The competition between two polarization states in two-dimensional random medium

In a two-dimensional random medium, when the transverse magnetic (TM) polarization state and the transverse electric (TE) polarization state share the same population inversion, there is a competition in the population inversion between the two states. Such competition is analyzed by using the finite difference time domain method to numerically solve Maxwell equations with a set of system parameters. The results indicate that TM state has a larger lasing threshold than TE state does so that TM state is strongly suppressed by TE state in the competition. The larger the size of the medium, the easier the lasing modes in TM state appears.