A theoretical presentation by using a three-dimensional finite difference beam propagating method (3-D FD-BPM) for the evanescent coupling is offered with respect to the refractive indexes between a side-polished optical fiber and an infinitely planar waveguide with a conductor cladding (PWGCC). The PWG is suspended at a constant distance from an unclad fiber core and attached with a perfect conductor (PEC) on one side. The coupling and propagation of light are found to depend on both the relationship between the refractive index values of two structures and the configuration of the side-polished fiber used in the PWGCC. The spreading of light in the unconfined direction of a PWGCC is presented with the distribution of electric fields in xy - plane and the absolute amplitude of electric fields along the x and y axis. The power of the light propagation in a fiber decreases exponentially along the fiber axis as it is transferred to the PWGCC, where it is carried away.