fig1r_data.csv contains all data to construct figure 1 right, from the simulation of the ideal AR-HCF design performed by COMSOL 5.3. In the simulation the loss show neglegible dependence on the polarization. In fig.1 right, only the average loss of two polarization states are plotted. fig2l.tif is the SEM picture of fabricated AR-HCF in fig.2 left. fig2r.dwg is the COMSOL model reconstructed from the SEM picture and used in simulating the loss property of AR-HCF in fig.2 left. The simulation is performed by COMSOL 5.3. fig3a_data.csv, fig3b_data.csv and fig3c_data.csv contain all data to construct figure 3 (a), (b) and (c). fig3a_data.csv contains the transmission spectra along 226 m and 46 m fiber lengths in a cutback measured by Bentham TMc300 monochromator. The resolution is 10 nm. The unit of spectra intensity is nA, representing the current of detector linearly scaling with the light intensity. fig3b_data.csv contains the measured attenuation of AR-HCF, the InF fiber attenuation provided by Thorlabs website and the COMSOL simulation results. The measured attenuation is calculated from the data in fig3a_data.csv. The COMSOL simulation uses COMSOL 5.3 based on the model of fig2r.mph. fig3c_data.csv contains the silica glass material absorption provided by Heraeus website.