Bessel Gaussian Research Articles

Propagation of Bessel–Gaussian beams through a double-apertured fractional Fourier transform optical system

Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

Two-mode superposition coherent states with spatial vortex structure for the quantized radiation field

Through superposing M two-mode coherent state a two-mode superposition coherent state with a spatial vortex structure in configuration space is constructed. Such quantum vortex state is an eigenstate of sum of squared two-mode annihilation operators and is always entangled. In the limiting condition of large M the quantum vortex state has a modified Bessel–Gaussian vortex structure with topological charge index n. Experimentally, such two-mode vortex states may be prepared by virtue of a multimode coherent state with currently available technology.

Non-Gaussian state with vortex structure of quantized radiation field

A new kind of quantum non-Gaussian state with vortex structure termed as a modified Bessel–Gaussian vortex state is constructed, and it is an eigenstate of sum of squared annihilation operator a2+b2. The quantum vortex state exhibits a rich variety of nonclassical signatures and is always entangled. The dependence of its statistical properties on state parameters is analyzed, and the non-Gaussianity is investigated in detail. It is found that, for sufficient small values of α, the properties clearly depend on the topological charge index n. Moreover, a scheme for generating such quantized vortex states is proposed.

The Wigner distribution functions of coherent and partially coherent Bessel—Gaussian beams

Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function (WDF) for a coherent or partially coherent Bessel—Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.

Vectorial structure and beam quality of vector-vortex Bessel–Gauss beams in the farfield

The far-field analytical expressions for the electromagnetic fields of amplitude of vector-vortex beams having a Bessel–Gauss (BG) distribution propagating in free space are obtained based on the vector angular spectrum and the method of stationary phase. The far-field energy flux distributions and the beam quality by the power in the bucket (PIB) in the paraxial and nonparaxial regimes are investigated. The PIB of the vector-vortex BG beams depend on the ratio of the waist width to wavelength and the polarization order. The analyses show that vector-vortex BG beams with low polarization order have better energy focusability in the farfield.

高阶贝塞尔高斯光束在非柯尔莫哥诺夫大气中的传输特性

高阶贝塞尔高斯光束在非柯尔莫哥诺夫大气中的传输特性

Bessel–Gauss beams as rigorous solutions of the Helmholtz equation

The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

Vector-vortex Bessel–Gauss beams and their tightly focusing properties

We demonstrate that the amplitude of vector-vortex beams has a Bessel-Gauss (BG) distribution through a rigorous vector electromagnetic analysis. We also investigate the intensity profiles in the focal plane of vector-vortex beams that are focused by a high numerical-aperture lens obeying the Helmholtz condition. Although the intensity of a vector-vortex BG beam with a topological charge n=1 is nonzero along the axis in the focal plane, the beams with n≠1 show discrete multiple spots which can be useful for optical trapping.

Improvement of lens axicon’s performance for longitudinally polarized beam generation by adding a dedicated phase transmittance

The focal field of high NA lens axicon with a binary-phase optical component is calculated by using vector diffraction theory. Numerical results show that for a radially polarized Bessel Gaussian input field, the proposed system generates a subwavelength (0.395λ) longitudinally polarized beam with large uniform depth of focus (approximately 6 λ).

Micro-ablation on silicon by femtosecond laser pulses focused with an axicon assisted with a lens

Micro-ablation of crystalline silicon was performed by irradiating a silicon substrate with femtosecond laser pulses of wavelengths 786nm or 393nm focused using a conical axicon assisted with a convex lens. Focusing the laser beam close to the tip of the axicon by means of the lens significantly improved the efficiency of concentration of laser pulse energy at the central spot of the resulting Bessel–Gaussian intensity distribution. As a result, micron-sized holes were formed with the diameter determined by the ablation threshold in the calculated fluence profile. It is possible to predict hole size from the laser pulse energy and the wavelength. Crystalline particles, a few tens of nanometers in size, were formed near the ablated zone.

Focusing of concentric piecewise vector Bessel–Gaussian beam

The focusing properties of a concentric piecewise vector Bessel–Gaussian beam are investigated in this paper. The beam consists of three portions: the center circular portion and outer annular portion are radially polarized, while the inner annular portion is generalized polarized with tunable polarized angle. Numerical simulations show that the evolution of focal pattern is altered considerably with different Bessel parameters in the Bessel term of the vector Bessel–Gaussian beam. The polarized angle also affects the focal pattern remarkably. Some interesting focal patterns may appear, such as two-peak, dark hollow focus; ring focus; spherical shell focus; cylindrical shell focus; and multi-ring-peak focus, and transverse focal switch occurs with increasing polarized angle of the inner annular portion, which may be used in optical manipulation.

Extreme spin-orbit coupling in crystal-traveling paraxial beams

The dynamics of the spin-orbit coupling in elegant and standard Hermite-Gaussian (HG), Laguerre-Gaussian (LG), and Bessel-Gaussian (BG) beams propagating through a uniaxial crystal are analyzed. We consider the structure of the electric fields of the paraxial beams and show that the extreme values of the spin and orbital angular momenta are inherent in the elegant HG and LG of high orders. The spin-orbit coupling in the BG beam of the lowest order can result in nearly 100% energy transport from a vortex-free beam to the vortex-bearing beam at a relatively small crystal length. The extreme spin-orbit coupling does not manifest itself in standard HG and LG beams.

