1. Patrick Norman and Hans Ågren
Kungl
Tekniska
Högskolan
First principle modeling of optical power limiting materials
Patrick Norman and Hans Ågren
November 22, 2004

2. 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

3. 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

4. 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

5. 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

6. Property Toolbox magnetic internal external electric linear time-dep
nonlinear
time-dep
Time-indep

12. TPA
3PA
Aug-cc-pVTZ

13. Three-Photon Absorption
DTT TS

14. Two-states model for asymmetrical molecule
Three-states model for symmetrical molecule
Two-states model

16. FewS

17. Two-photon absorption cross sections of multi-branched structures

19. s TPA = 3150 GM

20. 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.

22. Quantum modeling of multi-photon excitations
Two Photon Absorption (TPA) with Polarizable Continuum Model at the DFT level ω f
Theoretical Chemistry, Department of Biotechnology, KTH,
Stockholm 2004

23. In gas phase In acetone solvent
Charge-Transfer State Properties: solvent effects
Two-photon polymerization initiator
Density difference between the
charge-transfer and ground states
In gas phase
In acetone solvent

24. Simulating the full Jablonski diagram
Triplet-triplet absorption
Three-photon absorption
Excited state absorption
Two-photon absorption
One-photon absorption
Characteristic times
Intersystem crossing
Internal conversion
Stimulated emission
Internal conversion
Internal conversion
Phosphorescence
Fluorescence
Singlet manifold S2
Triplet manifold ps T2 S1
ns - ms
One-, two- and tree-photon absorption; stimulated emission; intersystem crossing; triplet-triplet absorption;
phosphorescence; fluorescence; internal conversion. fs
ps - ns T1 S0
ms - ms

25. (TD Schrödinger equation)
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

26. Some basic equations

28. Close to linear propagation of a 880 nm pulse
t = 1 ps
I0 = 1 W/cm2

29. Close to linear propagation of a 880 nm pulse
t = 1 ps
I0 = 1 W/cm2

30. Close to linear propagation of a 880 nm pulse
t = 1 ps
I0 = 1 W/cm2

31. Nonlinear transmission versus pulse duration and intensity
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