Waveguide Arrays for Optical Pulse-Shaping, Mode-Locking and Beam Combining

Nonlinear mode-coupling (NLMC) is a well-established phenomenon which has been both experimentally verified (1; 2; 3; 4; 5) and theoretically characterized (6; 7; 8). NLMC has been an area of active research in all-optical switching and signal processing applications using wave-guide arrays (2; 3; 4; 5), dual-core fibers (1; 6; 7), and fiber arrays (9; 10). Recently, the temporal pulse shaping associated with NLMC has been theoretically proposed for the passive intensity-discrimination element in a mode-locked fiber laser (11; 12; 13; 14; 15; 16). The models derived to characterize the mode-locking consist of two governing equations: one for the fiber cavity and a second for the NLMC element (11; 12; 13; 16) (See Fig. 1). Although the two discrete components provide accurate physical models for the laser cavity, analytic methods for characterizing the underlying laser stability and dynamics is often rendered intractable. Thus, it is often helpful to construct an averaged approximation to the discrete components model in order to approximate and better understand the modelocking behavior. Indeed, this is the essence of Haus’ master mode-locking theory (17). Here, we develop an averaged approximation to the discrete laser cavity system based upon NLMC and characterize the resulting laser cavity dynamics. The resulting averaged equations are the equivalent of a master mode-locking theory for a laser cavity based upon nonlinear mode-coupling. From an applications point of view, high-power pulsed lasers are an increasingly important technological innovation as their conjectured and envisioned applications have grown significantly over the past decade. Indeed, this promising photonic technology has a wide number of applications ranging from military devices and precision medical surgery to optical interconnection networks (17; 18; 19; 20). Such technologies have placed a premium on the engineering and optimization of mode-locked laser cavities that produce stable and robust high-power pulses. Thus the technological demand for novel techniques for producing and stabilizing high-power pulses has pushed mode-locked lasers to the forefront of commercially viable, nonlinear photonic devices. The performance of the waveguide array mode-locking model developed is optimized so as to produce high-power pulses in both the anomalous and normal dispersion regimes. The stability of the modelocked solutions are completely characterized as a function of the cavity energy and the waveguide array parameters. In principle, operation of a mode-locked laser (17; 18) is achieved using an intensity discrimination element in a laser cavity with bandwidth limited gain (17). The intensity