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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 Playback