Nonlinear optics of circular-grating distributed-feedback semiconductor lasers
AuthorKasunic, Keith John, 1957-
AdvisorWright, Ewan M.
MetadataShow full item record
PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
AbstractThis dissertation investigates the nonlinear optics of circular-grating distributed-feedback (CGDFB) semiconductor lasers. Included are gain saturation, index saturation, and self- and cross-phase modulation third-order nonlinearities. After a brief review of the historical and technical background needed to understand our results, a numerical model is developed for gain saturation. This model includes a radially-varying nonlinear gain and a uniformly-distributed grating loss in the solution of the coupled-mode equations. The results show that lossy, high-power operation results in an optimum coupling strength for efficient conversion of pump power into useful output pourer. Results also show a multi-mode spectrum for large coupling strengths, a consequence of mode selection governed by a spatially-varying gain distribution. Single-mode selection entails operating at approximately the optimum coupling coefficient determined for efficient pumping. These results are extended by including the gain/index coupling described by the linewidth enhancement factor. A unique feature of this coupling is the possibility of above-threshold, single-mode operation over a limited power range, even for the case of large coupling coefficients. Similar results are obtained for the circular-grating distributed-Bragg-reflector (CGDBR) laser. The excess spontaneous emission rate associated with the nonuniform CGDFB radial (longitudinal) field profiles is also calculated. The resulting above-threshold linewidth closely follows the inverse-power dependence predicted by the Schawlow-Townes relation. To include third-order nonlinearities, we derive coupled-mode equations which describe self- and cross-phase modulation effects via an intensity-dependent refractive index. It is then shown that the circular-grating structure acts as an all-optical switch. We also find that an additional pi/2 phase shift at the center of the grating permits the possibility of self-pulsing cylindrical gap solitons. For a positive nonlinearity (n2 it is shown numerically that these solitons are not physically allowable. That is, for a passive structure, time-dependent self-pulsing behavior is damped by the 1/beta r factor in the self- and cross-phase modulation terms. This damping can be compensated for by the addition of gain. In this case, self-pulsing with an excellent contrast ratio is obtained. The numerical methods used to obtain both steady-state and time-dependent solutions are also described. The steady-state results are obtained using a multi-dimensional Newton-Raphson technique known as the "shooting" method. Time-dependent data use a fourth-order predictor-corrector technique. The stability of the time-dependent solutions to the exact coupled-mode equations is reviewed. Coupled-mode equations based on a large-radius approximation for the Hankel functions are found to be stable over a wider range of variables. Numerical tests used to verify the time-dependent software are described.
Degree ProgramGraduate College