We show that the tilted-grating-assisted excitation of surface plasmon polaritons on gold coated single-mode optical fibers depends strongly on the state of polarization of the core-guided light, even in fibers with cylindrical symmetry. Rotating the linear polarization of the guided light by 90 degrees relative to the grating tilt plane is sufficient to turn the plasmon resonances on and off with more than 17 dB of extinction ratio. By monitoring the amplitude changes of selected individual cladding mode resonances we identify what we believe to be a new refractive index measurement method that is shown to be accurate to better than 5 x 10(-5).