Generalized Huygens-Fresnel Diffraction Integral Research Articles

Introduction and propagation properties of circular lorentz-bessel-gaussian beams

In this paper, circular Lorentz–Bessel–Gaussian beams (CLBGBs) are introduced as a novel member of the Lorentz-Gaussian beams family. The analytical expression of the propagation of these beams passing through a paraxial optical ABCD system is derived. The generalized Huygens-Fresnel diffraction integral of the form Collins’s formula and the expansion of the Lorentz distribution in terms of the complete orthonormal basis set of the Hermite-Gauss modes are used. The influences of the beam-order and Bessel part β, Gaussian and Lorentzian waists, and propagation distance z on the propagation of CLBGBs are investigated. Some numerical simulation results are done. The beams family in this work may be useful to the practical applications in free-space optical communications because they have vortex properties with their being experimentally realizable.

Transformation of a generalized Bessel–Laguerre–Gaussian beam by a paraxial ABCD optical system

An analytical expression of a Generalized Bessel–Laguerre–Gaussian (GBLG) beam passing through a paraxial ABCD optical system is developed by using the generalized Huygens–Fresnel diffraction integral. This result is regarded as the main finding of this paper. Several studies such as the propagation of fundamental Gaussian, flat-topped Gaussian, Bessel–Gaussian, Generalized Bessel–Gaussian and Laguerre–Gaussian beams, through an ABCD optical system, are derived as particular cases of our principle investigation. Numerical simulations are performed, in this work, to illustrate the propagation properties of GBLG beam through a free space, a thin lens, a Fractional Fourier transform system and a quadratic graded-index system.

Propagation of the finite Olver beams through an apertured misaligned ABCD optical system

In this paper, an analytical propagation expression of Finite Olver Beams passing through a misaligned ABCD optical system is derived using the generalized Huygens-Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions. Some numerical results are presented in the work for reason to illustrate the effect of misalignement on the distribution characteristics of the Finite Olver Beams passing through the misaligned optical system with a rectangular aperture.

Effects of a turbulent atmosphere on an apertured Lommel-Gaussian beam

In this paper, based on the generalized Huygens-Fresnel diffraction integral, the expansion of the hard aperture function into a finite sum of complex Gaussian functions and the Rytov theory method, we develop an approximate analytical expression of the on-axis intensity of Lommel–Gaussian beams passing through a turbulent atmosphere. The corresponding closed-forms for the unapertured Lommel–Gaussian, the aperture Lommel, the apertured/unapertured Bessel–Gaussian, the apertured Bessel and the apertured/unapertured fundamental Gaussian beams are derived in the work as special cases. Some of these theoretical results provide more accordance with other studies elaborated in the literature. Some numerical calculations are carried out to illustrate the effects of some parameters, such as the waist width, the wavelength, and the turbulence strength, on the on–axis intensity of Lommel–Gaussian at a z-plane of a turbulent atmosphere.

Propagation Properties of Finite Olver-Gaussian Beams Passing through a Paraxial ABCD Optical System

In this paper, an exact analytical propagation formula of Finite Olver-Gaussian Beams (FOGBs) passing through a paraxial ABCD optical system is developed and some numerical examples are performed. The propagation properties of the FOGBs through general optical systems characterized by given ABCD matrix are studied on the basis of the generalized Huygens-Fresnel diffraction integral, which permits to show the behavior of this laser beams family and its properties de-pending of the laser parameters. This research is of interest to prove some investigations done in the past by other researchers.

The propagation of hypergeometric beams through an annular apertured paraxial ABCD optical system

By means of expanding the hard aperture function into a finite sum of complex Gaussian functions and based on the generalized Huygens–Fresnel diffraction integral, a novel approximate analytical expression of hypergeometric (HyG) beams passing through a paraxial ABCD optical system with an annular aperture is derived. The results could be reduced to the case of a circular aperture or a circular black screen. Some numerical simulations are also performed and illustrated for the propagation characteristics and focusing properties of a HyG beam through a paraxial ABCD optical system with an annular aperture. The results obtained from the approximate analytical formula provide more efficiency than the usual way of using diffraction integral formula directly.

Propagation Characteristics of Airy-Gaussian Beams Passing through a Misaligned Optical System with Finite Aperture

Propagation characteristics of finite Airy-Gaussian beams through an apertured misaligned first-order ABCD optical system are studied. In this work, the generalized Huygens-Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions are used. The propagation of Airy-Gaussian beam passing through: an unapertured misaligned optical system, an apertured aligned ABCD optical system and an unapertured aligned ABCD optical system are derived here as particular cases of the main finding. Some numerical simulations are performed in the paper.

