Injection-locked semiconductor laser array using a graded-index rod: a computational model

We describe a computation which models the coupling among five widely separated laser emitters in a single monolithic array due to a GRIN rod lens. Individual emitter modes are characterized as to nearfield rectangular beam waist sizes by using an effective index waveguide calculation. The differential equations describing ray propagation in a medium with nonuniform index of refraction are solved using a Runge-Kutta algorithm. A ray bundle originating at each emitter is traced through free space, the GRIN rod, and back to the array. The fraction of (1/e**2) power entering an emitter from the front then defines the coupling from the source diode to the target diode. Provisions for describing array distances, offsets, and tilts are included. The model was tested for an array with 6-microm stripes on 250-microm centers. An array position and orientation was found which coupled all five laser elements together. The computed coupling coefficients were commensurate with values reqired to fully couple the array elements. Previous experimental results are now interpreted as a result of injection locking facilitated by the rod lens as opposed to an external cavity configuration.