Homogeneously broadened bidirectional ring laser: Theoretical analysis, numerical simulation and experiment in helium-xenon.

摘要

Theoretical and experimental studies of a homogeneously broadened bidirectional ring laser are reported. A model for a homogeneously broadened bidirectional ring laser is derived. The material variables, the population inversion and the atomic polarization, are written as infinite spatial harmonic series. Each of those series is truncated at fourth order in the spatial frequency, yielding a system of fifteen real equations. A numerical investigation of the validity of this trunction is performed. The rate of convergence of the spatial harmonic series of the population inversion and thereby the validity of the truncation of the series, is found to depend on the ratio of the relaxation rates of the population difference and the field and on the regularity of the dynamics.; The four steady-state solutions to this problem are found and a linearized stability analysis is performed on the zero-intensity steady state and the unidirectional steady states. The stability of the bidirectional solution is explored numerically.; Plots of intensity versus time from a numerical integration of the fifteen equations, is presented for parameter values appropriate to a Helium-Xenon laser and for a range of pump and detuning values, for later comparison with experimental results.; The experimental set-up is described and the determination of the values for the various parameters appearing in the model is presented. Experimental results in the form of plots of average intensity in the two directions of propagation versus empty cavity detuning, laser frequency versus empty cavity frequency, laser intensity versus discharge current and, in some cases, optogalvanic spectra are presented. Preliminary data in the form of plots of the average intensity in each of the two directions versus cavity detuning for various positions of an intra-cavity pinhole are also presented.; A summary and comparison of experimental findings and theoretical predictions is given. Good agreement is not found and speculations as to the source of the differences are put forward in conjunction with ideas for future experimental studies to increase understanding of this laser system.