QUANTUM DOTS

50 Optics & Photonics News ■ December 2002

QUANTUM DOTSAnomalous Carrier-InducedDispersion in SemiconductorQuantum DotsH. C. Schneider,W.W. Chow, P. M. Smowton,E. J. Pearce and S.W. Koch

Improvements in sample quality are mo-tivating more detailed investigations of

the physics and applications of quantum-dot systems. It is now clear that the ideal-ized “atom-like” description used in earlypredictions of the benefits of quantumdots is not entirely accurate. Surprisingly,in some cases, the real quantum-dot sys-tem may be even more advantageous forlaser operation. This is what was found inrecent experimental and theoretical inves-tigations on the dispersive properties ofquantum-dot laser structures. The realpart of the optical susceptibility, which de-termines the carrier-induced refractive in-dex change �n, is important because itcontributes to the fundamental laserlinewidth, as well as to the noise proper-ties and achievable single-mode power ofquantum-dot lasers.

This past year, we reported a theoreticalstudy indicating that because of theCoulomb coupling between bound andcontinuum states, the dispersive behaviorof a quantum-dot active medium differsin several important aspects from that ex-pected from an “atom-like” quantum-dotpicture, as well as from that observed inbulk or quantum-well structures.1 Specifi-cally, the Coulomb renormalizations leadto a positive differential refractive index∂�n/∂N, where N is the carrier density,and consequently a negative linewidth en-hancement factor � at gain peak [see Fig. 1(a)]. In contrast, the “atom-like” picturepredicts that �n spectra for different carri-er density cross at the gain peak, so thatboth ∂�n/∂N and � vanish there. For bulkand quantum-well gain media, �n de-creases with carrier density whenever gainis present, so that � is always positive.

Since the direct measurement of the re-fractive index is very difficult, the theoret-ical predictions were verified indirectly byexperimentally examining the filamenta-tion tendency in quantum-dot lasers.2 Theexperiment was performed using quan-tum-dot lasers consisting of InGaAs quan-tum dots embedded in GaAs quantum-well layers. To remove any complicationscaused by thermally induced self focusing,

the devices were operated pulsed. Figure 1(b) shows the near-field lateral intensityprofile for currents from twice to eighttimes the threshold value. The curvesshow decreasing intensity variation, i.e.,decreasing filamentation, with increasingexcitation. The experimental result is con-sistent with a negative � factor, and showsthat the anomaly in the dispersive behav-ior of a quantum-dot structure eliminatesthe longstanding beam-filamentationproblem which now limits high-powersingle-mode operation in semiconductorlasers.

AcknowledgmentsThe authors acknowledge support fromthe U.S. Department of Energy under con-tract DE-AC04-94AL85000, the U.K. En-gineering and Physical Sciences ResearchCouncil, the CASE award from Bookham(formerly Marconi Optical Components)and the Max Planck Research Prize of theHumboldt Foundation and Max-PlanckSociety.

References1. H. C. Schneider,W.W. Chow and S.W. Koch, Phys.

Rev. B 66, 041310 (Rapid Communication), 2002.2. P. M. Smowton, E. J. Pearce, H. C. Schneider,W.W.

Chow and M. Hopkinson, App. Phys. Lett. 81, 3251,2002.

H. C. Schneider and W.W. Chow (wwchow@somnet.sandia.gov) are with the Semiconductor Materials andDevice Sciences Department, Sandia National Labo-ratories, Albuquerque, New Mexico. P. M. Smowtonand E. J. Pearce are with the Department of Physicsand Astronomy, Cardiff University, Cardiff, UnitedKingdom. S.W. Koch is with the Physics Departmentand Material Sciences Center, Philipps University,Marburg, Germany.

Figure 1. (a) Carrier-induced refractive indexchange vs. energy for carrier densities 6 �1011 cm-2

(dotted curve), 8 � 1011 cm-2 (dashed curve) and 1012 cm-2. Gain is present within the energy rangeplotted. E0 is the unexcited quantum dot ground-state resonance. (b) Line scan of intensity throughcenter of near-field image of InGaAs quantum-dotlaser for increasing current (300 to 1200 A cm-2),showing the increase in filament width with in-creasing excitation, consistent with the predictionof a positive ∂�n /∂N region in (a).

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