Method of discrete singularities in the accurate modeling of a reflector beam waveguide

Numerical diffraction synthesis of 2-D quasioptical power splitter

“…In 2-D, such a field can be conveniently simulated with a Hankel function of the first kind and zero order of a complex argument due to complex-valued source point (CSP) -e.g. see [2,3]. This function is a rigorous solution to the Helmholtz equation; it behaves as a Gaussian beam in the near zone of paraxial domain and transforms into cylindrical wave off this domain.…”

“…To overcome this difficulty, fast-convergent and numerically efficient discretization of SIEs is offered by MDS [2]. Accurate MDS solutions to the direct scattering, i.e., the analysis, problems for 2-D quasioptical reflector antennas and beam waveguides have been reported in [2,3]. Due to its flexibility and speed, we have selected the SIE-MDS technique for the direct problem solver used as a full-wave engine for building a numerical synthesis code.…”

Semi-Analytical Diffraction Synthesis of Cylindrical Reflector Beam Splitters

“…(aI/axj, &x,)S =2Re{KPo,x P)S2} (7) Here, it becomes necessary to introduce adjoint integral operators, which are determined from the identity 0, GV = (G 0, V for some complex functions and Vw On performing certain derivations and using adjoint integral operators, we finally obtain i =2Re{ 0 a U 10+yfu0nctioi jo ,21nt (8) where auxiliary function;j satisfies an adjoint SIE (9) Note that the operators involved in (8), (9) are either smooth or have log-singular kernels. Therefore all of them can be efficiently computed with MDS discretization.…”

“…To overcome this difficulty and to improve convergence, convergent and numerically efficient discretization of SIEs is offered by the method of discrete singularities (MDS) [6,7]. Accurate MDS solutions to the direct scattering, i.e., the analysis, problems for 2-D quasioptical reflector antennas and beam waveguides have been reported in [8][9][10].…”