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

▶
photon driven transport in quantum cascade lasers
SMART_READER_LITE
LIVE PREVIEW

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

Apr 12, 2023 508 likes •706 views

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

slide-1
SLIDE 1

University of Michigan

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

slide-2
SLIDE 2

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 Ground state Excited state Ground state

Electronic transport Optical process

  • Classical transport
  • Photon generation, detection, etc
slide-3
SLIDE 3

University of Michigan

Motivations

  • Quantum Cascade Lasers

– A full quantum-transport system – Strong coupling between electron transport and intra-cavity photons

slide-4
SLIDE 4

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

4.5 5.0 5.5 6.0 0.0 0.5 1.0

Intensity (a.u.) Wavelength (µm)

QCL

resonant mid-IR pulse

  • J. Faist et al. Nature, vol. 387, 1997
slide-5
SLIDE 5

University of Michigan

Degenerate mid-IR Pump-Probe Differential-Transmission Spectroscopy

Polarizer

QCL below or above threshold

Polarizer

QCL is Operating

Pump (800 pJ) Probe (40 pJ)

Difference Frequency Generator λDFG=2.5-8.5µm Tuned to 5.3 µm Ti:Sapphire Regenerative Amplifier

  • Rep. Rate=250kHz

Power=1.4W Pulse width=100fs Optical Parametric Amplifier λsig=1.2-1.4µm λidlr=2.4-1.8µm

Signal Idler Pump Seed

Lock-in Amplifier InSb Detector

Half-wave plate

Probe Pump Delay stage

Computer

QCL

10um pin-hole

slide-6
SLIDE 6

University of Michigan

Gain Recovery Dynamics at 30 K

5 10 15 20 25

  • 1.0
  • 0.5

0.0

Normalized transmission (%)

Pump-probe delay (ps) 0.635 A rate equation n2 n1 nSL superlattice 2 J, SL 1 J, SL n2 n1 nSL

  • 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

3-

  • level rate equation

level rate equation: directly following the QCL level diagram

– Used to model steady-state L-I curve (self-consistent picture) – Excellent agreement within 0.03 % DT noise level

5 10 15 20 25

  • 1.0
  • 0.5

0.0

Pump-probe delay (ps)

  • 1.0
  • 0.5

0.0

Transmission changes (%)

  • 1.0
  • 0.5

0.0

0.645 A 0.625 A 0.4 A

N-432

slide-7
SLIDE 7

University of Michigan

3-Level Rate-Equation Model

SL SL SL c g P c g P SL SL sp p p c g P p

n n dt dn S n n g v n n dt dn S n n g v n n dt dn n N S n n g v N dt dS τ τ τ τ τ τ τ β τ − = − Γ + − = − Γ − − = + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − − Γ =

1 1 1 2 1 1 2 2 1 1 2 2 2 2 2 1 2

) ( ) ( 1 ) (

Upper lasing state Lower lasing state Superlattice state

n2 n1 nSL

slide-8
SLIDE 8

University of Michigan

Relaxation Dynamics in Energy Level

5 10 15 20 25

Pump-probe delay (ps)

upper lasing state lower lasing state superlattice state

Level density (a.u.)

upper-lasing lower-lasing superlattice

population inversion

  • 3 Recovery Components from rate

3 Recovery Components from rate-

  • equation model

equation model

– 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

slide-9
SLIDE 9

University of Michigan

Dynamics of the Upper-Lasing State

0.4 0.6 0.8 1 2 4 6 8 10 20 40 80 100 60

Upper lasing state lifetime τ (ps) Current (A)

0.3 0.6 0.9 1 2 4 6 8 10 20 40 80 100

2

60

Upper lasing state lifetime τ (ps) Current (A)

N-432 N-433

DT measurement

2

slide-10
SLIDE 10

University of Michigan

Dynamics of the Upper-Lasing State

0.4 0.6 0.8 1 2 4 6 8 10 20 40 80 100 60

Upper lasing state lifetime τ (ps) Current (A)

0.3 0.6 0.9 1 2 4 6 8 10 20 40 80 100

2

60

Upper lasing state lifetime τ (ps) Current (A)

N-432 N-433

DT measurement Phonon-limited relaxation (non-radiative lifetime)

2

slide-11
SLIDE 11

University of Michigan

Dynamics of the Upper-Lasing State

0.4 0.6 0.8 1 2 4 6 8 10 20 40 80 100 60

Upper lasing state lifetime τ (ps) Current (A)

0.3 0.6 0.9 1 2 4 6 8 10 20 40 80 100

2

60

Upper lasing state lifetime τ (ps) Current (A)

N-432 N-433

DT measurement Phonon-limited relaxation (non-radiative lifetime) Current-continuity equation (non-radiative lifetime)

