An efficient finite-element formulation for dielectric media with transverse anisotropy is applied to the analysis of optical fiber coupler. The two cores are curved in parabolic shapes, and between them there are index-matching liquid layers whose refractive index and the width of the liquid layer are taken into account as variable parameters. An analysis of this coupling procedure exploring leaky waves can be considered as future work, in this case a reduction of the coupling length is observed.