1. Gain Spectra in Photoexcited T-Shaped Quantum Wires
Nov. 15, 2005
Gain Spectra in Photoexcited
T-Shaped Quantum Wires
Ping Akiyama Lab

2. Problems to Solve Gain Spectra of Quantum Wires with Many-body effect
Realistic quantum confinement
Coupling to waveguide or cavity
Difference between Hartree-Fock and Free Electron Theory (Asada, Miyamoto, Suematsu)?
Effect of 1d DOS
Gain peak intensity, width, and position vs. carrier density and damping

3. Modal Gain of Single Quantum Wire
in a Waveguide
cgs Lx Ly Lz lx ly
Integration in both sides
G ->2 ×2 × g
spin
Confinement factor

4. Optical Properties of 2-Band Model
Dk : Band Gap Renormalization (BGR)
Conduction e
Eb : Exciton Binding Energy Dk
Absorption
without Coulomb
hw =Eg0+ee,k+eh,k Eb
Absorption
with Coulomb
hw =Eg0+ee,k+eh,k-Dk-Eb
Eg0
exciton h
Ẽ=Ẽ0exp(-iwt)
Heavy Hole
Dipole moment

5. Thermal Fermi Distribution
FE and HF Theory
Thermal Fermi Distribution
ne,k = fe,k nh,k = fh,k
Quasi-Equilibrium Condition
Free Electron (FE)
Hartree-Fock (HF)
Space-Filling factor : 1-fe,k-fh,k (FE and HF)
Band Gap Renormalization (BGR) : Dk (HF)
Exciton binding energy

6. Gain/Absorption CalculationFE HF
Parameters:
Finite width: g
(Å)

7. Coulomb Potentials in T-Shaped Quantum Wires
Arm Well
Stem Well
Quantum Wire
AlxGa1-xAs
Ground State
(Lx=Ly=0.5a0)
Confinement Potential Lｘ Lｙ
Long wavelength limit
ka0 <<1
Short wavelength limit
ka0 >>1

8. Gain Spectra in T-Shaped Quantum Wires
Unit of energy E0=4.2meV
(1a)
(1b)
In room temperature:
gain
High carrier density:
HF: broad gain peak, red shift (BGR), low gain peak
FE: sharp gain peak, no shift
density
Low carrier density:
HF: strong absorption peak (exciton)
FE: broad absorption (1d DOS)
absorption

9. Gain Spectra in Rectangular Quantum WireLz Ly Lx

10. Gain Peak Vs. Carrier Density
HF:
Lower gain peak in high density.
Lower transparency density, but smaller slope dG/dN.
FE:
Higher gain peak in high density.
higher transparency density, larger slope.

11. Gain Peak Vs. Damping Gain peak intensity HF: insensitive to g
FE: very sensitive to g
HF theory predicts large gain in room temperature (g=4.2meV)

12. Summary & Discussion
Coulomb interaction has strong effect on gain spectra.
HF theory predicts (vs. FE):
Sharp exciton peak in case of low carrier density.
Lower transparent density.
Lower & broad gain peak.
gain peak insensitive to damping.
Dipole moment relation to polarization.
Temperature dependence needs to be clarified.
Plasma screening of Coulomb interaction.
Dynamical screening of Coulomb interaction.