  Erbium-doped lithium niobate on insulator (Er:LNOI) is a promising platform
for photonic integrated circuits as it adds gain to the LNOI system and enables
on-chip lasers and amplifiers. A challenge for Er:LNOI laser is to increase its
output power while maintaining single-frequency and single (-transverse)-mode
operation. In this work, we demonstrate that single-frequency and single-mode
operation can be achieved even in a single multi-mode Er:LNOI microring by
introducing mode-dependent loss and gain competition. In a single microring
with a free spectral range of 192 GHz, we have achieved single-mode lasing with
an output power of 2.1 microwatt, a side-mode suppression of 35.5 dB, and a
linewidth of 1.27 MHz.
