Initial field and energy flux in absorbing optical waveguides. I. Theoretical formalism

An exact formulation of the electromagnetic field striking an optical waveguide is presented and compared with the decomposition relationship used in the literature. The expression for the critical angle is derived as a natural consequence of this formulation. Equations for the total fraction of power confined within a waveguide are derived and analyzed for the special case of absorbing waveguides. An explicit expression is derived for the fraction of energy confined within a waveguide supporting two sets of modes.