Series expansion of single variable functions is represented in Fourier-Bessel form with unknown coefficients. The proposed series expansions are derived for arbitrary radial boundaries in problems of circular domain....Series expansion of single variable functions is represented in Fourier-Bessel form with unknown coefficients. The proposed series expansions are derived for arbitrary radial boundaries in problems of circular domain. Zeros of the generated transcendental equation and the relationship of orthogonality are employed to find the unknown coefficients. Several numerical and graphical examples are explained and discussed.展开更多
The transverse magnetic (TM) radiation characteristics are investigated for a cylinder with N infinite axial slots of arbitrary opening size and location. The cylinder is a thin circular conductor and coated by an ecc...The transverse magnetic (TM) radiation characteristics are investigated for a cylinder with N infinite axial slots of arbitrary opening size and location. The cylinder is a thin circular conductor and coated by an eccentric material. Fields are found by applying the boundary conditions to the cylindrical wave functions. The addition theorem of Bessel functions is used to obtain an infinite series solution in Fourier–Bessel series form. Results are computed by shrinking the generated infinite series to a finite number of terms and compared to other available data. Numerical results in graphical forms for different values are also developed and discussed for small eccentricities.展开更多
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 ...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.展开更多
文摘Series expansion of single variable functions is represented in Fourier-Bessel form with unknown coefficients. The proposed series expansions are derived for arbitrary radial boundaries in problems of circular domain. Zeros of the generated transcendental equation and the relationship of orthogonality are employed to find the unknown coefficients. Several numerical and graphical examples are explained and discussed.
文摘The transverse magnetic (TM) radiation characteristics are investigated for a cylinder with N infinite axial slots of arbitrary opening size and location. The cylinder is a thin circular conductor and coated by an eccentric material. Fields are found by applying the boundary conditions to the cylindrical wave functions. The addition theorem of Bessel functions is used to obtain an infinite series solution in Fourier–Bessel series form. Results are computed by shrinking the generated infinite series to a finite number of terms and compared to other available data. Numerical results in graphical forms for different values are also developed and discussed for small eccentricities.
文摘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.
