# Digitally Chirped Multilayer Quantum Dot Lasers with Dual-Wavelength Lasing Emissions
## 1 Introduction  
Quantum dot (QD) heterostructures based on self-assembled growth are developed as ultimate control of free carriers over the nanometer scale in three dimensions. Semiconductor gain elements incorporating QD heterostructure have been emerging since the early 1990s [1]. The limited QD density and dispersed QD size render the optical gain characteristics quite different from quantum well (QW) heterostructure. At first, multiple QD layers were grown to prevent gain saturation in high modal gain devices of short cavity edge emitting lasers [2] and vertical cavity surface emitting lasers [3]. Then, Chirped QD multilayers were designed to achieve a wide emission spectrum in suplerluminescent diodes [4] and broadband laser diodes [5; 6]. Afterwards, chirped QD multilayers found novel applications in external-cavity QD lasers, mode-locked QD lasers, and dual-wavelength QD lasers [7; 8; 9; 10].  
The emission spectral range and luminescent peak of InAs QDs are quite sensitive to growth parameters as well as matrix materials. Stacking of multiple QD layers with different InAs monolayers in QDs is not practical as dot density and radiative efficiency are subject to large variation. To reproducibly control the gain bandwidth of chirped QD multilayers, it is preferred to vary either thickness or In composition of InGaAs matrix surrounding InAs QDs [6]. In practice, the emission wavelength of individual InAs/InGaAs QD layer is continuously chirped (CC) in multilayer QD (MQD) stacks and referred to as CC-MQD in short. However, the parameter of multilayer is neither fully exploited in experiments nor ingeniously introduced in simulation. We have patented the digitally chirped multilayer QD stacks, referred to as DC-MQD, by designing a plurality of QD emission wavelengths, each of which is stacked with different QD layer numbers [7]. The conventional multilayer QD stacks with uniform emission wavelength for individual QD layer are referred to as Uni-MQD.  
The features of DC-MQD gain media are in two folds. First, the chirped wavelengths are predetermined and clearly separated so that lasing wavelengths can be identified from different layers of QD stack. Second, the optical gain spectra can be engineered independently for individual wavelength through layer numbers. We have incorporated DC-MQD to develop novel devices of dual-wavelength QD edge emitting lasers with simultaneous two lasing wavelengths around threshold [8], low threshold current and widely tunable external cavity QD lasers [9], dual-wavelength and ground-state (GS) mode-locked QD lasers with a wide operation range [10].  
In this paper, QD edge emitters with dual-wavelength lasing emissions are revisited. The slope efficiency for individual lasing wavelength is investigated both experimentally and theoretically. This paper is organized as follows. Section 2 presented the wavelength-resolved light-current (L-I) characteristics of DC-MQD lasers. The device characteristics in DC-MQD lasers were discussed in comparison with those in Uni-MQD lasers. Theoretical model regarding to DC-MQD gain media is then constructed to simulate our experimental observation in Section 3. Section 4 summarizes and concludes this paper.