This thesis presents the first dynamic model for the simultaneous coherent combining and mode locking of fiber lasers. The model shows very good agreement with experiment and suggests a novel approach to producing high-peak-power pulse trains with tunable repetition rates in excess of a gigahertz for potential applications to optical clocking, telecommunications, and ultrafast optics.
Passive coherent beam combining relies on the use of evanescent coupling between individual lasers to create a phased array in order to scale up the output power and brightness of fiber lasers. Mode locking, on the other hand, is a method of generating short pulses with high peak power by coherently phasing all the longitudinal modes of a single laser. Our work combines the two techniques in a model based on the amplifying Nonlinear Schrödinger Equation (NLSE) for each fiber laser, a fast saturable absorber equation for mode locking, and a directional coupler matrix for combining the individual lasers. The coupling between individual lasers of different length leads to the formation of array modes created from the subset of longitudinal modes that are common to all the fibers. As the common longitudinal modes, the array modes naturally lead to a frequency comb with a tooth separation much greater than that of the single-cavity longitudinal modes. Locking of these modes by a saturable absorber results in a pulse train whose repetition rate, given by the array mode separation, is inversely proportional to the fiber length difference and is thus tunable.
Our model has been applied to both Erbium-doped fiber lasers operating in a wavelength region of anomalous dispersion (1.5 microns) and to Ytterbium-doped fiber lasers operating at 1.06 microns where the dispersion is normal. In the normal dispersion regime we find that the combination of saturable absorption and spectral filtering results in highly chirped dissipative solitons that contain more energy than those created in the anomalous dispersion region.
The dissertation concludes with a novel analysis of the optical tunneling process that underlies the operation of the directional couplers used in beam combining. The analysis explains some paradoxical phenomena that had hitherto been interpreted as superluminal propagation.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/102469/1/chaozh_1.pd
