1736 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 20, NO. 20, OCTOBER 15, 2008 Frequency-Dependent Linewidth Enhancement Factor of Quantum-Dot Lasers Sven Gerhard, Christian Schilling, Florian Gerschütz, Marc Fischer, Johannes Koeth, Igor Krestnikov, Alexey Kovsh, Martin Kamp, Sven Höfling, Member, IEEE, and Alfred Forchel, Member, IEEE Abstract—We present detailed measurements of the linewidth enhancement factor (LEF) of a quantum-dot distributed-feedback laser emitting around 1.3 m above and below threshold. The above threshold method is based on the measurement of the frequency modulation and amplitude modulation response of the laser and shows significant dependence on modulation frequency. Drive current dependent measurements with both methods yield LEF values between 1 well below and 3 well above threshold, converging around 2 close to threshold. Index Terms—Distributed-feedback (DFB) laser, Henry-factor, linewidth enhancement factor (LEF), quantum-dot (QD) laser. I. INTRODUCTION C ONSIDERABLE progress has been made in the fabri- cation of semiconductor lasers based on self-assembled quantum dots (QDs) in recent years, and today’s QD devices exhibit distinct advantages over quantum-well lasers, such as low threshold current, high temperature stability, and high ma- terial gain [1], [2]. An additional important parameter is the linewidth enhancement factor (LEF) , which affects the chirp, the linewidth, and the sensitivity to external optical feedback, which are important characteristics in telecommunication ap- plications [3]. One of the main motivations for investigating the LEF of QD lasers is that a Kramers–Kronig transformation of the symmetric gain curve of an ideal zero-dimensional gain medium leads to . Published experimental values of the LEF of real devices, however, vary over a wide range and can even be influenced, e.g., by p-doping or laser design [3]–[5]. This is believed to be a consequence of the nonresonant carriers present in the barrier, the wetting layer (WL), and the excited states of the QDs, which are not contributing to the laser transi- tion [6]. The dynamic of these carriers between WL, barrier, and QDs is a particular property of self-assembled QDs and leads to a finite and a modulation-frequency-dependent LEF of QD lasers. Manuscript received May 7, 2008; revised July 1, 2008. First published Au- gust 22, 2008; current version published September 26, 2008. This work was supported by the State of Bavaria. S. Gerhard, C. Schilling, M. Kamp, S. Höfling, and A. Forchel are with Uni- versität Würzburg, Technische Physik, D-97074 Würzburg, Germany (e-mail: sven.gerhard@physik.uni-wuerzburg.de). F. Gerschütz, M. Fischer, and J. Koeth are with Nanoplus, Nanosys- tems and Technology GmbH, D-97218 Gerbrunn, Germany (e-mail: marc.fischer@nanoplus.com). I. Krestnikov and A. Kovsh are with Innolume GmbH, D-44263 Dortmund, Germany (e-mail: igor.krestnikov@innolume.com). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2008.2004675 Fig. 1. DFB laser emission spectrum. The inset shows power–current and voltage–current characteristics. In this letter, we present detailed studies of the LEF of 1.3- m distributed-feedback (DFB) lasers based on QDs. The LEF is measured both above and below threshold. The above-threshold technique is based on a measurement of the frequency modu- lation (FM) and amplitude modulation (AM) response of the modulated laser diode. Frequency and current dependence of the LEF are shown, and are in line with a recently published theory that takes the influence of the nonresonant carriers on the LEF into account [6]. II. CONTINUOUS-WAVE DEVICE PERFORMANCE In our experiments, DFB lasers with an active region con- sisting of a stack of ten InAs QD layers in InGaAs quantum wells were used. The cavity length was 900 m, the ridge width 2 m, and the facets were as-cleaved. Fig. 1 shows the single- mode emission spectrum nm with a sidemode sup- pression ratio of 39 dB at a drive current of 80 mA. The inset of Fig. 1 shows the power–current and voltage–cur- rent characteristic measured at room temperature. The threshold current of the device is 61 mA; the maximum output power is 7 mW per facet. III. METHODS FOR LEF MEASUREMENTS A. Analysis of the Amplified Spontaneous Emission (ASE) For measurements of the ASE spectra, the test laser was op- erated in pulsed mode (1.2% duty cycle) in order to prevent a thermally induced change of the refractive index. The mea- surements were performed with currents ranging well below to slightly below threshold. The output of the laser is fed into a spectrometer using a single-mode lensed fiber. The blueshift of the Fabry–Pérot (FP) modes with increasing current yields the 1041-1135/$25.00 © 2008 IEEE