First principle modeling of optical power limiting materials

1. 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. Theoretical Chemistry, Department of Biotechnology, KTH, Stockholm 2004 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)

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. 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 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

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

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

19. sTPA = 3150 GM

20. Molecules containing one platinum atom aredenoted as monomers and those with two are denoted as dimers; the labelling of these compounds is (a) m, (b) M, and (c) D.

22. f ω ω 0 Theoretical Chemistry, Department of Biotechnology, KTH, Stockholm 2004 Quantum modeling of multi-photon excitations Two Photon Absorption (TPA) with Polarizable Continuum Model at the DFT level

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

24. Simulating the full Jablonski diagram Two-photon absorption Internal conversion Internal conversion Phosphorescence Triplet-triplet absorption Excited state absorption One-photon absorption Stimulated emission Three-photon absorption Characteristic times Intersystem crossing Internal conversion Fluorescence Singlet manifold S2 Triplet manifold ps T2 S1 ns - ms ps - ns T1 fs S0 ms - ms

25. 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 Playback