Controlling Coherent Nonlinear Optical Signals of Helical Structures by Adaptive Pulse Polarizations

Dmitri V. Voronine

Department of Chemistry, University of California, Irvine, CA 92697-2025

Outline: Goals of the project

Polarization Control of FWM

Pure Polarization Pulse Shaping

Controlling Pump-Probe Spectra of a Model Helical

Pentamer

Controlling 2D 2PPE Spectra of TPPS Aggregates

Spectroscopy of complex systems

Nature, 434, 625, 2005, FlemingJ. Phys. Chem. B, 109, 10542, 2005, Fleming

Polarization Control of Four Wave MixingWe consider an aggregate made of N interacting two level molecules linearly coupled to a harmonic bath described by the Frenkel-exciton Hamiltonian:

Three incident optical fields j = 1, 2, 3 mix through their coupling with the system to generate a signal field with a carrier frequency ωs wave vector ks and polarization δ.

The three terms represent the isolated aggregate, the interaction with the optical field and the interaction with a phonon bath, respectively.

Liouville space pathways

Double-sided Feynman diagrams and Liouville space paths contributing to FWM in a two-manifold excitonic system in RWA for the three possible directions: kI = -k1 + k2 + k3, kII = k1 – k2 + k3, and kIII = k1 + k2 – k3. The level scheme is shown in the top right panel. α, β, γ, δ are the polarization components of the electric field. The following diagrams contribute to the sequential pump-probe spectrum: c) and f) contribute to excited-state absorption (ESA), b) and d) to stimulated emission (SE), and a) and e) to ground-state bleaching (GSB).

Polarization Control of Four Wave Mixing

Adaptive Phase Control with Polarization Pulse Shaping

Iterative Fourier Transform

We have applied phase-controlled polarization pulse shaping to control the optical excitations of the helical pentamer. We assumed nearest-neighbor interactions J = 200 cm-1 between monomers along the backbone of the helix. The transition dipole moments in the molecular local basis (μx,

μy, μz) are μ1 = (1, 0, 0), μ2 = (Cos θ, Sin θ, 1), μ3 = (Cos 2θ, Sin 2θ, 2), μ4 = (Cos 3θ, Sin 3θ, 3), and μ3 = (Cos 4θ, Sin 4θ, 4) with the angle θ = 2.513 rad. In all calculations we used the Lorenzian model of the line-broadening function gab(t) = Γabt, where Γab = Γ = 100 cm-1 is the same homogeneous dephasing rate of all transitions (blue). Shown also is a spectrum with Γ = 10 cm-1 (black). Δω = ω – ω0 is the detuning from the transition energy of the monomer.

Model System: Helical Pentamer

Optimized Sequential Pump-probe Spectra of a Helical Pentamer With Polarization-Shaped

Pulses The pump-probe spectrum of excitons is controlled by pure polarization-pulse-shaping. The state of light is manipulated by varying the phase of two perpendicular polarization components of the pump, holding its total spectral and temporal intensity profiles fixed. Genetic and Iterative Fourier Transform algorithms are used to search for the phase functions that optimize the ratio of the signal at two frequencies. New features are extracted from the congested pump-probe spectrum of a helical pentamer by selecting a combination of Liouville space pathways. Tensor components which dominate the optimized spectrum are identified.

where τij = τi - τj

Pump-probe spectra of the helical pentamer

Pump-probe spectra of the helical pentamer at τ = 1.5 ps after excitation: (top) linearly-polarized with Δω1 = 0 (red) and the circularly polarized pump (black curve, bottom) with similar spectra and Δω1 = 500 cm-1. Linear ground-state absorption (blue) and the pump laser spectrum (thin solid black).

Tensor components of the pump-probe spectra for the circularly polarized pump with Δω1 = 0 cm-1 (top) and Δω1 = 500 cm-1 (bottom). ΔΑxxyy (black), ΔΑxyxy = ΔΑxyyx (red).

xxyy, xyxy,xyyx

Optimized pump-probe spectra and Tensor components

P1, W1

P2, W2

P2, W2

Distribution of the cost function in the population of the genetic algorithm (circles) and its evolution during optimization of W1 (top), W2 (middle) and W3 (bottom) Solid lines show the average cost values.

xyxy, xxyy,xyyx

Quasi-3D representations of the laser pulses P1, P2 & P3

Time evolves from left to right (z-axis) and spans 400 fs. The instantaneous frequencies are indicated by colors with an arbitrary color scheme where light blue is chosen for the center frequency ω0

P1 P2 P3

Optimized temporal phase profiles and elliptical parameters:(a) P1 (W1) (b) P2 (W2)

(c) P3 (W3)

TPPS Aggregates

Helical Decamer

Science, 292, 2063, 2001, Ribo

HNNH

N

N

SO3

SO3O3S

O3S-

--

-

tetrakis-(4-sulfonatophenyl)porphine

2D 2PPE Spectra of Helical TPPS Aggregates

FWHM = 24 fs FWHM = 47 fs

Re{SkI(w1,0,w3)}

w1 [cm-1] w1 [cm-1]

w3 [

cm-1]