Mathematical modeling of lasing in semiconductor microcavities by means of adequate eigenvalue problems

Abstract

From the analysis it follows that a thresholdless laser is not more realistic than a perpetual motion machine. In facts thresholdless lasing idea had appeared when it was noticed that infinite photonic crystals display frequency bandgaps, in which no electromagnetic wave can propagate. Therefore, it was suggested that a microcrystal or defect-cavity laser in a photonic crystal host medium might have zero threshold. However, no crystal is infinite, therefore the thresholds can be only made small. In fact, zero threshold is completely equivalent to zero output light. Therefore it appears that analyses of lasing in infinite photonic crystals are either erroneous, if done approximately or with coarse numerical methods like FDTD, or has no sense at all, if done with accurate methods, which correctly account for the radiation conditions. Instead, one must simply formulate the LEP with a finite-size photonic-crystal encasing a laser resonator and study the reduction of the thresholds as a function of elementary cell size, topology, filling, and number.