| Random laser systems are studied not only for their interesting physical properties, but also for their importance in technological applications. Their basic property is that the lasing phenomenon can appear in the random systems with gain. Randomness, which was thought to be detrimental to the lasing feedback mechanism, is a essential element in such lasing systems. The theoretical research of the random laser systems is based on the localization theory and laser physics.; In this dissertation we study the random laser systems in several aspects. First we will study the transmission and the reflection of the systems by the transfer matrix method. The analytical formula of the critical length or critical gain of random laser systems will be derived by the comparison between Lamb's theory and Letokhov's theory. Second, with the theoretical analysis and the numerical results, we will point out that the previous time-independent methods, which were widely used in the research of the random laser systems, will give us unphysical results when the gain is over the threshold of the system. Then, we will construct a model, with the FDTD method and the semiclassical laser physics, to study the new experimental results. This model can not only explain the multi-peak and anisotropic spectra of experiments, but also predict the lasing-mode number saturation in random laser systems. With this model, both of the time-evolving process and the final-stable solution of the random lasing modes can be studied. Finally, we will theoretically and numerically study the properties of the random lasing modes. We will derive the eigenequation and the magnitude equation of the modes to support our numerical results which will show that the wavefunctions of modes retain almost same in the lasing process, and the threshold of a mode can be predicted by the quality factor of the mode and the gain profile of amplifying medium. We suppose that these properties of the random lasing modes will be a new path for observing localization. |
