Klein Tunneling and Enhanced Phase Synchronization in Laser Arrays With Linear Gapless Dispersion

Phase synchronization (locking) of laser arrays remains a critical challenge in fundamental nonlinear physics [1] and practical applications [2], particularly when dealing with disorder among lasers' natural frequencies. In this work, we analytically and numerically study how the synchronization of coupled lasers is enhanced when the laser modes have a Dirac dispersion. We consider a particular case, when the spatial distribution of lasers' natural frequencies has a form of a rectangular barrier. According to Klein paradox [3], such linear gapless dispersion will lead to chiral tunneling through the barrier, independent of the barrier width. In this work, we demonstrate how this enhanced tunneling mediates stronger overlap and synchronization of the laser eigenmodes in both one- and two-dimensional arrays. The synchronization persists for much higher barriers than what one would expect from an array with only a dissipative coupling [4]. As in the linear Klein tunneling, in our non-linear system the synchronization threshold is nearly independent of barrier width. In addition to numerical simulations, we have analytically demonstrated in the continuum limit how the lasers in the array with linear gapless dispersion can adjust their phases to compensate for any smooth enough disorder that has a correlation length larger than a distance between nearest lasers.