  We probe the physical mechanism behind the known phenomenon of power
synchronization of two diode lasers that are mutually coupled via their delayed
optical fields. In a diode laser, the amplitude and the phase of the optical
field are coupled by the so-called linewidth enhancement factor, $\alpha$. In
this work, we explore the role of optical phases of the electric fields in
amplitude (and hence power) synchronization through $\alpha$ in such mutually
delay-coupled diode laser systems. Our numerical results show that the
synchronization of optical phases drives the powers of lasers to synchronized
death regimes. We also find that as $\alpha$ varies for different diode lasers,
the system goes through a sequence of in-phase amplitude-death states. Within
the windows between successive amplitude-death regions, the cross-correlation
between the field amplitudes exhibits a universal power-law behaviour with
respect to $\alpha$.
