Patrick Norman and Hans Ågren 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 magnetic internal external electric linear time-dep nonlinear time-dep Time-indep

TPA 3PA Aug-cc-pVTZ

Three-Photon Absorption DTT TS

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

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 Theoretical Chemistry, Department of Biotechnology, KTH, Stockholm 2004

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

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

(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

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