We present detailed Monte Carlo simulations of a simple model of a nematic liquid crystal channel waveguide investigating the effect of an applied electric external field. The simulations are based on the Lebwohl-Lasher lattice spin model with boundary conditions chosen to mimic the homeotropic anchoring appropriate for PDMS polymer walls. The external field is modeled by adding an additional term to the Hamiltonian which describes its coupling to the mesogenic molecules. We have investigated the effect of the external field on the optical transmission and the ordering across the cell.