Polarization analysis reveals the vectorial nature of nonlinear-optical spectral transformations of femtosecond Cr:forsterite laser pulses in a highly birefringent photonic-crystal fiber. The birefringence in this fiber is induced by elliptical shape of the core of the size of $2.0\mu \mathrm{m}$ by $5.7\mu \mathrm{m}$ . We demonstrate the possibility of polarization control of the blueshifted radiation at the fiber output originating from the Cherenkov emission of dispersive waves induced by solitons that are generated by input $1.25\mu \mathrm{m}$ laser pulses. Polarization-sensitive, two-color nonlinear-optical processes in such a fiber, pumped by the fundamental-frequency radiation of the Cr:forsterite laser and its second harmonic, are shown to allow the generation of a broadband spectrum covering the range from $430\text{to}660\mathrm{nm}$ .