Improved Phase Locking of Laser Arrays with Nonlinear Coupling

An arrangement based on a degenerate cavity laser for forming an array of nonlinearly coupled lasers with an intracavity saturable absorber is presented. More than 30 lasers were spatially phase locked and temporally $Q$ switched. The arrangement with nonlinear coupling was found to be 25 times more sensitive to loss differences and converged five times faster to the lowest loss phase locked state than with linear coupling, thus providing a unique solution to problems that have several near-degenerate solutions.

Figure 1

Degenerate cavity laser (DCL) arrangement and experimental temporal evolution of the laser array intensity. (a) DCL arrangement with a mask of holes in the near-field plane so as to form an array of lasers and a saturable absorber (SA) in the far-field plane so as to non-linearly couple them. (b) Time evolution of the laser array intensity without the SA. (c) Time evolution with the SA indicating temporal $Q$ switching.

Figure 2

Experimental and simulated near-field and far-field intensity distributions of the DCL arrangement. (a) Without and (b) with a SA in the far-field plane. The broad Gaussian far-field intensity distribution without the SA indicates that there is no phase relation between the lasers whereas the sharp peaks with the SA indicate near-perfect phase locking of the entire array. As evident, there is good agreement between the experimental results and the numerical simulations.

Figure 3

Typical experimental far-field intensity distributions for different pump pulse realizations. (a) In phase state with SA, (b) out of phase state with SA and (c) coexistence state of in phase and out of phase states with SA. (d) Distribution of the number of states for 50 different pump pulse realizations, top row: linear coupling (Talbot diffraction), bottom row: nonlinear coupling (SA) near lasing threshold.

Figure 4

The effect of the SA on the convergence to the lowest loss phase locked state. (a) Calculated losses of the in phase and out of phase states as a function of Talbot distance in the range $[1\mathrm{to}1.2]Z_T$. The SA increases the loss of the out of phase state by $\sim 0.5\%$ as compared to the in phase state thereby shifting the degeneracy distance between them from $1Z_T$. to $1.05Z_T$. (b) Measured relative occurrence of the in phase, out of phase, and coexistence states as a function of Talbot distance. (c) Measured expectation value of the in phase and out of phase states as a function of Talbot distance. (d) Typical far-field intensity distribution for single realizations and averaged distribution over the 100 realizations at $1.05Z_T$.