Rate equation approach for diode lasers

Abstract

The light output and the electron density within the active layer of a semiconductor laser have been calculated from the steady state solution of a rate equation approach. The assumed rate equation model takes into account the spontaneous emission into the lasing modes. Simple analytical approximation formulae have been found under the assumption of a power-law dependence between optical gain g and electron density n (g oc nl). The approximations are compared with numerical results from the rate equations. With the exception of a small region near the lasing threshold good agreement has been found.The theoretical results are compared with experimentally measured light outputs from single and double heterostructure lasers. From the comparison below threshold the power law exponent / may be evaluated. The comparison at threshold suggests that the spontaneous emission term decreases at threshold. This decrease is in agreement with experimentally measured changes of the emission bandwidth at threshold.

Optical Gain in Commercial Laser Diodes

“…The calculation of RS from experimental data is then a simple task. If one, indeed, evaluates the differential form of Equation ( 19), one gets an expression, Equation (20), that directly gives RS when the separation of the quasi-Fermi levels Clamping of quasi-Fermi levels is one of the most direct proofs of population inversion in a semiconductor [28], which experiments readily confirm: the plot of dV/dI displays (Figure 5) a sharp transition when the current I reaches the threshold value Ith and the curve flattens at a constant value that is the measurement of RS. The small decrease of the dV/dI curve after the threshold is due to geometric effects (progressive widening, after threshold, of the area of the inverted region), analyzed and explained in ref.…”

“…The calculation of R S from experimental data is then a simple task. If one, indeed, evaluates the differential form of Equation ( 19), one gets an expression, Equation (20), that directly gives R S when the separation of the quasi-Fermi levels qV J = φ n − φ p clamps and then the derivative is null, that is, when the forward current reaches and exceeds the threshold for laser action.…”

“…The calculation of RS from experimental data is then a simple task. If one, indeed, evaluates the differential form of Equation ( 19), one gets an expression, Equation (20), that directly gives RS when the separation of the quasi-Fermi levels…”

Modelling radiation-effects in semiconductor lasers for use in SLHC experiments

“…For a uniform electron density n in the conduction band of the active region of a semiconductor laser, the single-mode rate-equation can be written as [4,5]:…”

“…To compute the equations, the explicit form of the gain G must be known [4][5][6][7][8][9]. In the simplest case, it can be expressed as G(n) = kn, where k is a constant.…”