Fig. 1. (a) Schematic structure of the fabricated single-mode high-speed directly modulated OAM beam laser; (b) structure of the laser; (c) distribution of the gratings.

Fig. 2. Cross section of the modelling of the single-mode OAM laser.

Fig. 3. Typical distributions of the major electrical field components (a) E_r and (b) E_φ of the WGMs in the cross section of the microcylinder cavity.

Fig. 4. (a) Q factors of WGMs of the cavity added with only the side grating versus the azimuthal mode number; electrical field distributions of (b) the symmetrial mode and (c) the anti-symmetrical mode.

Fig. 5. Spectral distribution of the TE WGMs of the OAM laser with l = − 1.

Fig. 6. Near-field intensity distributions of the laser above the top grating, where the period number of the side grating N = 86 and that of the top grating M = 85. From the top to bottom row are three cases: (a) both the real and the imaginary grating, (b) only the real grating, and (c) only the imaginary grating are added to the microcylinder cavity and serve as the top grating.

Fig. 7. (a) Simulated far-field intensity and (b) phase pattern in the propagating direction of the near-field of the OAM beam laser. Various orders of −2, −1, 0, 1, and 2 from left to right are displayed.

Fig. 8. (a) L-I curves at the wavelength of 1310 nm, where both the total output power and the upward part are shown; (b) small signal modulation response of the OAM beam laser at different bias currents.