Fig. 1. Variation in the diameter of the SCF in 10% HF as a function of etching time. The insets (A1)–(A5) show cross-sectional images of SCF corroded to different diameters.

Fig. 2. (A) Phase matching curves of HFG with different cladding diameters: (a1) LP0,10 mode with fiber diameter of 150 μm, (b1) LP0,10 mode with fiber diameter of 140 μm, (c1) LP0,4 mode with fiber diameter of 70 μm, (d1) LP0,2 mode with fiber diameter of 17 μm. (B) Two-dimensional electric field distribution of LP0,4 cladding mode with the fiber diameter of 70 μm. (C) Two-dimensional electric field distribution of LP0,2 cladding mode with the fiber diameter of 17 μm. In (B) and (C), 1, 2, 3, and 4 represent the region at the interface between the cladding and the MF, respectively. (D) One-dimensional electric field distribution of LP04 and LP02.

Fig. 3. (A) Spectral evolution of the LP0,10 cladding mode during the etching process. (B) Spectral evolution of HFGs with the reduction of the cladding diameter. (C) Dependence of the mode order on the cladding diameter of the HFG.

Fig. 4. Schematic diagram of the transverse profile of the HFG immersion into MF. (A) Without an external magnetic field; applied magnetic field along the (B) vertical direction and (C) horizontal direction.

Fig. 5. The transmission spectral responses of the HFG with LP02 cladding mode to different magnetic field intensities at three different relative magnetic orientations: (A) θ=0°, (B) θ=15°, (C) θ=30°. (D) The dependence of the VWS on magnetic intensity at different orientations. The transmission spectral responses of the HFG with LP02 cladding mode to different orientations from (E) 0° to 30° and (F) 30° to 60° with a constant magnetic field intensity of 20.7 mT. (G) The dependence of the VWS on magnetic orientation θ.

Fig. 6. (A) The dependence of the VWS on magnetic intensity with magnetic orientation θ=30°. (B) The dependence of the VWS on magnetic orientation with magnetic intensity of 20.7 mT.

Fig. 7. The transmission spectra of the SCF-HLPGs with different periods.

Fig. 8. The dependence of the wavelength separation on SRI for the LP0,10,LP0,9,LP0,6,LP0,4, and LP0,2 cladding modes with fiber diameters of 140.64, 119.39, 75, 55, and 13.8 μm.

Fig. 9. (A) Schematic diagram of the magnetic field sensor based on the HFG packaged with MF. (B) Experimental setup for vector magnetic field sensing.