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Kungl
Tekniska
Högskolan
First principle modeling of optical power
limiting materials
Patrick Norman and
Hans Ågren
November 22, 2004
Modeling of Multiphoton Absorption
• Electronic structure: Wave funtion and Density functional
theory
• Response Theory
• Relativistic theory
• Classical modeling of Maxwells equations
• Scale extensive modeling
• Few-state models
• Beyond electronic structure: Vibrational effects, solvent
effects, solid state effects
• Combined quantum classical modeling of pulse
propagation in non-linear media
Quantum modeling of multi-photon excitations
Response functions for various reference methods
•Hartree-Fock Self Consistent Field
(HF)
•Multiconfigurational Self Consistent Field
(MCSCF)
•Coupled Cluster
(CC)
•Density Functional Theory
(DFT)
Theoretical Chemistry, Department of Biotechnology, KTH,
Stockholm 2004
Dalton Response Toolbox
• Response order: zero-, linear-, quadratic-, cubic ...
Property order: 1, 2, 3, 4…
• Hole-particle expansion: STEX h{p}: TDA {hp}:
RPA
{hp}+{ph}: SOPPA {hhpp}+ {pphh} ...
• Reference state: SCF/MCSCF/CI: MP : Coupled Cluster: DFT ...
Coupled Cluster:CCS, CCSD, CCSD(T)...CC1,CC2,CC3..
DFT: Beyond-ALDA, ”all functionals”
DALTON
Quantum modeling of multi-photon excitations
Response Theory Approach: Based upon Ehrenfest’s theorem and perturbation
expansion we obtain response functions by solving systems of linear equations
•Explicit summation over excited states is effectively replaced by system of
equations
•Frequency independent and frequency dependent properties are treated on
equal footing
•Arbitrary property is obtained by appropriate choice of operators A,B,C and D
to the response function
•Easy to calculate residues of response functions → multiphoton absorption
•Applicable for large dimensional problems
Theoretical Chemistry, Department of Biotechnology, KTH,
Stockholm 2004
Property Toolbox
TPA
3PA
Aug-cc-pVTZ
S
TS
Three-Photon Absorption
S
S
DTT
Two-states model for asymmetrical molecule
Three-states model for symmetrical molecule
Two-states model
FewS
FewS
Two-photon absorption cross sections of multi-branched structures
s TPA = 3150 GM
Molecules containing one platinum
atom are denoted as monomers and
those with two are denoted as dimers;
the labelling of these compounds is
(a) m, (b) M, and (c) D.
Quantum modeling of multi-photon excitations
Two Photon Absorption (TPA) with
Polarizable Continuum Model at
the DFT level
ω
f
ω
0
Theoretical Chemistry, Department of Biotechnology, KTH,
Stockholm 2004
Charge-Transfer State Properties: solvent effects
R
N
N
Two-photon polymerization initiator
R
R=CH2CH2CH2CH3
Density difference between the
charge-transfer and ground states
In gas phase
In acetone solvent
Simulating the full Jablonski diagram
Singlet manifold
S2
S1
fs
S0
Two-photon
Internal
Phosphorescence
conversion
absorption
Triplet-triplet
Excited
One-photon
Stimulated
state
absorption
emission
absorption
Three-photon
Intersystem
Characteristic
Fluorescence
crossing
times
Triplet manifold
ps
T2
ns - ms
ps - ns
ms - ms
T1
Algorithm of the quest
Cross section
Transmission
Conversion
Wave equation
(Maxwell’s equations)
Nonlinear
polarization
Dipole moments
and energies
(ab initio)
Density matrix
(TD Schrödinger equation)
Relaxation
times
Some basic equations
Close to linear propagation of
a 880 nm pulse
t = 1 ps
I0 = 1 W/cm2
Close to linear propagation of
a 880 nm pulse
t = 1 ps
I0 = 1 W/cm2
Close to linear propagation of
a 880 nm pulse
t = 1 ps
I0 = 1 W/cm2
Nonlinear transmission versus
pulse duration and intensity
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