Fig. 1. Two-dimensional schematic diagram used in the numerical simulation, and (b) the calculated internal-field intensity spectra at R=0 and 15 μm.

Fig. 2. Internal mode intensity distribution |Hy|2 at R=0 for (a) fundamental transverse mode at 1551.47 nm and (b) first-order transverse mode at 1550.82 nm.

Fig. 3. Mode Q-factor versus the inner radius R for fundamental (squares) and first-order (triangles) transverse modes.

Fig. 4. Normalized intensity versus the angular momentum index m for (a) the fundamental and (b) the first-order transverse modes. Positive (negative) values of m correspond to CCW (CW) traveling-wave components.

Fig. 5. (a) Top-view SEM image after the first-step ICP etching to the BCB bonding layer. (b) Top-view microscope image after metal electrode deposition. (c) Cross-sectional view SEM image of hybrid octagonal-ring laser coupled to a silicon waveguide.

Fig. 6. (a) Peak powers from the silicon waveguide versus the pulsed injection current. (b) Lasing spectra at pulsed injection currents of 13, 25, and 32 mA.