  We analyze the interaction of a propagating guided electromagnetic wave with
a quantum well embedded in a dielectric slab waveguide. First, we design a
quantum well based on InAlGaAs compounds with the transition energy of 0.8eV
corresponding to a wavelength of 1.55um. By exploiting the envelope function
approximation, we derive the eigenstates of electrons and holes and the
transition dipole moments, through solution of the Luttinger Hamiltonian. Next,
we calculate the electrical susceptibility of a three-level quantum system (as
a model for the two-dimensional electron gas trapped in the waveguide), by
using phenomenological optical Bloch equations. We show that the
two-dimensional electron gas behaves as a conducting interface, whose
conductivity can be modified by controlling the populations of electrons and
holes the energy levels. Finally, we design a slab waveguide in which a guided
wave with the wavelength of 1.55um experiences a strong coupling to the
conducting interface. We calculate the propagation constant of the wave in the
waveguide subject to the conducting interface, by exploiting the modified
transfer matrix method, and establish it linear dependence on the interface
conductivity. By presenting a method for controlling the populations of
electrons and holes, we design a compact optical modulator with an overall
length of around 60um.