2

slide-12
SLIDE 12

University of Michigan

Dynamics of the Upper-Lasing State

0.4 0.6 0.8 1 2 4 6 8 10 20 40 80 100 60

Upper lasing state lifetime τ (ps) Current (A)

0.3 0.6 0.9 1 2 4 6 8 10 20 40 80 100

2

60

Upper lasing state lifetime τ (ps) Current (A)

N-432 N-433

DT measurement Phonon-limited relaxation (non-radiative lifetime) Current-continuity equation (non-radiative lifetime) Stimulated emission rate 1 (Photon-density via rate-eq)

2

slide-13
SLIDE 13

University of Michigan

Dynamics of the Upper-Lasing State

0.4 0.6 0.8 1 2 4 6 8 10 20 40 60 80 100

Upper lasing state lifetime τ2 (ps) Current (A)

0.3 0.6 0.9 1 2 4 6 8 10 20 40 60 80 100

Upper lasing state lifetime τ2 (ps) Current (A)

DT measurement Phonon-limited relaxation (non-radiative lifetime) Current-continuity equation (non-radiative lifetime) Stimulated emission rate 1 (Photon-density via rate-eq) Stimulated emission rate 2 (Photon-density via L-I curve)

  • Remarkable speed

Remarkable speed-

  • up of the gain recovery (50

up of the gain recovery (50 ps ps few few ps ps) )

– Near threshold : # of intra-cavity photon density (a few hundred) – Electron transport is driven by quantum stimulated emission !

N-432 N-433

slide-14
SLIDE 14

University of Michigan

Intra-Cavity Photon-Driven Transport

miniband miniband miniband

slide-15
SLIDE 15

University of Michigan

Atomic, Solid-State, Interband Diode Lasers

  • vs. Quantum Cascade Lasers

100 200 300 400 500

Density (a.u.) Pump-probe delay (ps)

Population inversion Upper lasing state Lower lasing state Ground state

  • Closed

Closed-

  • or open
  • r open-
  • system gain

system gain-

  • recovery dynamics

recovery dynamics

– Transport delay : no analogues in any laser systems. – Large spontaneous emission factor in QCL: 10-2 ~ 10-3

n3 n2 n1 ground

3

2

n4

pump

4

3

2

1

n2 n1 nSL superlattice 2 J, SL 1 J, SL

5 10 15 20 25

Density (a.u.) Pump-probe delay (ps)

population inversion upper lasing state lower lasing state superlattice state

slide-16
SLIDE 16

University of Michigan

Other Recovery Components

0.4 0.5 0.6 0.7 0.0 0.5 1.0 1.5 2.0 2.5

τSL τ1 τSL τ1

Superlattice transport τSL (ps) Lower lasing state lifetime τ1 (ps) Current (A)

N-432 0.4 0.6 0.8 0.0 0.5 1.0 1.5 2.0 2.5

Superlattice transport τSL (ps) Lower lasing state lifetime τ1 (ps) Current (A)

N-433

superlattice state

  • Two other recovery dynamics

Two other recovery dynamics

– Lower-lasing state: emptying via scattering assisted tunneling – Superlattice state: analogue to dielectirc relaxation

slide-17
SLIDE 17

University of Michigan

Dynamics of the Lower-Lasing State

Tunneling time

2 2 2 1

1 1 2 1 1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∆ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Ω =

⊥ ⊥

η E

R

τ τ τ

2 4 6 8 10 12 14 16 18 20 10

  • 3

10

  • 2

10

  • 1

10 10

1

10

2

10

3

10

4

↓T2 = 10 fs ↓T2= 100 fs

Anti-crossing energy (meV) Tunneling time (ps) Electron-polar-optical-phonon scattering

10 20 30 40 50 60 70 80 90 100 0.5 1 1.5 2 2.5

Energy (meV) Phonon emission rate (ps)

  • 1

1/τ

76, phonon

1/τ

65, phonon

1/τ

54, phonon

100 200 300 400 500 600 700 800 900 200 400 600 800 1000 1200 1400 Length (Angstrom) Energy (meV)

slide-18
SLIDE 18

University of Michigan

Dynamics of the Superlattice State

Dielectric relaxation in superlattice

500 550 600 650 700 750 800 850 900

  • 100

100 200 300 400 500 600 Length (Angstrom) Energy (meV)

Superlattice Miniband

Upper

SL

τ

Superlattice

d

Lower Monte-Carlo Simulation

  • Scattering : intersubband optical-phonon scattering
  • Can include impurity and Auger-type e-e scattering
  • Back-scattering : ifexp(-Δ/kT)
  • In progress…
  • Inverse bias

Inverse bias-

  • dependence

dependence

– Observed in a various QC structures – Transport channel between active regions

slide-19
SLIDE 19

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