A simple model for the linewidth enhancement factor α and its frequency dependence in semiconductor lasers is presented. Calculations based on this model are in reasonable agreement with experimental results.
I. INTRQDUCTION M ODELING of semiconductor laser diodes combined with other electronic components requires an accurate representation of the laser. As a first step, a small-signal electrical circuit of a laser has been developed [1] , [2] . The purpose of this work is to extend the model to include noise sources. The extended equivalent circuit allows a straightforward calculation of the modulation and noise characteristics of a laser in dependence of the extrinsic elements, such as the driving source and the parasitic elements.Intrinsic intensity fluctuations in semiconductor laser diodes are caused by quantum-statistical photon generation and electron-hole recombination within the lasing medium. The intensity noise spectrum for laser light was first calculated by McCumber for a four-level laser system using rate equations with Langevin noise sources [3]. A quantum-mechanical justification of such an approach has been given by Lax [4]. Later, this model was adapted to semiconductor lasers [5], [6] . In early GaAs diode lasers the intrinsic light fluctuations were masked by excess noise due to inadequate transverse mode control, but measurements in stripe contact lasers were nevertheless able to confirm the basic features of the theory, namely large fluctuations at the onset of stimulated emission and a high-frequency noise peak at the resonance frequency of the laser [7] .Recently, it has been verified experimentally [8], [9] that mode stabilized lasers, such as the channeled-substrate planar and the buried heterostructure, operate at the quantum noise limit in excellent agreement with McCumber's noise theory. These intrinsic intensity fluctuations are usually very small and the noise performance of an optical communication system is normally determined by the receiver, but in some specific applications the quantum noise may significantly reduce the signal-to-noise ratio [ 101 . n and s are the total number of electrons in the gain medium and photons in the single lasing mode. The pump rate is i/q, rs is the spontaneous and 7 p h the photon lifetime. Ecvs is the downward stimulated rate (stimulated emission) and Eve s is the upward stimulated transition rate (stimulated absorption). The gain g, which is by definition the net stimulated emission, is g = ECV -Eve. p n/rS is the spontaneous emission coupled into the lasing mode. By setting
A direct measurement of electron and hole leakage in InGaAsP/InP lasers has been carried out. The effect of electron leakage on the temperature sensitivity of InGaAsP/InP lasers has been revealed.
We propose nonuniform structures of phase-locked diode lasers, which make it possible to discriminate efficiently against all the higher order array supermodes (lateral modes). In these nonuniform arrays, the effective mode index in each channel varies across the array. Consequently, the envelopes of the various supermodes, including the highest order one, differ significantly from each other. Thus, by proper tailoring of the gain distribution across the array, one can conveniently select the fundamental supermode. Such fundamental supermode oscillation is essential in order to obtain single lobe, diffraction limited beams and minimal spectral spread from phase-locked laser arrays.
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