Abstract
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--Pérot, distributed Bragg
reflector, DFB, random, and metamaterial active cavities illustrate the
capabilities of our method.
© 2009 IEEE
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