No abstract

A model to simulate the phenomenon of random lasing is presented. It couples Maxwell's equations with the rate equations of electronic population in a disordered system. Finite difference time domain methods are used to obtain the field pattern and the spectra of localized lasing modes inside the system. A critical pumping rate P c r exists for the appearance of the lasing peaks. The number of lasing modes increase with the pumping rate and the length of the system. There is a lasing mode repulsion. This property leads to a saturation of the number of modes for a given size system and a relation between the localization length ξ and average mode length Lm.

A transferable tight-binding model for silicon is found by fitting the energies of silicon in various bulk crystal structures and examining functional parametrizations of the tight-binding forms. The model has short-range radial forms similar to the tight-binding Hamiltonian of Goodwin, Skinner, and Pettifor but can be utilized in molecular dynamics with a fixed radial cutoff for all structural configurations. In addition to a very good fit to the energy of Si in different bulk crystal structures the model describes very well the elastic constants, defect-formation energies for vacancies and interstitials in crystalline silicon, the melting of Si, and short-range order in liquid silicon. Results for phonon frequencies and Griineisen constants in c-Si are also presented.