Spurious roots in nonlinear waveguide calculations and a new formatfor nonlinear waveguide dispersion equations

The existence of spurious roots in the widely used nonlinear waveguide dispersion equations is demonstrated. The spurious roots exist even when the linear waveguide dispersion equations are written in terms of the sine and cosine functions. The authors compare the similarities between the linear and nonlinear dispersion equations and present a new format of the nonlinear dispersion equations that simplify the numerical calculations and avoid the appearance of spurious roots