First principle modeling of optical power First principle modeling of optical power limiting materialslimiting materials

Patrick Norman and Hans Ågren

November 22, 2004

Kungl

Tekniska

Högskolan

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

Theoretical Chemistry, Department of Biotechnology, KTH, Stockholm 2004

•Hartree-Fock Self Consistent Field (HF)

•Multiconfigurational Self Consistent Field (MCSCF)

•Coupled Cluster (CC)

•Density Functional Theory (DFT)

Quantum modeling of multi-photon excitations

Response functions for various reference methods

Dalton Response Toolbox

• Response orderResponse order: zero-, linear-, quadratic-, cubic ... Property orderProperty order: 1, 2, 3, 4…

• Hole-particle expansionHole-particle expansion: STEX h{p}: TDA {hp}: RPA {hp}+{ph}: SOPPA {hhpp}+ {pphh} ...

• Reference stateReference state: SCF/MCSCF/CI: MP : Coupled Cluster: DFT ... Coupled Cluster:CCS, CCSD, CCSD(T)...CC1,CC2,CC3..

DFT: Beyond-ALDA, ”all functionals”

DALTON

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

•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

linearnonlinear

Property Toolbox

magnetic

electr

icinternal

external

time-dep

Time-indep

Aug-cc-pVTZ

3PA3PA

TPATPA

S

SS DTTTS Three-Photon AbsorptionThree-Photon Absorption

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

Two-states model

FewSFewSFewSFewS

Two-photon absorption cross sections of multi-branched structuresTwo-photon absorption cross sections of multi-branched structures

TPATPA = 3150 GM = 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.

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

ω

ωf

0

Charge-Transfer State Properties: solvent effectsCharge-Transfer State Properties: solvent effects

NN

R

R

R=CH2CH2CH2CH3

In gas phase

In acetone solvent

Two-photon polymerization initiator

Density difference between the

charge-transfer and ground states

Simulating the full Jablonski diagram

Singlet manifold

Triplet manifold

S0

S1

S2

T1

T2

fs

s - ms

ns - s

ps

One-photon absorptionTwo-photon absorptionThree-photon absorptionExcited state absorptionInternal conversionFluorescenceInternal conversionStimulated emissionInternal conversionIntersystem crossingTriplet-triplet absorptionPhosphorescenceCharacteristic times

ps - nsps - ns

Algorithm of the quest

Cross sectionTransmissionConversion Wave equation

(Maxwell’s equations)

Nonlinear polarization

Dipole momentsand energies

(ab initio)

Density matrix(TD Schrödinger equation)

Relaxationtimes

Some basic equationsSome basic equations

Close to linear propagation of a 880 nm pulse

I0 = 1 W/cm2 = 1 ps

Close to linear propagation of a 880 nm pulse

I0 = 1 W/cm2 = 1 ps

Close to linear propagation of a 880 nm pulse

I0 = 1 W/cm2 = 1 ps

Nonlinear transmission versus pulse duration and intensity

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