Fig. 1. (a) Schematic diagram of the metasurface for the generation and superposition of MCVBs. OAM components with equally spaced topological charge (l) are encoded within the output beam. LIBS: laser induced birefringent structure. The output light is confined with higher localized optical intensity due to the superposition effect. (b) Illustrate of the principle for MCVBs generation based on a sliced phase pattern in the azimuthal direction. Two-fold rotational symmetry (N=2), l₁=0, and l₂=1 are chosen for example. And θ is an initial phase delay that can be optimized to modify the properties of MCVBs, such as the OAM spectrum, for maximizing the intensity gain.

Fig. 2. Design of the metasurface phase based on a sliced phase pattern in the azimuthal direction. (a) Evolution of intensity gain at z=1 m with respect to the initial phase delays β₁ and β₂. (b–d) Phase profile of the desired metasurface, OAM spectrum, and intensity distribution at a distance of 1 m for β₁=0 and β₂=0. (e) Intensity distribution along the propagation direction for β₁=0 and β₂=0. The intensity distribution is normalized to the maximum intensity of the Gaussian beam along the propagation direction.

Fig. 3. Laser-induced form birefringence with different pulse durations, pulse densities, and pulse energies. (a, c) Angle of the fast axis, intensity, and retardance image of laser-modified regions induced by different pulse durations and pulse densities, respectively. (b, d) Dependence of transmittance and retardance of laser-modified regions on pulse duration and pulse density, respectively. (e, f) Pseudo color maps of retardance and transmittance of laser-modified regions induced by different pulse energies and pulse densities. The birefringence was characterized at a wavelength of 655 nm, and the transmittance was measured at a wavelength of 808 nm.

Fig. 4. Prepared metasurfaces with type II and type X modifications. (a, b) Photographs of metasurfaces with type II and type X modifications inside silica glass. (c, d) Images of the fast axis angle of the fabricated metasurfaces.White lines in (d) indicate the fast axis angle of the fabricated birefringent nanostructures. Orange curves in (d) indicate the fast axis angle of the catenary structures. (e) Phase evolution in the azimuthal direction of the designed and fabricated metasurfaces. (f) Transmission spectra of the two fabricated metasurfaces with reference to pristine silica glass. Transmittance of the type X metasurface is greater than 99.4% in the near-infrared range.

Fig. 5. Characterization of optical field distribution modulated by the prepared metasurfaces. (a) Intensity distribution of the modulated beam along the propagation direction. The simulated patterns modulated by continuous phase and multi-level phase as well as the measured patterns modulated by metasurfaces of type II and type X are compared. (b) Normalized intensity distribution along the dashed lines indicated in (a) for both the simulated and measured optical patterns. The normalized intensity of each line is expressed as: I_nor(x_l)= I(x_l)/max[I(x_l)], where I(x_l) is the intensity along the line. (c) Intensity gain along the propagation distance.

Fig. 6. LIDT of the prepared metasurfaces with (a) type II and (b) type X birefringent nanostructures.