Design and modeling of a single-ring exceptional-point ring-laser gyroscope with improved angular random walk

We report a novel exceptional-point (EP) ring laser gyro (RLG) that utilizes a single ring resonator to significantly increase the temperature stability compared to a two-ring EP RLG. The ring is made of a two-mode waveguide, and a tilted grating couples the two modes together to create an EP. An S-shaped waveguide placed inside the ring enables lasing of one mode in one direction and the other in the other direction. An analytical model is presented to quantify the improvement in angular random walk (ARW) that this EP gyro provides over a conventional RLG with the same ring size and loss. This model accounts for the frequency dependence of the gain that arises from hole burning, and for the fact that under rotation the RLG lases at two distinct frequencies in both directions. Simulations show that each mode lases in one direction only, and that when the homogenous linewidth of the gain medium is sufficiently narrow, both eigenfrequencies lase simultaneously in both directions, leading to a beat note proportional to the square root of the rotation rate, the hallmark of EP gyros. The thermal stability is shown to be improved by five orders of magnitude over that of a two-ring EP RLG. For the ARW to be improved, the homogeneous linewidth of the gain medium must be 1 MHz or less, which eliminates semiconductor quantum well and rare-earth-doped gain media because of their broad (~THz) linewidths. Using stimulated Brillouin scattering instead (linewidth of ~1 MHz), for a 1-cm ring diameter the predicted ARW is 22 times better than a conventional RLG. This design points the way to a potential avenue forward to an EP gyro with improved ARW.