systems

Electromagnetic wave beam propagation through a chiral slab

A stable tractor beam for long range pulling of particles by acoustic Bessel beams requires a simultaneous trapping in the lateral direction. Trapping force acting on a sphere centered on the axis of Bessel beams is examined to guide the selection of material and beam parameters. It is found that a heavy and rigid sphere in the Rayleigh regime can be trapped at central pressure maximum of zero-order Bessel beam, which is contrary to the repelling behavior at the pressure anti-nodes of one- or two-dimensional standing waves. The trapping results from the three-dimensional features of the velocity fields and the momentum projection. The projection leads the trapping of an elastic sphere or a droplet at the axis of ordinary and vortex Bessel beams in the Rayleigh regime to be reversed when reducing the conical angle of the beam at the situation when there is a strong contrast of mass density between the particle and the surrounding fluid. Ranges of conical angle and material parameters for simultaneous trapping and pulling a spherical object are identified.A stable tractor beam for long range pulling of particles by acoustic Bessel beams requires a simultaneous trapping in the lateral direction. Trapping force acting on a sphere centered on the axis of Bessel beams is examined to guide the selection of material and beam parameters. It is found that a heavy and rigid sphere in the Rayleigh regime can be trapped at central pressure maximum of zero-order Bessel beam, which is contrary to the repelling behavior at the pressure anti-nodes of one- or two-dimensional standing waves. The trapping results from the three-dimensional features of the velocity fields and the momentum projection. The projection leads the trapping of an elastic sphere or a droplet at the axis of ordinary and vortex Bessel beams in the Rayleigh regime to be reversed when reducing the conical angle of the beam at the situation when there is a strong contrast of mass density between the particle and the surrounding fluid. Ranges of conical angle and material parameters for simultaneous trapp...

We first demonstrate the Terahertz quasi-zero-order Mathieu-Gauss beams with a 0.1-THz continuous wave. To generate these beams, two diffractive elements, a cylindrical lens and an axicon bearing specific phases are fabricated via 3D printing technology. The related numerical simulations are conducted to study intensity distributions and properties on non-diffraction and self-healing of THz quasi-zero-order Mathieu-Gauss beams in free space. Experimental results are in good agreement with numerical ones. Based on the characteristic of terahertz Mathieu-Gauss beams, they can be applied to terahertz linear array imaging system and terahertz communication.

This letter presents a field expansion of the solution to three-dimensional electromagnetic scattering problems of a uniaxial anisotropic spheroidal particle illuminated by an off-axis Hermite-Gaussian (HG) beam. Using the complex-source-point method, and the relationship between spherical and spheroidal vector wave functions (VWFs), a method is put forward to expand the incident Hermite-Gaussian beam in terms of the spheroidal VWFs. By utilizing the complete relationship between spherical and spheroidal VWFs, the expansion formats of the EM fields in a uniaxial anisotropic spheroid in terms of the spheroidal vector wave functions are derived. The unknown expansion coefficients of the internal fields and scattered field are determined by applying the boundary conditions of the continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. These theory works are hopeful to provide an effective test for further research on the numerical analysis of the interaction between a uniaxial anisotropic spheroid and laser beam.

Propagation properties of partially coherent modified Bessel–Gauss beams

Using a multi-variable series method, we successfully investigated the global property of perturbation description for fundamental Gaussian beam. We explicitly proved that as long as the perturbation parameter s≠0, although it includes the Gaussian factor \(\exp(-\frac{\rho^{2}}{4\zeta^{2}+1})\) (ρ and ζ are normalized cylindrical polar coordinates defined in the text), the complete perturbation solution for fundamental Gaussian beam always diverges.

This study proposes a method to achieve excitation of surface plasmon polaritons (SPPs) with tunable directions and intensity ratios on a designed two thin slit structure by the phase control of dual fundamental Gaussian beams. Simply modulating the phase difference between two incident fundamental Gaussian beams (i.e. TEM0,0 mode laser beam) controls the propagating direction of the resulting SPP wave between two opposite linear directions and also the value of the intensity ratio between propagating SPP waves in two opposite directions. The proposed method achieves a wide dynamic SPP intensity ratio adjusting range from -20 dB to 20 dB. This easy method of changing the direction of SPPs makes the dynamic control of the direction of SPP waves practicable, which shows great potential in plasmonic applications.

A new kind of laser beam, called a decentered elliptical Gaussian beam (DEGB), is defined by a tensor method. The propagation formula for a DEGB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formula for a fundamental elliptical Gaussian beam and a decentered Gaussian beam under certain conditions. As an example application of the derived formula, the propagation characteristics of a DEGB in free space are calculated and discussed. As another example we study the properties of a generalized laser beam array constructed by use of a DEGB as the fundamental mode.

Deep-penetration laser beam welding is highly dynamic and affected by many parameters. Several investigations using differently sized laser spots, spot-in-spot laser systems, and multi-focus optics show that the intensity distribution is one of the most influential parameters; however, the targeted lateral and axial intensity design remains a major challenge. Therefore, a laser processing optic has been developed that coaxially combines two separate laser sources/beams with different beam characteristics and a measuring beam for optical coherence tomography (OCT). In comparison to current commercial spot-in-spot laser systems, this setup not only makes it possible to independently vary the powers of the two laser beams but also their focal planes, thus facilitating the investigation into the influence of specific energy densities along the beam axis. First investigations show that the weld penetration depth increases with increasing intensities in deeper focal positions until the reduced intensity at the sample surface, due to the deep focal position, is no longer sufficient to form a stable keyhole, causing the penetration depth to drop sharply.

The power transfer efficiency of a partially obstructed wireless link operating in the Fresnel region is studied in this work. The wireless link consists of two equal apertures, axially aligned, radiating weakly-diffractive beams (truncated Bessel beams). A metallic obstacle is considered along the propagation path of the radiated beam to analyze its impact on the power transfer efficiency with respect to a clear line of sight link. The power transfer efficiency in the obstructed case is derived by resorting to a scattered field formulation. In the proposed approach, the distance between the apertures is considered larger than their radius, which is also bigger than the operating wavelength. A paraxial approximation is then applied to the formulation. Numerical results validate the proposed approach. It appears that the transverse propagation constant of the Bessel Beam and resulting non-diffractive range strongly affects the distance of operation of the wireless link in both the clear and obstructed cases. In addition, we observe how the self-healing property of Bessel beams preserves the efficiency of the partially obstructed link by establishing a resilient link under defined conditions for the propagating beam and size of the obstruction.

Transformation of ordinary laser beams of Gaussian type into the ones of Bessel type gives a number of advantages. In particular, it may improve a multi-mode beam energy distribution in the far zone and keep it stable over a long range of propagation distances. A usual method of the Bessel beam formation is based on the use of one or a pair of axicons, at that the latter is used for creating annular beams with small conic angles optimized for long range propagation. The disadvantage of axicons is their fixed geometry not allowing the beam parameter adjustment. An additional Bessel beam improvement allowing to reach a finer energy distribution comes from injection into it a controllable amount of spherical aberration. This requires development of a specialized optical system, which adds adjustable spherical aberration to the laser beam. Efficient design of such an optical system has been created and experimentally tested on the transformation of a multi-mode laser beam into Bessel beam.

Transmission of electromagnetic beam through a uniaxial anisotropic slab

The excitation of two-dimensional periodic structures of fields of the first and second radiation harmonics due to the modulation instability of fundamental Gaussian beams is studied in a medium with a quadratic nonlinearity. The distances are found at which soliton matrix structures with a specified period are formed and destroyed. Optical gratings formed due to nonlinear aberration of broad Gaussian beams are considered.