Determination of TM and TE modes of the circular waveguide with a cross-shaped insert using eigenfunction expansions and domain matching

Abstract

TM and TE modes and eigenvalues for the metallic circular waveguide with a cross-shaped insert are studied by the method of eigenfunction expansions and domain matching. As the cross size is increased from zero, the cut-off TM eigenvalue rises singularly. The cut-off TE eigenvalue falls singularly to zero as the cross approaches the outer circular shield. Higher modes are also determined. The structure can be utilized to promote TE mode propagation and increase frequency separation.

Keywords:

• Helmholtz equation
• circular waveguide
• cross-shaped insert
• mode shapes