V-2 derivative measurements of the light-current-voltage characteristics of (Al,Ga)As double heterostructure lasers and comparison with the theory of an ideal laser

Abstract

It appears that derivative techniques will become quite useful in the characterization of semiconductor lasers.1.2 In this paper, a simple modulation and detection scheme for applying derivative techniques to the investigation of stripe-geometry (A1,Ga)As double-heterostructure lasers is described. It is shown that modulating the current at constant modulation index (Ai/i = constant) allows the desired quantities i dV/di and i2d2V/di2 to be directly and sensitively obtained, in the same apparatus, at the first and second harmonics of the modulation frequency, respectively. Particularly strong indications of laser threshold and of other optoelectronic interactions in the laser are contained in the second-harmonic-voltage response. The same apparatus may be used to obtain derivatives of the light-current relation. These are found to sensitively reveal light-current nonlinearities which are believed due to filaments and other spatial inhomogeneities and instabilities. This paper also clarifies the signal responses expected with the derivative techniques by calculating the fundamental and second-harmonic voltages which would be observed in the case of an ideal laser driven with a component of its current sinusoidally modulated. The previously untreated, nonanalytic, lasing-threshold region is explicitly included and the results are exact for any modulation amplitude. The harmonic voltages are then related to the first and second voltage derivatives and to the parameters characterizing (A1,Ga)As doubleheterostructure lasers.