Investigation of Bessel beam propagation in scattering media with scalar diffraction method

Bessel beam propagation in scattering media is simulated using the angular spectrum method combined with slice-by-slice propagation model. Generating Bessel beams with a spatial light modulator, which provides a means to adjust flexibly the parameters of the Bessel beam, allows us to validate the simulation results experimentally. The study reveals that the self-reconstructing length changes oppositely with the axicon angle （i.e., the larger the axieon angle, the shorter the self-reconstructing length）. The radius of the incident beam has little influence on the self-reconstruction of the Bessel beam central lobe.     

Generation of partially coherent vortex bottle beams

Intensity distribution of the partially coherent Bessel vortex beams focused by an aperture lens is investigated. It is found that the intensity distribution in the neighborhood of the geometrical focus is not only dependent on the topological charge and the radial frequency of the incident partially coherent Bessel vortex beam, but also on its coherence length. Based on this, the desired partially coherent vortex bottle beams can be obtained by choosing appropriate values of parameters. Because such bottle beams possess characteristics of low coherence and vortex, it may be used in microscopic particles guiding, trapping, and inducing rotation.     

Generation of partially coherent vortex bottle beams

Intensity distribution of the partially coherent Bessel vortex beams focused by an aperture lens is inves- tigated.It is found that the intensity distribution in the neighborhood of the geometrical focus is not only dependent on the topological charge and the radial frequency of the incident partially coherent Bessel vortex beam,but also on its coherence length.Based on this,the desired partially coherent vortex bottle beams can be obtained by choosing appropriate values of parameters.Because such bottle beams possess characteristics of low coherence and vortex,it may be used in microscopic particles guiding,trapping,and inducing rotation.     

Scattering of an unpolarized Bessel beam by spheres

The scattering process of an unpolarized Bessel beam through spherical scatterers is investigated. We derive the analytical solutions of scattered fields of x-and y-polarized Bessel beams using a sphere, after which the dimensionless scattering function for an unpolarized Bessel beam is obtained. The dimensionless scattering function is applicable to spherical scatterers of any size on the beam axis or near it. Through numerical simulations, we demonstrate that extreme points exist in the direction or neighboring direction of the conical angle for spherical scatterers on the beam axis, whereas the existence of extreme points depends on the ratio between the spherical scatterers size and central spot size of the Bessel beam.     

Influence of laser intensity in second-harmonic detection with tunable diode laser multi-pass absorption spectroscopy

Tunable diode laser absorption spectroscopy （TDLAS） has been widely employed in atmospheric trace gases detection. The ratio of the second-harmonic signal to the intensity of laser beam incident to the multi-pass cell is proved to be proportional to the product of the path length and the gas concentration under any condition. A new calibration method based on this relation in TDLAS system for the measurement of trace gas concentration is proposed for the first time. The detection limit and the sensitivity of the system are below 110 and 31ppbv （parts-per-billion in volume）, respectively.     

Higher-order harmonics of general limited diffraction Bessel beams

In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-thorder Bessel beam. The analysis is based on successive approximations of the Khokhlov–Zabolotskaya–Kuznetsov(KZK)equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example.     

Numerical Investigation on Scattering of an Arbitrarily Incident Bessel Beam by Fractal Soot Aggregates

Scattering of an arbitrarily incident Bessel beam by fractal soot aggregates is numerically investigated. The incident beam is described by the vector expressions of the zero-order Bessel beam in combination with rotation Euler angles. The scattering problems involving fractal soot aggregates are formulated with a hybrid vector finite element-boundary integral-domain decomposition method. Some numerical results are included to show the scattering behaviors of fractal soot aggregates when they are illuminated by Bessel beams.     

Analysis for the Potential Function of the Digital Microstructure Image of Porous Media

Making use of the full information obtained in our previous discussions, a new analytical solutions for the potential function of the digital microstructure image of porous media is reported in this paper. It is demonstrated that the distribution of potential function depends on the zeroth order Bessel function. All these will be helpful for analyzing the similar subjects in porous media.     

Density Transition Based Self-Focusing of cosh-Gaussian Laser Beam in Plasma with Linear Absorption

Density transition based self-focusing of cosh-Gaussian laser beam in plasma with linear absorption has been studied. The field distribution in the plasma is expressed in terms of beam width parameter, decentered parameter,and linear absorption coefficient. The differential equation for the beam width parameter is solved by following Wentzel–Kramers–Brillouin(WKB) and paraxial approximation through parabolic wave equation approach. The behaviour of beam width parameter with dimensionless distance of propagation is studied at optimum values of plasma density,decentered parameter and with different absorption levels in the medium. The results reveal that these parameters can affect the self-focusing significantly.     

Propagation of light in （2＋1）-dimensional nonlinear optical media with spatially inhomogeneous nonlinearities

The （2＋1）-dimensional nonlinear SchrSdinger （NLS） equation with spatially inhomogeneous nonlinearities is investigated, which describes propagation of light in （2＋1）-dimensional nonlinear optical media with inhomogeneous nonlinearities. New types of optical modes and nonlinear effects in optical media are presented numerically. The results reveal that the regular split of beam can be obtained in （2＋1）-dimensional nonlinear optical media with inhomogeneous nonlinearities, by adjusting the guiding parameter. Furthermore, the stability of beam regular split is discussed numerically, and the results reveal that the beam regular split is stable to the finite initial perturbations.     

