based on the theoretical model of a microfiber double-knot resonator with a parallel structure, numerical simulations on the transmission spectrum, the phase, and the group time delay of the resonator as a function of wavelengths are given. we find that with this kind of resonator both slow light and fast light can be obtained at different resonant wavelengths. experimentally, such a kind of microfiber resonator was fabricated successfully. the transmission spectrum of the fabricated resonator is well consistent with the theoretical simulation. a slow-light delay of about 38 ps and a fast-light advance of about 40 ps are demonstrated at different wavelengths, which might benefit the resonator to the applications in data delay lines, optical buffers, and optical memories. (c) 2016 optical society of america