  Five methods of calculating electrical field distributions in one dimensional
wave-guide arrays are reviewed. We analytically solve the scalar Helmholtz
Equation and, based on the computed Bloch functions and associated bands of
propagation constants, generate the exact field distribution maps. For the
approximated slowly varying envelope equation we show that the base Bloch
functions are identical to those in the exact case, and study the differences
in the bands of propagation constants. We demonstrate that by selecting the
reference refractive index value, it is possible to minimize the error in
propagation constants of any desired band. For the distributions calculated by
the coupled mode theory, we reveal the similarity and differences of the band
made of eigenvalues of the coupled mode equations matrix when compared to the
first band of propagation constants found by the exact solution. Analysis of
two numeric beam propagation methods shows that the relative accuracy of the
calculated field distributions of each of these methods depends on excitation
conditions. The presented analysis of the slowly varying envelope equation
provides guide lines for selecting the value of the reference refractive index
to be incorporated in these numeric methods where an analytic solution is
difficult to work out or in the frequently occurring cases where an analytic
solution does not exist at all.
