Electronic Structure Engineering of the Linewidth Enhancement Factor in Mid-Infrared Semiconductor Laser Active Regions
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to select a mode with negligible linewidth enhancement factor. INTRODUCTION Many of the potential applications for mid-infrared semiconductor lasers, in particular those involving molecular spectroscopy and remote sensing, require coherent sources with narrow linewidths. Spectral purity in a semiconductor laser is degraded by the coupling between phase and amplitude noise, and thus the linewidth is broadened beyond the Schawlow-Townes limit according to Av = Avo,(1 + ajwe), where Avo is the SchawlowTownes linewidth and clwe is the linewidth enhancement factor.[1l The linewidth enhancement factor is also a measure of the likelihood of formation of optical filaments. At high powers, optical filamentation can lead to catastrophic facet damage in the localized optical fields. Devices with small linewidth enhancement factors have the capability of producing larger output powers without facet damage. The linewidth enhancement factor (a,,,) is defined as the ratio of the density derivative of the real (Xv) and imaginary (Xj) parts of the complex susceptibility. However, when the fractional change in the index of refraction is small compared to the fractional change of the absorption coefficient, the linewidth enhancement factor can be written in terms of the density derivatives of the index of refraction (n) and the net gain (')net). Because dn/dN 29 Mat. Res. Soc. Symp. Proc. Vol. 607 0 2000 Materials Research Society
can be related to the differential gain spectrum by a Kramers-Kr6nig transformation, the linewidth enhancement factor can be written entirely in terms of the differential gain spectrum, =
dXr/dN
we =d/d---N
47r dn/dN A d-yet/dN
-
4cfj(w'2
A
-
w 2)-(dnet(W')/dN)dw' (dynet(w)/dN)
,
(1)
where N is the carrier density and w is the photon energy. Whereas dn/dN (and hence atwe) vanishes near the peak of the differential gain spectrum, lasers operate at the frequency of the peak of the gain spectrum. In interband semiconductor lasers, unlike atomic lasers, the peak of the differential gain is shifted away from the peak of the gain due largely to the imbalance between conduction and valence band densities of states. [2] Because of this, semiconductor lasers typically have 'aLWE'S significantly different from zero. Typical values for near-infrared semiconductor lasers range from 2 - 6.[3] Three primary strategies have been employed for reducing the linewidth enhancement factor in near-infrared lasers.[2,4,5] The first is to reduce the imbalance between the conduction and valence band densities of states through the use of strain and quantum confinement. The second is to p-dope the active region, which helps to offset the density of states imbalance. Third, a distributed feedback grating (DFB) can be used to detune the lasing energy from the peak of the gain towards the peak of the differential gain. The amount of detuning that can be used is limited by the range of energies over which there is positive gain. When the peak of the differential gain spectrum lies in the region of positive gain, it is possi
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