In this paper, a collimated femtosecond Gaussian beam with a central wavelength of 800 nm and a pulse duration of 50 fs is converted into a Bessel beam by an axicon with an apex angle of 140. By adjusting the femtosecond Gaussian beam incidence angle on the axicon, both anastigmatic and astigmatic femtosecond Bessel beams can be generated. Single- and double-core optical waveguides are fabricated in silica glass respectively by using anastigmatic and astigmatic femtosecond Bessel beams. Anastigmatic femtosecond Bessel beams with different single pulse energies (0.39 mJ and 0.47 mJ) are employed to fabricate the single-core optical waveguides in silica glass. The fabricated single-core waveguide's core diameter and refraction index change are found to be dependent on both the single pulse energy and pulse number used to fabricate the waveguide. By rotating the axicon, femtosecond Bessel beam with astigmatism is generated, which is used to fabricate double-core optical waveguides in silica glass. In the experiments 50 fs laser pulses with single pulse energy of 0.36 mJ are employed to fabricate the double-core optical waveguide. Experimental results show that when the rotation angle of the axicon is relatively small (1), i.e., the incidence angle of the femtosecond Gaussian beam on the axicon is 89, the distance between the two cores of the fabricated double-core waveguide is only 5.6 m. In this case the energy ratio of the coupled He-Ne laser between the two cores varies periodically as the waveguide's position changes towards one specific direction. When the axicon is rotated 3 and 5, the distances between the two cores increase respectively up to 9.1 m and 16.1 m, and no periodic variation of the coupled light energy ratio between the two cores is observed. It is inferred that the waveguides fabricated using the axicon with rotation angles of 3 and 5 are in fact optical waveguides with double parallel cores. According to the experimental results shown above, it is deduced that the double-core optical waveguide can be used as a highly sensitive differential displacement sensor, and the minimal detectable displacement is found to be less than 3 m. The light energy difference between the two cores is used to measure the displacement, so the displacement sensor made by double-core optical waveguide is a kind of differential detector with a higher signal-to-noise ratio than the frequently-used single-core waveguide displacement sensor. In addition, because the core zone of the double-core waveguide is composed of two cores separated by a distance which can be changed by adjusting the angle of the axicon before the fabrication process, the resulting larger core zone greatly facilitates the assembly process of the displacement sensor while the high detection sensitivity of the displacement is simultaneously achieved due to the using of the differential measurement method.