Theoretical Study On The Emission Characteristics Of Terahertz-waves And Light-waves In Random Lasers

In conventional lasers, the optical cavity that confines the photons also determines essential characteristics of the lasing modes such as wavelength, directivity, and polarization. In random lasers, which do not have mirrors or a well-defined cavity, light is confined within the gain medium by means of multiple scattering. Random laser theory is complicated, which concern localization theory and laser physics. Random lasing is intensively investigated for its wide prospective.In this dissertation we investigate several theoretical problems of random lasing system as follows.(1) we build a novel model for 1D active disordered medium made of ruby grains with a three-level atomic system to discuss random lasing phenomenon in THz domain. Our results suggest that THz random lasing could occur under suitable conditions. Our findings are significant for expanding random laser concept into THz domain and have potential application to construct new type of THz source.(2) By numerically solving Maxwell's equations and rate equations in a two-dimensional (2D) active random media made of ruby grains with a three-level atomic system, the threshold gain behavior for a THz random laser is investigated. The spectral intensity variation with the pumping rate is calculated for both the transverse magnetic (TM) field and the transverse electric (TE) field. The computed results show that THz random lasing could occur in a 2D disordered medium for both the TM and TE cases. Further analysis reveals that the THz lasing threshold for TM fields is lower than that for TE fields.(3) Random terahertz lasing is studied numerically for two-dimensional disordered media made of ruby grains with a three-level atomic system. A method via adjusting pumping area to control the polarization of THz wave is proposed. Computed results reveal that transverse electric THz lasing modes could occur if supplying pumping on the whole medium, while transverse magnetic THz lasing modes could occur if appropriately supplying pumping on partial area of the medium.(4) A model, by combining Maxwell's equations with all-parameters of Sellmeier's fitting equations and four-level rate equations, is built to investigate linear dispersive effect on the property of random lasing modes. Computed results show that the first excited mode for both dispersive and non-dispersive scattering cases has almost the same resonant frequency but the spectral intensity for dispersive case is lower than that for non-dispersive case, and there exist more modes in the whole spectra for dispersive case. Further analysis demonstrates that threshold of random lasing in dispersive case is higher than that of the non-dispersive case.(5) A four-level two-electron model, in which transitions between the energy levels are governed by coupled rate equations and the Pauli Exclusion Principle (PEP), is used in FDTD method for simulating random lasing of disordered semiconductor gain medium. For the sake of contrast, the gain threshold behavior of optically pumped random lasing is investigated in three atomic systems:a four-level two-electron atomic system with PEP, a four-level two-electron atomic system without PEP and a four-level one-electron atomic system without PEP. Computed results show that the first excited mode for two-electron atomic system with PEP is different from the other two cases. Further analysis demonstrates that threshold with PEP is higher than that without PEP about an order of magnitude.(6) By numerically solving Maxwell's equations and rate equations a comprehensive calculation on spectrum intensity and spectral widths of three localized modes via different pumping rates in one-dimensional (1D) disordered medium is investigated, in which pumping rate is described by a time function with duration of 80 fs. The spectral intensities varying with the peak value of femtosecond pumping pulse are calculated in the same disordered medium, and the calculated spectral intensities are compared with those with fixed pumping (simulation time is 6 ps). These results show that excited modes with fs pulse pumping rates are only slightly different from those with fixed pumping (ps pulse), which suggests the excited modes largely depend on the medium rather than the pumping rate at least for those of which pumping rates are fs and ps. At last, lifetimes of three excited modes are calculated. It is found that there is a certain corresponding relation between the mode's lifetime and its threshold-pumping rate, which is the longer lifetime with lower threshold.