Higher-order moments and overlaps of rotationally symmetric beams

We introduce a closed-form expression for the overlap between two different circular beams (CiBs) with azimuthal symmetry. A full description of the propagation of the higher-order moments of the CiBs through paraxial ABCD systems is presented. Our formalism can be easily applied to calculate relevant beam parameters such as the normalization constants, the M2 factors, the kurtosis parameters, the expansion coefficients of the CiBs, and therefore of all its relevant special cases, including the standard, elegant, and generalized Laguerre–Gaussian beams, Bessel–Gaussian beams, hypergeometric–Gaussian beams, quadratic Bessel–Gaussian beams, and optical vortex beams, among others.

Mathieu–Gauss beams: A thermal consideration

The generation of Helmholtz–Gauss beam families such as Mathieu–Gauss (MG) and Bessel–Gauss (BG) beams can be dramatically suffered from heat-induced thermal effects. This work is devoted to the generation of MG beams under severe induced thermal loads. The output MG beams of a solid-state laser were assumed to pass through an ABCD system matrix. The simulated results which were achieved by characterization of the transfer matrix of the thermally affected inhomogeneous medium report systematic variations of the intensity profile of MG beams from pump power of 1–5 W. It is shown that for high values of pump power, the thermal effects are so influential and the beam intensity profile is so changed that the identification of MG beams is not easily possible at first hand. The results can facilitate this identification and can be utilized for deeper understanding of thermal effects phenomena.

Nonparaxial propagation of linearly polarized modified Bessel–Gaussian beams and phase singularities of the electromagnetic field components

Based on an operator transformation technique and the nonparaxial propagation results of linearly polarized Gaussian beams, the nonparaxial propagation formulas of linearly polarized modified Bessel–Gaussian beams with optical vortices are constructed. Numerical investigations indicate that electromagnetic field components associated with the beams exhibit different phase singularities.

Generation of extreme ultraviolet radiation with a Bessel–Gaussian beam

The generation of few high-order harmonics in the extreme ultraviolet is enhanced by focusing the fundamental femtosecond laser beam with a combination of lens and axicon in an infinite gas cell. We show that this combination leads to an improvement in the phase-matched generation of harmonics in the cutoff region, with a higher photon flux and a better spatial beam profile. A high atom density through the use of a high gas pressure can be used and the absorption limit of the harmonic generation is obtained for an interaction length of a few millimeters.

Propagation properties of Bessel and Bessel–Gaussian beams in a fractional Fourier transform optical system

The properties of Bessel–Gaussian beams (BGBs) and Bessel beams (BBs) propagating through a fractional Fourier transform (FRT) optical system have been investigated. The analytical transformation formulae for BBs and BGBs propagation through a FRT optical system are derived based on definition of the FRT in the cylindrical coordinate system. By using the derived formula, numerical examples are illustrated.

Area scintillations of Bessel Gaussian and modified Bessel Gaussian beams of zeroth order

As an extension of our previous study, the area scintillation aspects of Bessel Gaussian and modified Bessel Gaussian beams of zeroth order are investigated. The analysis is carried out on the basis of equal source sizes and equal source powers. It is found that, when compared on equal source size basis, modified Bessel Gaussian beams always have less area scintillations than a Gaussian beam, while Bessel Gaussian beams exhibit more area scintillations. Comparison on equal source power basis, however, removes the advantage of modified Bessel Gaussian beams, that is, their area scintillations become nearly the same as those of the Gaussian beam. On the other hand, for the case of equal source powers, Bessel Gaussian beams with larger width parameters continue to have higher area scintillations than the Gaussian beam. We provide graphical illustrations for profiles of equal source size beams, equal source power beams and the curves to aid the selection of equal source power beams.

Phase singularities of high numerical aperture radially and azimuthally polarized beams in the focal region

The phase singularities of high numerical aperture (NA) radially and azimuthally polarized Bessel–Gaussian beams of order 1 in the focal region are studied, and the dependence of phase singularities of the radial, longitudinal and azimuthal electric field components on the truncation parameter and NA is illustrated and compared by numerical examples.

Focal switching of partially coherent modified Bessel–Gaussian beams passing through an astigmatic lens with circular aperture

The axial intensity distribution of partially coherent modified Bessel–Gaussian (PCMBG) beams passing through an astigmatic lens with circular aperture is derived on the basis of Collins formula. The influences of truncation parameter δ and astigmatic coefficient α on the axial intensity distribution are presented. The research shows that the axial intensity changes with the variation of α, and twice focal switches have been found. Furthermore, the physical interpretation of the twice focal switches is given and is also illustrated by numerical calculations. It has been revealed that the existence of astigmatism and the effect of the truncation parameter are the two main reasons for the twice focal switches of PCMBG beams passing through an astigmatic lens with circular aperture.