Fig. 1. (a) Sketch of tapered optical fiber with trilinear shape. dwaist, waist diameter. (b) Schematic of experimental setup. L, lens; HWP, half-wave plate; PBS, polarizing beam splitter; M, mirror; MC, cavity mirror; IPC, in-line polarization controller; BS, beam splitter; QWP, quarter-wave plate, which was inserted to calculate S3; LP, linear polarizer; CCD, camera; MMF, multimode fiber; and PD, photodiode.

Fig. 2. Simulations of (a) TE01, (b) HE21e, (c) TE01+HE21e, and (d) lemon. The red and blue SOPs indicate right- and left-handed ellipticities, respectively. The scale bars show the normalized intensity (from 0 to 1) and the Stokes phase (from 0 to 2π). Stokes singularity points of σ12, σ23, and σ31 are indicated as pink, orange, and blue dots, respectively. An L-line is indicated in green.

Fig. 3. (a) Typical spectrum for an HOM cavity with an SM-ONF as the laser is scanned over 150 MHz. The spectrum over a single FSR is indicated by the red box. (b) Mode intensity profiles showing the SOPs (top) and corresponding Stokes phases (bottom) for (i) Mode 1 and (ii) Mode 2. The red and blue SOPs indicate right- and left-handed ellipticities, respectively. The scale bars show the normalized intensity (from 0 to 1) and the Stokes phase (from 0 to 2π).

Fig. 4. (a) Typical spectrum for a cavity with an HOM-ONF as the laser is scanned over 150 MHz. The spectrum over a single FSR is indicated by the red box. (b) Mode intensity profiles showing the SOP (top) and the corresponding Stokes phases (bottom) for (i) Mode 1, (ii) Mode 2, (iii) Mode 4, and (iv) Mode 5. The red and blue SOPs indicate right-handed and left-handed ellipticities, respectively. The scale bars show the normalized intensity (from 0 to 1) and the Stokes phase (from 0 to 2π). Stokes singularity points of σ12, σ23, and σ31 are indicated as pink, orange, and blue dots, respectively. L-lines are indicated in green. (c) Corresponding simulated results.

Fig. 5. (a) Mode intensity profiles for quasi-donut-shaped cavity modes from the cavity containing an HOM-ONF with their SOPs (top) and Stokes phases (bottom) similar to the fiber eigenmodes of (i) HE21e, (ii) HE21o, (iii) TE01, and (iv) TM01. The red and blue SOPs indicate right-handed and left-handed ellipticities, respectively. Scale bars show intensity (from 0 to 1) and Stokes phase (from 0 to 2π). Stokes singularities of σ12, σ23, and σ31 are indicated as pink, orange, and blue dots, respectively. L-lines are illustrated as green lines. (b) Corresponding simulated results.