High-order approximation of wave propagation constants in a uniformly curved waveguide

New high-accuracy approximations of the angular propagation constants of LE_pm and LM_pm modes in a continuously curved rectangular waveguide are derived. They are high-order asymptotic expansions that are obtained using analytical computations. The formulas can be used for both propagating modes and an arbitrary number of evanescent ones. The approximations are applicable over a broad range of curvature variation and a wide range of wavenumber values. They are efficient tools for the numerical solution of modal equations