a Numerical Study of a Coupled-Cavity Color Center Laser

The nonlinear effects in a coupled-cavity laser make it difficult to investigate the theory with only analytic methods, though numerical methods can be used. This dissertation discusses the development of computer models of the coupled -cavity laser; portions of FORTRAN code are included. The research goal is to find practical rules of coupled-cavity operation for the laser engineer. The model's foundation is the additive-pulse mode -locking (APM) theory. This theory states that the pulse -shortening mechanism is the coherent superposition of the electric fields of the two cavities at the output coupler of the main cavity. The nonlinearity of the external cavity (only self-phase modulation in the optical fiber is treated) causes a frequency chirp on its pulse. If the phases are correct, the interference of the pulses results in a shorter combined pulse. The first model investigates the nature of the combined pulse, which is reinjected into the main cavity. Although this model is incomplete (it ignores the gain medium), it provides insight into the operation of the laser. This model shows, and experimental results support, that there is an optimum amount of self-phase modulation and that anomalous dispersion in the fiber (which can support soliton propagation) results in longer pulses than normal dispersion. The multi-pass models include the gain medium in order to model the complete laser system. The first of these models uses an iterative method in which the pulses propagate through the simulated system, much as laser pulses propagate through the actual laser. This continues for as many iterations (round trips) as necessary to reach a steady state. The other multi-pass method imposes a steady-state condition to find a closed-form, self-consistent recursion relation which is used to numerically generate the steady-state pulse directly. This latter model generates pulses as short as 500 femtoseconds, which corresponds reasonably to laboratory results. Both simulated mode -locked and ultrashort operation also compare favorably with our experience in the laboratory. This model confirms the existence of an optimum amount of self-phase modulation in the fiber.