Finite Difference Time Domain Modeling of Light Amplification in Active Photonic Band Gap Structures

The paper deals with the modeling, based on the Finite Difference Time Domain method, of active oneand twodimensional photonic crystals. The onset of laser oscillation is observed by simulating the active substance as having a negative frequency-dependent Lorentzian-shaped conductivity so including into Maxwell’s equations an electric current density. Particular attention is devoted to the implementation of uniaxial perfectly matched layer absorbing boundary conditions for the simulation of infinitely extending structures having gain features. Laser behaviour is simulated as a function of various parameters; the threshold wavelength and conductivity are evaluated as the wavelength and conductivity where the transmittance diverges. Moreover, the properties of the active two-dimensional photonic band gap structures are given in terms of a Q quality factor which increases by increasing the crystal size and strongly depends on the lattice shape. For the square lattice, when the crystal size increases from N = 2 to N = 8 the Q-factor increases by about an order of magnitude (from 0.027 to 0.110) for TE polarization while for TM polarization it decreases from 0.025 to 0.022. At last the Q-factor pertaining to the chess-board lattice, to parity of other parameters, assumes greater values and already for N = 4, it reaches the values obtained for the 16× 8 square lattice, for both TE and TM polarizations.