Nonlinear gain and carrier temperature dynamics in semiconductor laser media

Abstract

The macroscopic behavior of a semiconductor laser medium is described by use of modified rate equations. The model, valid on time scales greater than 10 Ϫ13 s, explicitly treats carrier temperature as a dynamic variable and includes the nonlinear dependence of the gain function on carrier density and temperature. Gain suppression that is due to carrier heating is a natural consequence of the model and gives a qualitative explanation of subpicosecond gain dynamics experiments without introducing gain nonlinearity phenomenologically. We demonstrate the temperature behavior of the laser during transient dynamics near and well above threshold. By including carrier temperature as a dynamic variable we show that the laser response to an external perturbation exhibits a noticeable change in the damped oscillations of the photon density compared with that in models without temperature dynamics. Variation in the evolution of the gain function for different external pulse energies is also demonstrated.

Gain and carrier temperature response of semiconductor laser media to short optical pulses

“…In this section we consider for the medium a simple model that allows us to obtain the desired analytical expressions and to describe carrier temperature dynamics in semiconductor laser media (e.g., gain suppression due to carrier heating in semiconductor amplifiers 15,16 ).…”

“…Integrals (11) and (12) can be simplified with the assumptions that are used to obtain Eqs. (9) and (10) and with the following approximation for the Fermi-Dirac function 15,16 : This approximation is more accurate for lower temperatures and is exact at 0 K. The resulting expressions for the electron ensemble are 15,16 N͑, ͒…”

“…This type of gain response is believed to be a result of the peculiar behavior of the carrier ensemble on short time scales, specifically, that of dynamic carrier heating; this belief is supported by theoretical calculations. [6][7][8][9][10][11][12][13][14][15][16] Although the carrier heating influence on gain dynamics has attracted much attention, the dynamic behavior of the carrier temperature is usually not a target of research. In most cases carrier temperature appears only as part of an ad hoc explanation of the nonlinear behavior of the gain.…”

“…Therefore it is reasonable to choose the microscopic description [17][18][19][20][21][22] over a combination of rate and energy balance equations. 15,16 The above arguments suggest the following limits for using the carrier temperature as a dynamic variable in a description of the gain dynamics on a short time scale: (i) The time scale should be long enough for the quasiequilibrium approximation to be reasonable (longer than ϳ0.1 ps); (ii) the approach based on carrier temperature dynamics should offer significant simplicity, in both the solution of the problem and the interpretation of results, as compared with the microscopic approach. With these limits the carrier temperature is a useful parameter in the description of the dynamics of semiconductor diode laser, amplifiers, and passive systems, and it deserves special attention from the points of view of both physics and applications.…”

“…Our theory is based on modified rate equations, including an equation for carrier energy density. 15,16 The paper is organized as follows. The model equations and the gain func-tion are described in Section 2, while the relations among dynamic variables are discussed in Section 3.…”