Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media

By use of the time dependent theory for random lasers, we make a comprehensive calculation on the spectrum intensity as well as the pump rate dependence of the peak intensity and the spectral width of localized modes in two-dimensional random media for both transverse electric and transverse magnetic polarization fashions. For any mode, there is a jump in the curve of the spectral width vs the pump rate. A method based on the trailing edge of the jump to determine the pump threshold of a mode is confirmed to be available and effective.