On Straightening of Locally Deformed Waveguide

Locally deformed planar wave guide, i.e. the strip limited to two curves, coinciding with couple of parallel straight lines out of some compact, is considered. By conformal map this strip can be straightened in a strip with rectilinear borders (straight waveguide). Thus the problem about initiation of electromagnetic oscillations in locally deformed waveguide can be reduced to a problem about excitement of a straight waveguide with non-homogeneous filling. This problem is simpler than an initial problem both for the theoretical analysis, and for practical calculations by, e.g., partial Galerkin method. For calculation of conformal map of the deformed strip on a straight strip is given the boundary problem for one of the map functions. Proved that this problem has the unique decision solution decreasing on infinity, and also that this solution is classical in case of smooth borders. For the solution of this problem the finite element method (FEM) is used, solutions for locally squeezed and locally stretched waveguides are given. Shown that entering corners in the boundary don’t change a character of map and a convergence of applied numerical method. It is shown that transformation coincides graphically with identical out of place of local stretching or compression; this is important for the formulation of partial radiation conditions.

mathematical model, conformal map, planar waveguide