Efficient Computation of Longitudinal Lasing Modes in Arbitrary Active Cavities: The Bidirectional Time Evolution Method

In this paper, we develop the Bidirectional Time Evolution Method (BTEM) as an efficient technique to determine the frequencies of the longitudinal lasing modes in arbitrary 1-D active cavities. The BTEM is based on a mathematical property of linear Maxwell equations for active media at real frequencies: the backward Fourier transform of their frequency-domain solution provides nonphysical time-reversed fields when the threshold condition is fulfilled (i.e., the round-trip gains overcome the round-trip losses). Although such time-reversed fields are not physically feasible, they can be easily computed and their spectrum provides all the (real) frequencies at which the threshold condition is fulfilled. On the other hand, the phase condition is given by the peaks of the cavity transmittance modulus. Numerical examples of Fabry-Perot, distributed Bragg reflector, DFB, random, and metamaterial active cavities illustrate the capabilities of our method.