  Topological lasers have been intensively investigated as a strong candidate
for robust single-mode lasers. A typical topological laser employs a
single-mode topological edge state, which appears deterministically in a
designed topological bandgap and exhibits robustness to disorder. These
properties seem to be highly attractive in pursuit of high power lasers capable
of single mode operation. In this paper, we theoretically analyze a large-scale
single-mode laser based on a topological edge state. We consider a sizable
array laser consisting of a few hundreds of site resonators, which support a
single topological edge mode broadly distributed among the resonators. We build
a basic model describing the laser using the tight binding approximation and
evaluate the stability of single mode lasing based on the threshold gain
difference $\Delta\alpha$ between the first-lasing edge mode and the
second-lasing competing bulk mode. Our calculations demonstrate that stronger
couplings between the cavities and lower losses are advantageous for achieving
stable operation of the device. When assuming an average coupling of 100
cm$^{-1}$ between site resonators and other realistic parameters, the threshold
gain difference $\Delta\alpha$ can reach about 2 cm$^{-1}$, which would be
sufficient for stable single mode lasing using a conventional semiconductor
laser architecture. We also consider the effects of possible disorders and
long-range interactions to assess the robustness of the laser under non-ideal
situations. These results lay the groundwork for developing single-mode
high-power topological lasers.