Effect of bifocal lens on propagation of Bessel beam

In this paper, we study the influence of the bifocal lens on the focusing properties of Bessel beam. Based on the generalized Huygens-Fresnel diffraction integral, a more general expression of the light intensity distribution of nonsymmetrical optical system which is described by 4×4 matrix is deduced. The optical field distribution of Bessel beam passing through bifocal lens is given and simulated numerically. The influence of the focal length of the bifocal lens on Bessel beam is analyzed in detail. The generalized expression of the light intensity distribution can involve three cases, i.e., ordinary lens, bifocal lens and cylindrical lens. The greater the astigmation, the poorer the bottle beam quality will be. The ability to imprison microscopic particles decreases.

Generation of dark hollow beam by focusing a sine-Gaussian beam using a cylindrical lens and a focusing lens

Based on the generalized Huygens–Fresnel diffraction integral, a closed-form propagation equation related to sine-Gaussian beams through a cylindrical lens and a focusing lens is derived and illustrated with numerical methods . It is found that a sine-Gaussian beam through such a system may be converted into a dark hollow beam (DHB) with topological charge index one and its bright enclosure is approximately an elongated ellipse with very high ellipticity . Moreover, the parameter values at which the DHBs have perfect intensity patterns are designed. The optimal relative orientation between the dislocation line of the input sine-Gaussian beam and the axial orientation of the cylindrical lens is specified. And the ellipticity of the elliptical DHBs is mainly defined by the focal length of the cylindrical lens and the Fresnel number of the optical system. • Convert sine-Gaussian beams into elliptic dark hollow beams with high ellipticity. • Design an optical system consisting of a cylindrical lens and a focusing lens. • Optimize the designing system parameters.

平顶高斯光束在梯度折射率介质中的传输特性

By using the method of generalized Huygens-Fresnel diffraction integral, the transmission analytical expression of flattened Gaussian beams in gradient-index media is deduced. The influence on the propagation properties of the medium gradient refractive index coefficient and the beam order is discussed. The results show that when flattened Gaussian beams propagate in gradient-index media, the intensity distribution on the axis varies periodically. Its change period is decided by the gradient-index coefficient, and has nothing to do with the beam order. The transverse intensity distribution of the peak on the axis is affected largely by the gradient-index coefficient and the beam order. The maximum on the plane with transversal intensity increases with the increase of the gradient-index coe

Changes in the state of polarization of apertured stochastic electromagnetic modified Bessel–Gauss beams in free-space propagation

By using the generalized Huygens–Fresnel diffraction integral, the analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse of apertured stochastic electromagnetic modified Bessel–Gauss beams (MBGBs) through a paraxial optical ABCD system are derived, and used to study the changes in the state of polarization of apertured stochastic electromagnetic MBGBs propagating in free space. The invariance of the on-axis state of polarization of unapertured stochastic electromagnetic MBGBs propagating through paraxial optical ABCD systems is illustrated analytically and numerically. For apertured stochastic electromagnetic MBGBs, the on-axis spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse increase with increasing propagation distance, and approach asymptotic values when the propagation distance is large enough. There is a uniform distribution region of the state of polarization around the center of the beams whose range decreases with increasing truncation parameter. In addition, the state of polarization of apertured stochastic electromagnetic MBGBs upon propagation can be modulated by controlling the truncation parameter.

Studies on propagation of laser beam array with initial phase distributions in a turbulent atmosphere

Based on the coherent superposition principle and the generalized Huygens-Fresnel diffraction integral, the properties of a radial beam array with definite initial phase distributions propagating through a turbulent atmosphere are analytically investigated. It is shown that, when the propagation distance is short, the output intensity distribution will gradually take on a spiral shape, which means an optical vortex. However, under the effect of the atmospheric turbulence, the output vortex property gradually disappears, and changes to a bright-cantered beam without vortex property. Furthermore, the weaker the atmospheric turbulence is, the longer distance the output optical vortex （the center-dark beam） can propagate over.

