Markov model of quantum fluctuations at the transition to lasing of semiconductor nanolasers

Abstract

A Markov model of semiconductor nanolaser is constructed in order to describe finely the effects of quantum fluctuations in the dynamics of the laser, in particular by considering the transition to lasing. Nanolasers are expected to contain only a small number of emitters, whose semiconductor bands are simulated using true carrier energy states. The model takes into account carrier-carrier interactions in the conduction and valence bands, but the result is a huge Markov chain that is often too demanding for direct Monte-Carlo simulation. We introduce here a technique to split the whole chain into two subchains, one referring to thermalization events within the bands and the other to laser photonic events of interest. The model is applied to the analysis of laser transition and enlightens the coexistence of a pulse regime triggered by the quantum nature of the photon with the birth of the known coherent cw regime. This conclusion is highlighted by calculated time traces. We show that on the ultrasmall scale of nanolasers, we are unable to define perfectly the threshold.

Modeling the Lamb mode-coupling constant of quantum well semiconductor lasers

“…Anyway, as β decreases, the error bars increase more and more to exceed by far the critical value C = 1, which is a sign of increasing instability. It has been shown in [23] that low values of β promote a mode shutdown whose duration is inversely proportional to its value. This results in large emission peaks when this mode is re-ignited, causing a large increase in photon number variance and in turn the observed increasing error bars.…”

“…Monte Carlo and stochastic laser models calculate the time-dependent traces of the intensity evolution. They have been developed most of the time from the laser master equation [24,25] and were often applied to nanolasers with aim to understand their noise performance [26,27] or specific transition to lasing [23,28,29] because fluctuations are intrinsically taken into account. Recently we studied the mode competition within a dual-mode QW laser using our specific model that includes the carrier competition within bands via their thermal relaxation and Pauli's exclusion principle [22].…”

“…This was done in another work and applied to the emission properties of nanolasers during the transition to lasing. We extend it here to QW dual-mode semiconductor lasers and recall only its main features which are detailed in [23]. Our picture of a QW dual-mode semiconductor laser consists of two quantized electromagnetic modes resonant with a dual-mode cavity containing m 1 and m 2 photons and a finite number of electrons occupying the valence band and the conduction band.…”

“…Eventually the calculation requirements were reduced by a factor of more than 5 000, without loss of accuracy [23]. Thanks to this gain, the first results proposed in [22] can now be extended by adding a recursive procedure to automatically find the balance between the modes by adjusting the cavity losses and finding an appropriate couple α bal i .…”

“…Due to the recent improvement of the Monte Carlo model [23], we are able to derive in the following a numerical strategy to illustrate the stability of dual-mode lasers with active QW regions. We achieve this by evaluating the constant C with a numerical procedure that replicates the experimental procedure [13,18,19].…”