Starting from the zeroth order vector modes we have derived the Eigen value equations for the transverse electric ( \(TE\) ) and transverse magnetic ( \(TM\) ) modes of an all-dielectric cylindrical optical waveguide structure. The results are then extended to study the behavior of an optical fiber consisting of a dielectric core over which a semi-infinite layer of surface-plasmon (SP) supporting metal cladding layer is deposited using thermal evaporation technique. A complex Eigen value equation is derived for the metal-clad/dielectric-core optical fiber. This complex equation is further simplified by defining some new parameters to yield two real coupled transcendental equations. Computer simulation is done in cylindrical coordinate system using Python programming to solve these two real coupled equations to calculate the propagation constant for the fundamental \(SP\) mode (which is \(TM\) in nature) excited at the cylindrical metal–dielectric interface. The mathematical analysis reported in this article can be used in optimizing the performance of surface plasmon resonance (SPR) based optical fiber sensors and \(TE/TM\) polarizers.