  Marcatili's famous approximate analytical description of light propagating
through rectangular dielectric waveguides, published in 1969, gives accurate
results for low-index-contrast waveguides. However, photonic integrated circuit
technology has advanced to high-index-contrast (HIC) waveguides. In this paper,
we improve Marcatili's model by adjusting the amplitudes of the components of
the electromagnetic fields in his description. We find that Marcatili's
eigenvalue equation for the propagation constant is also valid for HIC
waveguides. Our improved method shows much better agreement with rigorous
numerical simulations, in particular for the case of HIC waveguides. We also
derive explicit expressions for the effective group index and the effects of
external forces on the propagation constant. Furthermore, with our method the
phenomenon of avoided crossing of modes is observed and studied.
