Fig. 1. Schematic of an HBGW created in coreless fiber by femtosecond laser direct-writing technique. Insets: (a) schematic in cross-sectional view of the HBGW; (b) side-view microscope image of a fabricated HBGW sample with a diameter of 10 μm.

Fig. 2. Schematics of the experimental setup for characterizing the optical properties, including the near-field profile of transmission modes, reflection spectra, and polarization-resolved transmission spectra, of the fabricated HBGWs.

Fig. 3. Microscope images, transmission modes, and reflection spectra of three fabricated HBGW samples S1, S2, and S3 with decreasing diameters of 30, 20, and 10 μm, respectively. (a) Cross-sectional and (b) side view microscope images of S1–S3; (c) near-field profiles of transmission mode in S1–S3 at the resonant wavelength of 1547.50 nm; (d) corresponding reflection spectra of S1–S3.

Fig. 4. Transmission spectra of two orthogonal linear polarization modes (x and y) in the single-mode HBGW S3.

Fig. 5. Refractive index distribution in the cross section of the fabricated single-mode HBGW S3. (a) 3D view and (b) 2D view.

Fig. 6. (a) Reflection spectra of the HBGWs S4–S6 fabricated with increasing pulse energies, and (b) reflection spectra of the HBGWs S7–S9 fabricated with increasing grating pitches.

Fig. 7. Five single-mode HBGWs (S10–S14) with distinct Bragg wavelengths fabricated with increasing helical pitches (1.04, 1.05, 1.06, 1.07, and 1.08 μm) and corresponding pulse energies (21, 21.5, 23, 26, and 27.5 nJ).

Fig. 8. (a) Measured Bragg wavelength of the fabricated single-mode HBGW as a function of increasing and decreasing temperature ranging from 18 to 100°C, and (b) measured Bragg wavelength of the single-mode HBGW as a function of increasing and decreasing strain ranging from 0 to 1000 με.

Fig. 9. Long-term isothermal annealing of the fabricated single-mode HBGW at 700°C for 15 h. (a) Reflection spectra of the HBGW before and after long-term annealing at high temperature; (b) evolutions of the measured peak reflection and Bragg wavelength during the annealing process.