The dynamics of mutually coupled nano-lasers subject to direct current modulation has been analyzed using rate equations, which include the Purcell cavity-enhanced spontaneous emission factor $F$ and the spontaneous emission coupling factor $\beta $ . Subject to two different modulation frequencies, the mutually coupled nano-lasers display two general types of response. The laser with the lower modulation frequency simply exhibits a response at that modulation frequency. Thus, we term a zero cross-talk response. On the other hand, at higher modulation frequencies the system displays a variety of dynamical responses which, in addition to zero cross-talk, includes a range of behaviors, which are classified from low cross-talk through to a complicated non-linear response. The precise behavior being dependent on the depth of modulation and the laser bias currents. The operational significance of the zero cross-talk regime is that it permits access to a simple periodic response at the modulation frequency. With a view to utilization, it is established that the region of zero cross-talk response enlarges with increasing modulation depth and increasing bias current. In this way, conditions are established, in which the lasers may act independently. The propensity for zero cross-talk response under stronger driving is consistent with previous analysis wherein modulated nano-lasers may have superior characteristics in the large-signal regime.
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