t. meier, b. pasenow, m. reichelt, t. stroucken, p. thomas, and …cophen04/talks/meier.pdf ·...
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Optical Properties of Semiconductor Photonic-Crystal Structures
T. Meier, B. Pasenow, M. Reichelt, T. Stroucken, P. Thomas, and S.W. Koch
Department of Physics and Material Sciences Center,Philipps-University Marburg, Germany
http://www.physik.uni-marburg.de/~meier/
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Photonic crystals and semiconductorsPhotonic crystals
• 1D, 2D, 3D
• photonic bandstructure
• light propagation,nonlinearities, …
Semiconductors and heterostructures
• bulk and quantum wells, wires, dots
• electronic bandstructure andconfinement
• Coulomb interaction important for optical properties (excitons, etc.)
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Outline
Brief description of theoretical approach
Influence of modified transverse fields
• consequences of inhibited spontaneous emission• changes of exciton statistics and photoluminescence
Influence of modified longitudinal fields
• dielectric shifts result in spatially inhomogeneous band gap,exciton binding energy, and carrier occupations
• wave packet dynamics
Self-consistent solutions of Maxwell-Bloch equations
• enhanced light-matter interaction due to light concentration• strongly increased absorption and gain
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-
--
Interband-Polarisation
k
E c
v
++
Lichtfeld
- - -
light field
Interband polarization
Electron-hole attraction⇒ hydrogenic series of
exciton resonancesbelow band gap
Photoexcited semiconductors
energy
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Theoretical description of semiconductor optics
many-particleinteraction
Vq
interband excitationk
E c
v
minimal Hamiltonian
single-particle states
Coulomb interaction introduces many-body problem⇒ Consistent approximations required: Hartree-Fock,
second Born, dynamics-controlled truncation, cluster expansion,...
cv
.
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Equations of motion and light-matter interaction
• Maxwell equation
• semiclassical equations of motion for material excitations(density matrix): semiconductor Bloch equations
• material response described by
and similar equations for carrier occupations and
=Coulomb renormalization scattering
andcorrelations
phase space filling
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Theoretical description of semiconductor optics
• classical light field:
semiconductor Bloch equations + Maxwell’s equations
• quantized light field:
semiconductor luminescence equations= coupled dynamics of material and light-field modes
including photon-assisted density matrices
⇒ Consistent solution of coupled dynamics of light and material system
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Influence of transverse fields on semiconductor optics
Exciton resonance lies in a photonic band gap
Tra
nsm
issi
on Absorption
Energy
Model study of exciton formation after injection ofthermal electrons and holes in the bands:
Quantum wire in a photonic crystal.
Lowest exciton level lies inside photonic band gap (modeled by reduced recombination).
Solution of semiconductor luminescence equations.
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Exciton distribution in quantum wire
• T = 10 K, strong vs. weak recombination(free space) (1/100 due to photonic band-gap)
• strong depletion of q = 0 excitons in free space• overall shape NOT Bose-Einstein distribution• resulting influence on photoluminescence
Phys. Rev. Lett. 87, 176401 (2001)
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• 2D photonic crystal (air cylinderssurrounded by dielectric medium)
• cap layer• semiconductor quantum well
• ellipsoidal shape ofcylinder bottom
Influence of longitudinal fields on semiconductor optics
model system
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Influence of longitudinal fields on semiconductor optics
longitudinal part: generalized Poisson equation
generalized Coulomb potential VC
solution for piecewise constant ε(r)
J. Opt. Soc. Am. B 19, 2292 (2002)
⇒ near a periodically structured dielectricthe Coulomb potential varies periodically in space
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• position-dependent band gap:biggest increase underneath center of the air cylinders
Corrections due to generalized Coulomb potential
• position-dependent electron-hole attraction: strongest underneathcenter of the air cylinders
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Excitons in photonic crystals
⇒ spatial variation of band gap ( ∼ 4EB) and exciton binding energy ( ∼ 2.5 EB)with periodicity of photonic crystal
numerically calculated absorption spectra for fixed c.o.m. positions
Appl. Phys. Lett. 82, 355 (2003)
-4 -2 0 2 40.0
0.2
0.4
0.6
Im χ
(arb
.uni
ts)
E-Egap
(EB)
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Spectrally selective excitation
-4 -2 0 2 40.0
0.2
0.4
0.6
Im χ
(arb
.uni
ts)
E-Egap
(EB)
⇒ energetically lowest (highest) excitation in between (underneath) air cylinders
phys. stat. sol. (b) 238, 439 (2003)
⇒ spatially inhomogeneous carrier occupationsexcited by spectrally-narrow andspatially-homogeneous pulses
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Excitons in photonic crystals II
Quantum wires underneath one-dimensional ridges of dielectric material
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⇒ variety of inhomogeneous excitons
Excitons in photonic crystals II
⇒ spectrally selective excitation leads to spatiallyinhomogeneous carrier distributions
fe
Quantum wires underneath one-dimensional ridges of dielectric material
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Coherent wave packet dynamics
Spectrally selective excitation in quantum wire,relaxation modeled by T1 time (4ps)
⇒ spatially inhomogeneous carrier occupations evolve in timedue to wave packet dynamics
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Solution of Maxwell-Bloch equations
• 2D array of dielectric cylinders surrounded by air
• Cylinders filled with thin semiconductor quantum wire
• Incoming plane wave polarized in direction of wires
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Optical spectra of photonic crystal
⇒ photonic bandstructure leads to frequency dependence ⇒ transmission vanishes in photonic band gap
(E-E ) [E ]G B
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Optical spectra
⇒ photonic bandstructure modifies absorption spectrum
(E-E ) [E ]G B
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Absorption spectra
⇒ strongly enhanced absorption
(E-E ) [E ]G B
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Field concentration
⇒ field concentrates in dielectric cylinders
Pasenow, et al., to be published
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SummaryDue to inhibited spontaneous emission a photonic band gap strongly influences material properties
• exciton formation and statistics, and photoluminescence
Coulomb interaction is altered near a photonic crystal
• spatially-varying band gap and exciton binding energy
• wave packet dynamics
• spatially-inhomogeneous quasi-equilibrium carrier occupations
Light-matter interaction can be tailored
• enhanced absorption (and gain) due to light concentration
Outlook: self-consistent treatment oftransversal and longitudinal effects
• combining carrier and light concentration effects
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Interested in photonic crystals?
Activities of the groups funded by the DFG priority program“Photonic Crystals”are described in this book(published Spring 2004)
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Acknowledgments
Priority program “Photonic Crystals”
cpu-time on parallelsupercomputer
Interdisciplinary Research Center Optodynamics,Philipps University Marburg
Heisenberg fellowship (TM)