Controlling Synchronization in Large Laser Networks

Synchronization in large laser networks with both homogeneous and heterogeneous coupling delay times is examined. The number of synchronized clusters of lasers is established to equal the greatest common divisor of network loops. We experimentally demonstrate up to 16 multicluster phase synchronization scenarios within unidirectional coupled laser networks, whereby synchronization in heterogeneous networks is deduced by mapping to an equivalent homogeneous network. The synchronization in large laser networks is controlled by means of tunable coupling and self-coupling.

Figure 1

A schematic sketch of the experimental arrangements include a degenerate laser cavity, a coupling arrangement and a detection arrangement for detecting the phase synchronization between any desired set of lasers with a CCD camera. The degenerate laser cavity, that supports many independent uncoupled lasers, includes a calcite crystal that displaces each beam into two parallel beams of orthogonal polarization so that a mask with eight apertures leads to 16 lasers, as shown in the insets. The coupling arrangement, with its four coupling mirrors $R_1$, $R_2$, $R_3$, and $R_4$ that control a variety of different unidirectional homogeneous and heterogenous coupling connectivities, also includes delayed self-feedback coupling controlled by mirror $R_5$.

Figure 2

(a) Connectivity arrangement in a unidirectional loop of 16 lasers. The colored arrows, added to the near-field intensity distributions of 16 lasers, denote which pairs of lasers are coupled by which mirrors (see mirror colors of Fig. 1 online). (b) Three different networks of 16 lasers, all with 4 ns unidirectional time-delayed couplings. For a single directed loop of 16 lasers, the far-field intensity distribution indicates the lack of synchronization among all 16 lasers (left). For a network with 16 and 12 laser loops, the FF intensity distributions of different pairs of lasers indicates four synchronized clusters, each including lasers marked by a specific color (center). For a network with 16 and 14 laser loops, the FF intensity distribution indicates two separate synchronized clusters (right).

Figure 3

(a) A directed loop of eight lasers, where the lack of interference fringes in the FF intensity distribution of all eight lasers indicates no synchronization and eight separate clusters. (b) A directed loop of eight lasers with an additional self-feedback loop, where high contrast interference fringes along both horizontal and vertical directions indicate high synchronization with one cluster $\mathrm{GDC}(8,1)=1$. (c) A directed loop of eight lasers with an additional bidirectional loop of size 2, where high contrast interference fringes along the vertical direction only indicate two clusters, $\mathrm{GDC}(8,2)=2$. (d) A directed loop of eight lasers with an additional loop of six lasers obtained with unidirectional coupling between laser 8 and laser 3, where high contrast interference fringes along the vertical direction only indicate two clusters, $\mathrm{GDC}(8,6)=2$. (e) Phase correlation (fringe visibility) between all pairs of lasers for a network with directed loops of eight and four lasers, indicating four clusters $\mathrm{GCD}(8,4)=4$.

Figure 4

(a) Heterogeneous network of six lasers with $\tau =4\mathrm{ns}$ and $2\tau =8\mathrm{ns}$ time delays (top) and the equivalent homogenous network of eight lasers (bottom). The FF interference patterns of different pairs of lasers indicate the formation of two clusters $\mathrm{GCD}(8,6)=2$. (b) Heterogeneous network of eight lasers with $\tau =4\mathrm{ns}$, $\tau /2=2\mathrm{ns}$, and $3\tau /2=6\mathrm{ns}$ time delays (top) and the equivalent homogenous network of 17 lasers (bottom). The FF interference pattern of all lasers indicates a single synchronized cluster $\mathrm{GCD}(17,1)=1$.