An approach of open-path gas sensor based on tunable diode laser absorption spectroscopy

Tunable diode laser absorption spectroscopy(TDLAS)is a new method to detect trace-gas qualitatively or quantificationally based on the scan characteristic of the diode laser to obtain the absorption spectroscopy in the characteristic absorption region.A time-sharing scanning open-path TDLAS system using two near infrared distributed feedback(DFB)tunable diode lasers is designed to detect CH_4 and H_2S in leakage of natural gas.A low-cost Fresnel lens is used in this system as receiving optics which receives the laser beam reflected by a solid corner cube reflector with a distance of up to about 60 m.High sensitivity is achieved by means of wavelength-modulation spectroscopy with second-harmonic detection.The minimum detection limits of 1.1 ppm·m for CH_4 and 15 ppm·m for H_2S are demonstrated with a total optical path of 120 m.The simulation monitoring experiment of nature gas leakage was carried out with this system. According to the receiving light efficiency of optical system and detectable minimum light intensity of detection,the detectable optical path of the system can achieve 1-2 km.The sensor is suitable for natural gas leakage monitoring application.     

General formula for phonon-assisted n-photon absorption in solids

A general formula for phonon-assisted n-photon absorption in solids is obtained by (n+1)-th order perturbation technique. The complicated calculation process for transition element of n-photon absorption is simply demonstrated by a diagram approach that is proposed in this work. We find that the transition element for the n-photon absorption has a simple form, i.e., it is just the first term of the n-th order fist kind Bessel function.     

Induced Diffraction in Phase-Mismatched Second-Harmonic Generation

We show analytically that in phase-mismatched second-harmonic generation, an effective diffraction is induced at the second-harmonic （SH） frequency. Numerical simulation results agree with the analytical predictions. Compared to the case of linear propagation, the effect of the overall diffraction at the SH frequency becomes doubled due to the induced diffraction, which causes an interesting result that the SH beam width will be larger than that of the fundamental field.     

Computation and analysis of the Bessel beam scattering by a submerged elastic sphere

Taking an elastic sphere for example,the acoustic scattering of a submerged object illuminated by a Bessel beam is studied.The partial wave series representation for an elastic sphere has been extended to the case of Bessel beam scattering.Referring to the scattering of a plane wave,the peak to peak intervals in backscattering form function caused by the interference of the specular wave and the Franz wave have been analyzed in geometry.The influence of the characteristic parameterβof a Bessel beam on the peak to peak intervals has been indicated,and a predictive formula of the peak to peak intervals has been established for the first time.Meanwhile the elastic scattering of each partial wave has been separated based on the Resonance Scattering Theory.The influence ofβon the pure elastic resonance has been studied further.The results show that selecting specificβcan reduce the contribution of a certain partial wave.Therefore the resonance at the corresponding frequency and the nearby region in the backscattering is remarkably suppressed.The work of this paper could be helpful to the applications of Bessel beams on the acoustic detection of submerged objects.     

Numerical optimization and multi-particle dynamics simulation of the radial matching section of the RFQ

The ABC code is an optimization program for the development of matching channels and dynamical matchers in radio frequency quadrupole (RFQ) structures, and a new approach to this code to define the geometry of the radial matching section of the RFQ has been developed. This approach is based on the application of the numerical optimization step by step. This optimization is intended to search for the initial matching condition of a beam, the optimization of parameters of a cell of the channel on given characteristic parameters and traces of a beam in linear channels in both forward and backward directions. To further verify the results of the optimization, multi-particle beam dynamics simulations have been carried out using the BEAMPATH and TRACK codes. The result of the beam dynamics simulation shows that the optimization result of the ABC code is reasonable and this approach provides an opportunity to redesign the structure of the radial matching section of the RFQ.     

Propagation of Lorentz–Gaussian Beams in Strongly Nonlocal Nonlinear Media

In this paper the propagation of Lorentz-Gaussian beams in strongly nonlinear nonlocal media is investi- gated by the ABCD matrix method. For this purpose, an expression for field distribution during propagation is derived and based on it, the propagation of Lorentz-Gaussian beams is simulated in this media. Then, the evolutions of beam width and curvature radius during propagation are discussed.     

Focal Shift of Paraxial Gaussian Beams in a Left-Handed Material Slab Lens

Focal shift is inevitable in conventional lens systems due to the Fresnel number and angular aperture. In this Letter, we demonstrate that there is no focal shift when a paraxial Gaussian beam passes through a left-handed material slab lens without absorption or gain. However, the effect is exhibited in the presence of absorption or gain, and becomes larger as the absorption or gain increases. When the absorption is equal to the gain, the phenomenon of the focal shift caused by the gain is more obvious. In addition, the field distribution is not affected by the absorption or gain and always remains Gaussian both in internal and external focus planes.     

A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-Ⅱ beam

Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometricGaussian type-Ⅱ beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre–Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.     

Internal and near-surface fields for a chiral sphere under arbitrary laser beam illumination

A general scheme for the investigation of scattering by a chiral sphere under arbitrary monochromatic laser beam illumination is presented. The scattered and internal fields are expanded by using appropriate spherical vector wave functions, and their expansion coefficients are determined by the boundary conditions and the projection method. Targeting multiple incidence forms such as Gaussian beam, Hermite–Gaussian beam, doughnut mode beam and zero-order Bessel beam, the influence and propagation of near-surface intensity field for a chiral sphere are analyzed. These properties are very important for studying the properties of chiral media, and for manipulating the optical tweezers and super-resolution imaging of particles.     

A Formula of Propagating Beams Driven by Few-Cycle Gaussian Pulse in Dispersive Media

A formula is developed to describe the propagation of beams driven by few-cycle Gaussian pulse in a media with group velocity dispersion （GVD）. With the method, the spatiotemporal evolution of the pulsed beam can be straightforwardly quantified as long as the monochromatic beam solutions in free space, which have been widely investigated in previous works, are known. The method makes it possible to analytically deal with the few-cycle pulsed beams with transverse profiles other than the Gaussian one, which is, to our knowledge, the one mainly investigated previously, in GVD media.