Fig. 1. Annular-core fiber supporting second-order mode. (a) Structure and refractive index profile of annular-core fiber; (b) normalized field intensity profiles of LP01, LP11, LP21, and LP02 modes in annular-core fiber

Fig. 2. Description of offset and tilt parameters. (a) φ represents tilt angle; (b) m represents offset distance and d represents horizontal distance between fibers

Fig. 3. Simulation results of tapered and lensed SMF. (a) Trend of coupling efficiency varies with horizontal distance between fibers; (b) variation of mode field diameter during propagation of beam in tapered and lensed SMF and free space (illustration shows variation of normalized mode field intensity)

Fig. 4. Simulation results under different tilt angles. (a) Purities of LP01, LP11, LP21, and LP02 modes vary with tilt angle; (b) total mode coupling efficiency varies with tilt angle

Fig. 5. Simulation results under different offset distances. (a) Purities of LP01, LP11, LP21, and LP02 modes vary with offset distance when tilt angle is 8°; (b) total mode coupling efficiency varies with offset distance when tilt angle is 8°

Fig. 6. Experimental setup to generate second-order OAM mode in annular-core fiber by adding tilt angle (illustration in bottom left corner is end face of annular-core fiber)

Fig. 7. Intensity patterns of modes. (a) LP01 mode when tilt angle is 0°; (b) LP11 mode when tilt angle is 5°; (c) LP21 mode with low purity when tilt angle is 6.5°; (d) LP21 mode with high purity when tilt angle is 8°; (e) LP02 mode when tilt angle is 10°

Fig. 8. Intensity pattern and interference patterns of second order OAM mode. (a) Intensity pattern of excited second-order OAM mode when tilt angle is 8° and offset distance is 2 μm; (b) interference pattern with L=+2; (c) interference pattern with L=-2