Formation of optical vortices using coherent laser beam arrays

We present a proposal to generate an optical vortex beam by using the coherent-superposition of multi-beams in a radially symmetric configuration. In terms of the generalized Huygens–Fresnel diffraction integral, we have derived the general propagation expression for the coherent radial arrays of laser beams. Using the derived formulae, we have analyzed the effects of the beamlet number N, the separation distance ρ of the beamlets and the topological charge m on the intensity and phase distributions of the resultant beams. Our simulation results show that optical vortices could be efficiently generated due to the coherent-superposition effect of all beamlets, during the propagation process of the coherent radial array of laser beams with the initial well-organized phase distributions through the free space. In the focusing system, the resultant beam near the focusing plane has the strong rotational effect with the phase helicity.

Partially coherent vortex beams focused by an aperture lens with coma

We investigate the influence of the coma of the lens on the focusing of partially coherent vortex beams. On the basis of the generalized Huygens-Fresnel diffraction integral, the formula for the intensity distribution in the focal plane is derived. The numerically calculated results are given to show that the coma of the lens leads to the asymmetry of focused intensity distribution. The influence of coherence length on the focused intensity distribution is also investigated. It is found that the effect of coma is not obvious when the coherence length is small. Intensity profiles for three different values of the azimuthal angle are plotted to illustrate the effect of coma and the influence of coherence length.

Changes in the intensity distribution and polarization of non-uniformly polarized beams focused by a spherically aberrated lens with annular aperture

Based on the generalized Huygens–Fresnel diffraction integral and beam coherence polarization (BCP) matrix formulation, the focusing properties of a type of non-uniformly polarized (NUP) beam through a spherical aberrated lens with annular aperture are studied. The dependence of focal shift, intensity distribution, power in the bucket (PIB) and degree of polarization on the spherical aberration coefficient, obscure ratio and polarization parameters is illustrated numerically. The focusing of NUP beams by a spherically aberrated lens with circular aperture is treated as a special case, where the inner radius of the aperture is equal to zero.

Propagation of hollow Gaussian beam through a misaligned first-order optical system and its propagation properties

Propagation properties of hollow Gaussian beam through a misaligned first-order ABCD system is studied using the generalized Huygens-Fresnel diffraction integral, augmented matrix. It is shown that, as a hollow Gaussian beam passes through the misaligned first-order ABCD system, the beam shape is not preserved, the out-put beams have differences when passing different misaligned optical systems. We can adjust the size of dark region through adjusting the misaligned transverse vector E.

Focusing properties and focal shift in hyperbolic-cosine-Gaussian beams

Based on the generalized Huygens–Fresnel diffraction integral the expression of the focused hyperbolic-cosine-Gaussian (ChG) beams is derived for any transverse plane in the focal region. The properties of the focused ChG beams and the focal shift are studied, and their dependence on the Fresnel number and the decentered parameter β are illustrated with detailed numerical calculations.

Propagation of elegant Laguerre–Gaussian beams through an annular apertured paraxial ABCD optical system

Based on the generalized Huygens–Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression of elegant Laguerre–Gaussian beams passing through a paraxial ABCD optical system with an annular aperture is derived. Meanwhile, the corresponding closed-forms for the unapertured, circular apertured or circular black screen cases are also given. The obtained results provide more convenience for studying their propagation and transformation than the usual way by using diffraction integral formula directly. Some numerical examples are given to illustrate the propagation properties of elegant Laguerre–Gaussian beams.

Propagation properties of Hermite-cosine-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture

Based on the generalized Huygens–Fresnel diffraction integral, a recurrence propagation equation of Hermite-cosine-Gaussian (HcoG) beams through a paraxial optical ABCD system with hard-edge aperture is derived, which permits us to obtain the analytical propagation expression for HcoG beams of any order. Furthermore, the closed-form propagation expressions for the Gaussian, Hermite–Gaussian, cosine (sine)-Gaussian, cosh (sinh) and cosine (sine) beams passing through a paraxial optical ABCD system with hard-edge aperture can be obtained by treating them as special cases of the analytical propagation expression for HcoG beams. The advantages of our analytical results are analyzed, and the applications are illustrated with numerical examples.

Relative phase shift in laguerre-gaussian beams propagating through an apertured paraxial ABCD system

Based on the generalized Huygens-Fresnel diffraction integral, closed-form expressions for the relative phase shift of Laguerre-Gaussian beams propagating through an apertured paraxial optical ABCD system are derived. The dependence of the relative phase shift on the beam and system parameters, and the condition for eliminating phase shift are analysed and illustrated with numerical examples.