  Phase-locked laser arrays have been extensively investigated in terms of
their stability and nonlinear dynamics. Specifically, enhancing the
phase-locking stability allows laser arrays to generate high-power and
steerable coherent optical beams for a plethora of applications, including
remote sensing and optical communications. Compared to other coupling
architectures, laterally coupled lasers are especially desirable since they
allow for denser integration and simpler fabrication process. Here, we present
the theoretical effects of varying the spontaneous emission factor $\beta$, an
important parameter for micro- and nanoscale lasers, on the stability
conditions of phase-locking for two laterally coupled semiconductor lasers.
Through bifurcation analyses, we observe that increasing $\beta$ contributes to
the expanding of the in-phase stability region under all scenarios considered,
including complex coupling coefficients, varying pump rates, and frequency
detuning. Moreover, the effect is more pronounced for $\beta$ approaching 1,
thus underlining the significant advantages of implementing nanolasers with
intrinsically high $\beta$ in phase-locked laser arrays for high-power
generation. We also show that the steady-state phase differences can be widely
tuned - up to $\pi$ radians - by asymmetrically pumping high-$\beta$ coupled
lasers. This demonstrates the potential of high-$\beta$ nanolasers in building
next-generation optical phased arrays requiring wide scanning angles with
ultra-high resolution.
