Photon-Driven Transport in Quantum Cascade Lasers Hyunyong Choi, - PowerPoint PPT Presentation

Photon-Driven Transport in Quantum Cascade Lasers Hyunyong Choi, Zong-Kwei Wu, and Theodore B. Norris Center for Ultrafast Optical Science, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-2099, USA Marcella Giovannini and Jérôme Faist Institute of Physics, University of Neuchatel, CH-2000, Switzerland Laurent Diehl and Federico Capasso School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA CLEO/QELS, May 8, 2007 University of Michigan

Motivations • Electron transport in presence of AC electromagnetic field – Modern semiconductor devices : transistors, laser diodes, detectors, etc. – Classical transport regime : drift-diffusion equations – Optical process is separate from electronic transport Excited state Excited state Ground state Ground state Electronic transport Optical process - Classical transport - Photon generation, detection, etc University of Michigan

Motivations • Quantum Cascade Lasers – A full quantum-transport system – Strong coupling between electron transport and intra-cavity photons University of Michigan

Gain recovery dynamics in QCLs • Our approaches : Time-resolved pump-probe by resonant perturbation – Degenerate mid-IR pump-probe (250 fs) pulses – Spectrum of mid-IR resonant with QCL emission wavelength 1.0 QCL resonant mid-IR pulse Intensity (a.u.) 0.5 0.0 4.5 5.0 5.5 6.0 Wavelength ( µ m) J. Faist et al. Nature, vol. 387, 1997 University of Michigan

Degenerate mid-IR Pump-Probe Differential-Transmission Spectroscopy Ti:Sapphire D ifference O ptical Regen erative F requency P arametric Amplifier G enerator A mplifier Delay stage Seed Idler Pump Signal λ DFG =2.5-8.5 µ m λ sig =1.2-1.4 µ m Rep. Rate=250kHz Tuned to 5.3 µ m λ idlr =2.4-1.8 µ m Power=1.4W Pulse width=100fs Probe Pump Lock-in Amplifier QCL Half-wave plate Polarizer Computer InSb Detector QCL is Operating 10um pin-hole Pump (800 pJ) Probe (40 pJ) QCL below or above threshold Polarizer University of Michigan

Gain Recovery Dynamics at 30 K J, � SL N-432 n 2 Transmission changes (%) � 2 0.0 n 2 0.645 A -0.5 n 1 � 1 J, � SL n 1 -1.0 n SL n SL superlattice 0.0 0.625 A -0.5 transmission (%) -1.0 0.0 Normalized 0.635 A 0.0 rate equation -0.5 0.4 A -0.5 -1.0 -1.0 0 5 10 15 20 25 0 5 10 15 20 25 Pump-probe delay (ps) Pump-probe delay (ps) • Bias-dependent recovery: 3 time-constants are observed. – 0.7 0.7 ps ps, 2 , 2 ps ps, and 20 , and 20- -50 50 ps ps recovery recovery – • 3- -level rate equation level rate equation: directly following the QCL level diagram • 3 – Used to model steady-state L-I curve (self-consistent picture) – Excellent agreement within 0.03 % DT noise level University of Michigan

3-Level Rate-Equation Model ⎡ ⎤ dS 1 n = Γ − − + β ⎢ ⎥ 2 N v g ( n n ) S N τ τ p P g c 2 1 p ⎢ ⎥ dt ⎣ ⎦ p sp Upper lasing state dn n n = − − Γ − 2 SL 2 v g ( n n ) S n 2 τ τ P g c 2 1 dt 2 SL Lower lasing state dn n n = − + Γ − n 1 1 2 1 v g ( n n ) S τ τ P g c 2 1 dt 2 1 n SL dn n n Superlattice state = − SL 1 SL τ τ dt 1 SL University of Michigan

Relaxation Dynamics in Energy Level Level density (a.u.) population inversion upper lasing state lower lasing state upper-lasing superlattice state lower-lasing superlattice 0 5 10 15 20 25 Pump-probe delay (ps) • 3 Recovery Components from rate- -equation model equation model • 3 Recovery Components from rate – Upper-lasing state : 20-50 ps, phonon-limited lifetime (below th) – Lower-lasing state : ~ 1 ps, emptying via tunneling – Superlattice transport : coupling with adjacent active region University of Michigan

Dynamics of the Upper-Lasing State N-432 N-433 Upper lasing state lifetime τ (ps) Upper lasing state lifetime τ (ps) 100 100 DT measurement 80 80 2 2 60 60 40 40 20 20 10 10 8 8 6 6 4 4 2 2 1 1 0.4 0.6 0.8 0.3 0.6 0.9 Current (A) Current (A) University of Michigan

Dynamics of the Upper-Lasing State N-432 N-433 Upper lasing state lifetime τ (ps) Upper lasing state lifetime τ (ps) 100 100 DT measurement 80 80 2 2 60 60 40 40 Phonon-limited relaxation (non-radiative lifetime) 20 20 10 10 8 8 6 6 4 4 2 2 1 1 0.4 0.6 0.8 0.3 0.6 0.9 Current (A) Current (A) University of Michigan

