We discuss the complex dispersion relation of a one dimensional metallo-dielectric photonic crystal, produced by a
dielectric photonic crystal with extremely thin metallic inserts with the same periodicity. We have carried out the
analytical and numerical analysis. Also, we show a method to avoid the problem of solving the complicated system of
transcendental equations of the dispersion relation that was proposed previously for us and we extended it to the oblique
incidence, i.e., for calculating transversal electric and magnetic modes. Moreover, we demonstrated a metallic band gap
not only at the bottom but also at high frequencies.
In the present work we analyze the nonlinear modes of silicon-on-insulator (SOI) nanowires and supermodes of the
coupled SOI waveguides. A generalized analysis of the nonlinear modes of silicon nanowires is given where we have
considered the scalar approximation and its vectorial nature to obtain the analytical profiles. In the scalar approximation,
the analytical analysis of the profiles of the transversal modes is based on the solutions of the Helmholtz equation for
nonlinear periodic media, where we obtain an integral solution for the intensity which is identified with the help of the
elliptic functions. Those modes are characterized by two constants of motion of particular physical significance and in
some approximations the solution could become a soliton or cosenoidal type. Therefore, we describe the solutions on
terms of the movement and integration constants. This is an important result because defines the nature of the solutions,
therein the analysis of the third order polynomials roots of those elliptic functions. The general theoretical model
includes the two-photon absorption (TPA) and the nonlinear Kerr effect implicit in the refraction index.