C ontrolling Coherent Nonlinear Optical Signals of Helical Structures by Adaptive Pulse Polarizations Dmitri V. Voronine Department of Chemistry, University of California, Irvine, CA

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, Fleming J. Phys. Chem. B, 109, 10542, 2005, Fleming

Polarization Control of Four Wave Mixing We 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 ω s wave vector k s 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: k I = -k 1 + k 2 + k 3, k II = k 1 – k 2 + k 3, and k III = k 1 + k 2 – k 3. 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 (μ x, μ y, μ z ) are μ 1 = (1, 0, 0), μ 2 = (Cos θ, Sin θ, 1), μ 3 = (Cos 2θ, Sin 2θ, 2), μ 4 = (Cos 3θ, Sin 3θ, 3), and μ 3 = (Cos 4θ, Sin 4θ, 4) with the angle θ = rad. In all calculations we used the Lorenzian model of the line-broadening function g ab (t) = Γ ab t, where Γ ab = 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 – ω 0 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 τ ij = τ i - τ j

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 Δω 1 = 0 (red) and the circularly polarized pump (black curve, bottom) with similar spectra and Δω 1 = 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 Δω 1 = 0 cm -1 (top) and Δω 1 = 500 cm -1 (bottom). ΔΑ xxyy (black), ΔΑ xyxy = ΔΑ xyyx (red). xxyy, xyxy, xyyx

Optimized pump-probe spectra and Tensor components P 1, W 1 P 2, W 2 Distribution of the cost function in the population of the genetic algorithm (circles) and its evolution during optimization of W 1 (top), W 2 (middle) and W 3 (bottom) Solid lines show the average cost values. xyxy, xxyy, xyyx

Quasi-3D representations of the laser pulses P 1, P 2 & P 3 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 ω 0 P 1 P 2 P 3

Optimized temporal phase profiles and elliptical parameters: (a) P 1 (W 1 ) (b) P 2 (W 2 ) (c) P 3 (W 3 )

TPPS Aggregates Helical Decamer Science, 292, 2063, 2001, Ribo tetrakis-(4-sulfonatophenyl)porphine

2D 2PPE Spectra of Helical TPPS Aggregates FWHM = 24 fsFWHM = 47 fs Re{S kI (w 1,0,w 3 )} w 1 [cm -1 ] w 3 [cm -1 ]