Dynamics of the Upper-Lasing State N-432 N-433 Upper lasing state lifetime τ (ps) Upper lasing state lifetime τ (ps) 100 100 DT measurement 80 80 2 2 60 60 40 40 Phonon-limited relaxation (non-radiative lifetime) 20 20 Current-continuity equation 10 10 (non-radiative lifetime) 8 8 6 6 4 4 2 2 1 1 0.4 0.6 0.8 0.3 0.6 0.9 Current (A) Current (A) University of Michigan

Dynamics of the Upper-Lasing State N-432 N-433 Upper lasing state lifetime τ (ps) Upper lasing state lifetime τ (ps) 100 100 DT measurement 80 80 2 2 60 60 40 40 Phonon-limited relaxation (non-radiative lifetime) 20 20 Current-continuity equation 10 10 (non-radiative lifetime) 8 8 6 6 4 4 Stimulated emission rate 1 (Photon-density via rate-eq) 2 2 1 1 0.4 0.6 0.8 0.3 0.6 0.9 Current (A) Current (A) University of Michigan

Dynamics of the Upper-Lasing State N-432 N-433 Upper lasing state lifetime τ 2 (ps) Upper lasing state lifetime τ 2 (ps) 100 100 DT measurement 80 80 60 60 40 40 Phonon-limited relaxation (non-radiative lifetime) 20 20 Current-continuity equation 10 10 (non-radiative lifetime) 8 8 6 6 4 4 Stimulated emission rate 1 (Photon-density via rate-eq) 2 2 Stimulated emission rate 2 1 1 0.4 0.6 0.8 0.3 0.6 0.9 (Photon-density via L-I curve) Current (A) Current (A) ps � � few • Remarkable speed- -up of the gain recovery (50 up of the gain recovery (50 ps few ps ps) ) • Remarkable speed – Near threshold : # of intra-cavity photon density (a few hundred) – Electron transport is driven by quantum stimulated emission ! University of Michigan

University of Michigan miniband Intra-Cavity Photon-Driven Transport miniband miniband

Atomic, Solid-State, Interband Diode Lasers vs. Quantum Cascade Lasers J, � SL n 4 n 2 � 4 n 3 � 2 3 pump � 3 n 1 2 � 1 n 2 � 2 J, � SL n SL superlattice 1 ground n 1 Density (a.u.) Density (a.u.) Population inversion population inversion Upper lasing state upper lasing state Lower lasing state lower lasing state Ground state superlattice state 0 100 200 300 400 500 0 5 10 15 20 25 Pump-probe delay (ps) Pump-probe delay (ps) • Closed- - or open or open- -system gain system gain- -recovery dynamics recovery dynamics • Closed – Transport delay : no analogues in any laser systems. Large spontaneous emission factor in QCL: 10 -2 ~ 10 -3 – University of Michigan

Other Recovery Components Lower lasing state lifetime τ 1 (ps) Lower lasing state lifetime τ 1 (ps) 2.5 2.5 N-432 Superlattice transport τ SL (ps) Superlattice transport τ SL (ps) N-433 2.0 2.0 τ SL τ SL 1.5 1.5 1.0 1.0 τ 1 τ 1 0.5 0.5 superlattice state 0.0 0.0 0.4 0.5 0.6 0.7 0.4 0.6 0.8 Current (A) Current (A) • Two other recovery dynamics • Two other recovery dynamics – Lower-lasing state: emptying via scattering assisted tunneling – Superlattice state: analogue to dielectirc relaxation University of Michigan

Dynamics of the Lower-Lasing State Tunneling time 4 10 ⎛ ⎞ 1 1 3 Ω ⎜ ⎟ 2 ⎜ ⎟ 10 τ R Tunneling time (ps) ⎝ ⎠ 2 1 = ⊥ 2 τ 10 2 ⎛ ⎞ ⎛ ∆ 2 ⎞ 1 E 1 ⎜ ⎟ + ⎜ ⎟ 1 ⎜ ⎟ 1400 τ η ⎝ ⎠ 10 ⎝ ⎠ ⊥ 0 ↓ T 2 = 10 fs 10 1200 -1 ↓ T 2 = 100 fs 10 -2 10 1000 -3 10 0 2 4 6 8 10 12 14 16 18 20 Energy (meV) 800 Anti-crossing energy (meV) 600 Electron-polar-optical-phonon scattering Phonon emission rate (ps) 2.5 1/ τ 76, phonon 1/ τ 400 65, phonon 1/ τ 54, phonon 2 -1 200 1.5 1 0 100 200 300 400 500 600 700 800 900 Length (Angstrom) 0.5 0 0 10 20 30 40 50 60 70 80 90 100 Energy (meV) University of Michigan

Dynamics of the Superlattice State Dielectric relaxation in superlattice Superlattice Miniband 600 500 Upper Superlattice 400 τ Lower Energy (meV) 300 SL 200 d 100 Monte-Carlo Simulation 0 - Scattering : intersubband optical-phonon scattering -100 500 550 600 650 700 750 800 850 900 - Can include impurity and Auger-type e-e scattering Length (Angstrom) - Back-scattering : � if � exp(- Δ /kT) - In progress… • Inverse bias- -dependence dependence • Inverse bias – Observed in a various QC structures – Transport channel between active regions University of Michigan

Summary • Electronic transport in presence of oscillating electromagnetic fields • Femtosecond time-resolved QCL gain recovery dynamics – Upper-lasing state, lower-lasing state, superlattice dynamics • Electronic transport is driven by Intra-cavity photon density University of Michigan