Hollow cylindrical waveguides that have pie-shaped cross sections are described. The explicit equations for the field components of the TE (transverse electric) and TM (transverse magnetic) waves are given, and the modal patterns for a number of modes are plotted. The relation between the field distributions inside the circular and sectoral waveguides is discussed. It is shown that the electric and magnetic fields of the modes TE/sub 1n/ and TM/sub 1n/ display edge singularity when the sectoral angle is greater than pi . Formulas convenient for the evaluation of Bessel functions of fractional order on a personal computer are given. >