Transcript Slide 1

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
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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:
The three terms represent the
isolated aggregate, the interaction
with the optical field and the
interaction with a phonon bath,
respectively.
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.
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 excitedstate 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
Model System: Helical Pentamer
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.
Optimized Sequential Pump-probe Spectra
of a Helical Pentamer With PolarizationShaped 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
xxyy, xyxy,
xyyx
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).
Optimized pump-probe spectra and Tensor components
xyxy, xxyy,
xyyx
P1, W1
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.
P2, W2
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
tetrakis-(4-sulfonatophenyl)porphine
O3S
-
-
SO3
N
HN
NH
N
O3S
-
-
SO3
Helical Decamer
Science, 292, 2063, 2001, Ribo
2D 2PPE Spectra of Helical TPPS Aggregates
Re{SkI(w1,0,w3)}
FWHM = 47 fs
w3 [cm-1]
FWHM = 24 fs
w1 [cm-1]
w1 [cm-1]