Propagation properties of partially coherent Hermite-Gaussian beams through non-Kolmogorov turbulence

The propagation properties of partially coherent Hermite-Gaussian beams through non-Kolmogorov atmospheric turbulence are studied. The effects of non-Kolmogorov turbulence and beam nonparaxiality on the average intensity evolution and the beam-width spreading are stressed. It is found that the evolution of the average intensity distribution and the beam-width spreading depends on the generalized exponent factor, namely, on the non-Kolmogorov turbulence strength for the paraxial case. For the non-paraxial case the effect of the turbulence is negiigibl% while the beam-width spreading becomes very large. The analytical results are illustrated numerically and interpreted physically.

Geometrical Optics from the Ground up

We review, with proper derivation and proofs, the common undergraduate formulas for building images of objects using a system of lenses with spherical surfaces. This is done using the first-order approximation which assumes that light rays deviate from the symmetry axis by only small angles. Yet, even this most basic approximation results in surprisingly complex theory, which is then applied to explain workings of everyday optical instruments.

Transverse shift of the transmitted beam of a non-uniformly polarized paraxial light beam at dielectric interfaces

This paper reports that the central position of the reflected and transmitted beams of a nonlinear polarized light beam at the interface between two media undergoes transverse shifts. It presents a solution to the problem of transverse shift of a non-uniformly polarized paraxial light beam transmitting through interfaces between two homogeneous media by using a two-form amplitude and an extension matrix to represent the vector angular spectrum of a three-dimensional （3D） light beam. It derives general formula for the transverse shift of the transmitted beam, and discusses the shift of a well-collimated beam transmitting through an interface between two homogeneous media and a thin dielectric slab.

An exact solution to paraxial propagation of laser beams in longitudinal inhomogeneous plasmas

An exact, general solution for laser beams propagating in longitudinally inhomogeneous plasmas is obtained in the form of the diffraction integral. The Gaussian beam and the Hermite-Gaussian beam are taken for example. In the case of an increasing plasma density along the propagation distance, natural diffraction of the Gaussian beam is retarded. This retardance has a less effect on the central part of the Hermite-Gaussian beam while a considerable rise of the power in bucket （PIB） occurs in the surrounding part of the beam.

Solving multi-object radar cross section based on wide-angle parabolic equation method

Based on a Pade approximation, a wide-angle parabolic equation method is introduced for computing the multiobject radar cross section （RCS） for the first time. The method is a paraxial version of the scalar wave equation, which solves the field by marching them along the paraxial direction. Numerical results show that a single wide-angle parabofic equation run can compute multi-object RCS efficiently for angles up to 45 ° . The method provides anew and efficient numerical method for computation electromagnetics.

The Wigner distribution function of a super Lorentz–Gauss SLG_(11) beam through a paraxial ABCD optical system

An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.

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 hypergeometric- Gaussian 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.

Characteristics of paraxial propagation of a super Lorentz-Gauss SLG_(01) mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss（SLG） 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.

Finite Element Analysis with Paraxial &Viscous Boundary Conditions for Elastic Wave Propagation

In this study, two studies are performed. One is to apply paraxial boundary conditions which are local boundary conditions based on paraxial approximations of the one-way wave equations to finite element analysis. To do this, a penalty functional is proposed and the existence and uniqueness of the extremum of the proposed functional is demonstrated. The other is to improve the capacity of viscous boundary conditions using dashpots. To do this, customary viscous boundary conditions are modified to maximize the efficiency according to angles of incidence and materials. For the numerical analysis of elasticity with paraxial boundary conditions and the modified viscous boundary conditions, the coding of the finite element models is implemented, and the efficiency of those boundary conditions is investigated.

Nonlinear Interaction of Elliptical Laser Beam with Collisional Plasma：Effect of Linear Absorption

In the present work,nonlinear interaction of elliptical laser beam with collisional plasma is studied by using paraxial ray approximation.Nonlinear differential equations for the beam width parameters of semi-major axis and semi-minor axis of elliptical laser beam have been set up and solved numerically to study the variation of beam width parameters with normalized distance of propagation.Effects of variation in absorption coefficient and plasma density on the beam width parameters are also analyzed.It is observed from the analysis that extent of self-focusing of beam increases with increase/decrease in plasma density/absorption coefficient.

Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers

This paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave number.Rigorous matrix analysis is conducted in investigations and the oscillation-free computational procedure is proven to be stable in an asymptotic sense.Simulated examples are given to illustrate the conclusion.

Gaussian Beam Propagation in a Kerr Type Metamaterial Medium Using ABCD Matrix Method

In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps.Meanwhile, Gaussian beam profile in every step is obtained by finding the ABCD matrix of that particular step, and is used to find the ABCD matrix of the next step. Results of the suggested matrix method have been compared with the results of numerical split-step Fourier method for a Kerr medium, which indicates a good agreement. Then, we use the ABCD matrix to investigate Gaussian beams propagation in a Kerr type metamaterial, which is also in agreement with pervious results by other methods.