Gain Recovery Dynamics and Photon-Driven Transport in Quantum Cascade Lasers

Hyunyong Choi, Laurent Diehl, Zong-Kwei Wu, Marcella Giovannini, Jérôme Faist, Federico Capasso, and Theodore B. Norris

Phys. Rev. Lett. 100, 167401 – Published 24 April 2008

Abstract

Quantum cascade lasers are semiconductor devices based on the interplay of perpendicular transport through the heterostructure and the intracavity lasing field. We employ femtosecond time-resolved pump-probe measurements to investigate the nature of the transport through the laser structure via the dynamics of the gain. The gain recovery is determined by the time-dependent transport of electrons through both the active regions and the superlattice regions connecting them. As the laser approaches and exceeds threshold, the component of the gain recovery due to the nonzero lifetime of the upper lasing state in the active region shows a dramatic reduction due to the onset of quantum stimulated emission; the drift of the electrons is thus driven by the cavity photon density. The gain recovery is qualitatively different from that in conventional lasers due to the superlattice transport in the cascade.

Received 12 May 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.167401

Authors & Affiliations

Hyunyong Choi¹, Laurent Diehl², Zong-Kwei Wu¹, Marcella Giovannini³, Jérôme Faist³, Federico Capasso², and Theodore B. Norris¹

¹Center for Ultrafast Optical Science and Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109-2099, USA
²School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
³Institute of Physics, University of Neuchâtel, CH-2000 Neuchâtel, Switzerland

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Vol. 100, Iss. 16 — 25 April 2008

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Images

Figure 1
Self-consistent band structure calculation of the ${In}_{0.6} {Ga}_{0.4} As / {In}_{0.44} {Al}_{0.56} As$ strained layers for two periods of the cascade heterostructure (N-432). Layer thicknesses are given in nm. The wave functions for the upper (level 2) and lower lasing state (level 1) are shown, illustrating the diagonal nature of the transition in real space. The wavy arrow indicates the lasing transition. The miniband is indicated by the shaded gray region. The horizontal segments show the doped region for each period; $N$ is the donor density. Another QCL sample used in this experiment (N-433) with slightly different design parameters shows similar laser performance.Reuse & Permissions
Figure 2
(a) Bias-dependent DT measurements of the gain recovery at 30 K for QCL from N-432. Carrier heating via TE-pump/TM-probe DT measurement is experimentally shown to be negligible. (b) Three-level rate-equation simulation of the population dynamics of upper state, lower state, and superlattice state (upper panel) and a fit to the the normalized DT signal at 0.635 A (lower panel) are displayed.Reuse & Permissions
Figure 3
Bias-dependent level-2 lifetime $τ_{2}$ is shown for N-432 in (a) and N-433 in (b) (threshold is indicated by the red tick mark). The filled squares are $τ_{2}$ obtained from rate-equation fits to the gain recovery DT data. The red solid lines in (a) and (b) are $τ_{2}$ due to optical-phonon scattering calculated using the bias-dependent wave functions; the errors obtained by assuming monolayer fluctuations of the barrier width are around 10 ps. The filled circles are an estimate of the level-2 lifetime using $J = e N / τ_{2}$ and assuming the level-2 population $N$ is simply the doping density. The vertical blue, black lines in (a) and blue, green lines in (b) are explained in the text. (c) Steady-state rate-equation fits (dashed line) to the measured $L − I$ curves (solid lines) are displayed. Black and green color are for N-432 and N-433, respectively. The only free parameter required to fit the $L − I$ curves with the rate-equation model is the $β$ factor.Reuse & Permissions
Figure 4
(a) Extracted time constants for N-432 from the rate-equation fit. $τ_{1}$ is the level-1 lifetime (red), and $τ_{SL}$ is the time constant of gain recovery due to the superlattice transport (blue), as explained in the text. (b) Extracted time constants for N-433. $τ_{1}$ and $τ_{SL}$ have same meaning as in (a). The error bars are determined from the chi-square values obtained in the rate-equation fit.Reuse & Permissions

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