Semiconductor Laser Arrays: Phase-Locked Solutions and their Stability
We have investigated the dynamic behavior of semiconductor laser arrays with evanescent coupling. Arrays of semiconductor lasers are capable of operating with high output powers and may therefore be useful in such areas as free-space communications, high-speed printing, and high-speed optical recording. In order to produce the single and narrow beam that is necessary for applications, the array must operate in phase. Consequently, the ability to analyze and theoretically predict the response of coupled lasers is critical for the further development of the technology. We have investigated the response 'of a system that models N (N arbitrary) lasers configured in a ring geometry. The system consists of 3N coupled, firstorder, nonlinear, ordinary differential equations that describe the carrier density, amplitude and phase of the electric field for each laser element . We have taken the coupling constant to be complex in order to consider the effect of a phase shift that is introduced as the electric field of one laser couples with another. In particular, we have obtained analytical expreSSions for the steady state solutions and determined the stability of those solutions. We have also explained the loss of stability as resulting from a Hopf bifurcation. The analysis has been carried out for general parameter values using perturbation techniques . In addition, we have explored particular parameter regimes numerically with the help of the program AUTO  designed to identify and track steady state and periodic solution branches.
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