a Semiclassical Analysis of a Detuned Ring Laser with a Saturable Absorber: New Results for the Steady States and a Formulation of the Linearized Stability Problem.
This dissertation presents new results for the steady states of a detuned ring laser with a saturable absorber. The treatment is based on a semiclassical model which assumes homogeneously broadened two-level atoms. Part 1 presents a solution of the Maxwell-Bloch equations for the longitudinal dependence of the steady states of this system. The solution is then simplified by use of the mean field approximation. Graphical results in the mean field approximation are presented for squared electric field versus operating frequency, and for each of these versus cavity tuning and laser excitation. Various cavity linewidths and both resonant and non-resonant amplifier and absorber line center frequencies are considered. The most notable finding is that cavity detuning breaks the degeneracies previously found in the steady state solutions to the fully tuned case. This lead to the prediction that an actual system will bifurcate from the zero intensity solution to a steady state solution as laser excitation increases from zero, rather than to the small amplitude pulsations found for the model with mathematically exact tuning of the cavity and the media line centers. Other phenomena suggested by the steady state results include tuning-dependent hysteresis and bistability, and instability due to the appearance of another steady state solution. Results for the case in which the media have different line center frequencies suggest non-monotonic behavior of the electric field amplitude as laser excitation varies, as well as hysteresis and bistability. Part 2 presents a formulation of the linearized stability problem for the steady state solutions discussed in the first part. Thus the effects of detuning and the other parameters describing the system is incorporated into the stability analysis. The equations of the system are linearized about both the mean field steady states and about the longitudinally dependent steady states. Expansion in Fourier spatial modes is used in the latter case to eliminate the spatial derivatives from the linearized equations while retaining the spatial dependence. This results in an infinite matrix of coefficients, which must be truncated for a numerical solution of the problem. The stability of the steady state solutions found and discussed in Part 1 can now be determined. In addition to the above core material, this dissertation contains prefactory material, an introduction, a brief concluding section, and eight appendices. The Introduction provides background material and an overview of the methods used in Parts 1 and 2. The concluding section outlines possibilities for future work based on the developments presented in the dissertation. The appendices are bound as a second volume and document the FORTRAN code used for the numerical calculations of Part 1.
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- Physics: Optics