Phase-lock control considerations for coherently combined lasers

Fundamental performance limitations of a phase-lock control loop used to coherently combine the output of two lasers are presented. The phase-lock loop is designed to lock the differential phase (frequency and phase) between the two lasers to a specified reference phase. An optical heterodyne configuration is used to determine the differential phase of the laser pair, which in turn is compared with the reference phase to create an error voltage. The error voltage is filtered and used to frequency modulate one of the lasers in an attempt to null the error. An integro-differential loop equation, valid for the linear operating range, is derived in terms of the reference phase, the heterodyne measurement noise, and the various laser phase instabilities. The solution of the equation results in an expression for the phase error variance in terms of the closed-loop noise equivalent bandwidth W(H). An expression for the value of W(H) which minimizes the phase error variance is developed. In addition to the noise effects, the steady-state and dynamic performance of the loop is examined for different loop filters and modulation formats. A design example pairing a CO(2) waveguide and conventional laser is presented. Implications for coherent laser arrays are discussed.