The fields in continuously curved waveguides of rectangular cross section are represented in terms of the exact eigenmodes. The formulas and numerical methods for computing Bessel functions of imaginary orders are presented

and the problem of computing eigenmodes and their angular propagation constants in curved waveguides of arbitrary curvature with high precision

is therefore completely solved. Typical numerical results are given. It is shown that there is a one-to-one correspondence between the eigenmodes in curved guide and the corresponding modes in staight guide

and that the equivalent propagation constants for curved guide close numerically to the propagation constants for staight guide

while the radial distribution of the modal fields is in an attenuated standing-wave form.