Abstract:
Planar optical waveguides are the key elements in a modern, high-speed optical network. An important problem facing the optical fiber communication system, specifically planar optical waveguides, is coupling. The current study presents a coupling model for planar optical waveguides and optical fibers. The various effects of the optical properties of the coupling interface were analyzed by the scalar finite difference beam propagation method, including the thickness, with or without the matching refractive index of the interface adhesive. The findings can serve as a guide for planar optical waveguide packaging.

Abstract:
A generalized type of spiral Bessel beam has been demonstrated by using a spatially displaced helical axicon (HA). The topological charge of the spiraling Bessel beams is determined by the order of the input Laguerre-Gaussian (LG) beam and the topological charge of the HA. The obtained spiraling Bessel beams have an LG type of modulation along their propagation direction and exhibit annihilation-reconstruction properties. Theoretical analysis is presented, including that of the stability, propagation distance, topological charge, and spiraling dynamic characteristics. The mathematical and numerical results show that the propagation distance and helical revolution of the spiraling Bessel beams can be controlled through choosing appropriate radius of the HA.

Abstract:
The propagation of hollow Gaussian beams in strongly nonlocal nonlinear media is studied in detail. Two analytical expressions are derived. For hollow Gaussian beams, the intensity distribution always evolves periodically. However the second-order moment beam width can keep invariant during propagation if the input power is equal to the critical power. The interaction of two hollow Gaussian beams and the vortical hollow Gaussian beams are also discussed. The vortical hollow Gaussian beams with an appropriate topological charge can keep their shapes invariant during propagation.

Abstract:
this paper presents the approach adopted to teach diffraction and laser beam propagation to under graduation students of mathematics. first it is presented a phenomenological approach for the huyghens principles and how an adequate mathematical analysis of this principle can result the basics of the fourier optics. later it was postulated an laser beam with a electric field amplitude distribution given by a gaussian function and the propagation of this beam was calculated by using the fourier optics. as result of this calculation it was obtained the propagation properties of a gaussian laser beam. although the propagation of gaussian beams is largely known in the literature, the approach showed to be very useful to introduce students into the wave physics without using the electromagnetism theory

Abstract:
The concept of a quadratic vortex beam is proposed, in which phase term of the beam is given by exp(i mθ2). The phase of the quadratic vortex beam increases with azimuthal angle nonlinearly. This change in phase produces several unexpected effects. Unlike the circularly symmetric beam spot of normal vortex beams, the intensity distribution of the quadratic vortex beam is shown to be asymmetric. The phase singularities will shift in the transverse beam plane on propagation.

In this work, we present the study of electromagnetic
wave propagation through a medium with a variable dielectric function using the
concept of Gaussian Beam. First of all, we start with wave equation with which we obtain
the solution in terms of the electric field and intensity distributions
approximate to Gaussian Function, . With this, we analyze the dependency of r on Gaussian beam distribution spread, the
distant from the axis at which the intensity of the beam distribution begins to
fall at a given estimate of its peak value. The
influence of the optimum beam waist w_{o} and the beam spread on the intensity distribution will also be analyzed.

The propagation of an optical vortex in a hexagonally
arranged single mode multicore fiber structure is investigated for possible
generation of additional vortices and their spread dynamics. Fields are
separated into a slowly varying paraxial envelope and a rapidly changing exponential
component. Solutions are derived from the paraxial inhomogeneous Schrodinger
equation in two dimensions along with the index of refraction of the proposed
structure. Numerical analyses are based on the beam propagation method and
transparent boundary conditions in matrix form with different parameters to
represent the intensity and phase of all derived fields. Vortices are
numerically identified by their points of zero intensity and their phase change
or polarity. The optical interferogram with a plane wave reference is also
employed to distinguish the dislocation points in the transverse directions of
the propagating fields.

Abstract:
In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.

Abstract:
This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.

Abstract:
For Laguerre Gaussian vortex beam, the analytical expression of the electric field is derived in the observation plane after propagation. Theoretical analysis shows that the definition of Gaussian beam is unsuitable to describing the size of the laguerre Gaussian vortex beam while propagation. It is more convenient that the radius of the point where intensity is maximum is used to define the vortex beam after propagation. Besides the beam broadening effect induced by diffraction, phase distribution exhibits special change in the observation plane. Isophase line changes from radial to arc. If the topological charge of the vortex beam is positive, the isophase line will bend clockwise after propagation; if the topological charge of the vortex beam is negative, the isophase line will bend anticlockwise.