Exact solutions are presented to the steady-state coupled-mode equations that govern the nonlinear parametric interaction of a central-frequency wave with a pair of upshifted and downshifted sidebands in isotropic single-mode optical fibers. This solution accounts for pump depletion as well for as a possible phase mismatch among the waves. The existence is predicted of eigensolutions propagating unchanged along the fiber, which may be either spatially stable or spatially unstable, depending on the total power and the propagation-constant mismatch. The presence of spatially unstable eigensolutions dramatically affects the power exchange among the three waves. The physical implications of this instability for the frequency-conversion process, as well as its potential application to all-optical switching, are discussed.

We present a model for the dielectric function of semiconductors. It has been tested successfully for Si, Ge, GaAs, and ZnSe. In conjunction with the single plasmon-pole approximation it yields plasmon-energy dispersions in fair agreement with experiments. It allows one, moreover, to deduce an analytical expression for the Coulomb-hole part of the static self-energy operator.

The ab initio pseudopotential method within the local-density approximation and the quasiparticle approach have been used to investigate the electronic excitation properties of hexagonal (6H, 4H, 2H) and zinc-blende (3C) silicon carbide. The quasiparticle shifts added to the density-functional eigenvalues are calculated using a model dielectric function and an approximate treatment of the electron self-energy concerning local-field effects and dynamical screening. The inverse dielectric function and the auxiliary function are generalized to hexagonal crystals. Good agreement with the experimental results is obtained for the minimum indirect energy gaps. The k-space location of the corresponding conduction-band minima is clarified. Other excitation energies are predicted. The infuence of the quasiparticle effects on band discontinuities and the electron effective masses is studied.