Ultrafast techniques

•Laser systems• Ti:Saph oscillator/regen, modelocking• NOPA’s

•Pump-probe absorption difference spectroscopy• Two-color• Dispersed detection

• Fluorescence spectrosopy• Photon counting • Streak Camera imaging• Upconversion

• Nanosecond time scale, FTIR

Elementary Reactions in Biology

Reactant

Product

Free Energy

Configuration

Diffusive motion On ground statePotential well (ms)

h

Ballistic motion on excited state potential (fs-ps)

Lasers

Light Amplification by Stimulated Emission Radiation:

•Population inversion•Cavity•Gain medium -> Titanium:sapphire

Single mode, CW laser Many modes with phase relation leads to a pulse in the cavity

Cavity

Leaky mirror

Pump laser

For Ti:sapphire oscillatorsλ = 800 nm,Rep. rate = 80 MHzLow power ~10 nJPulses can be as short as ~10 fs

Amplify from nanoJ to milliJoules -> peak power 20 fs pulse if focussed to 100 micrometer = 1012W/cm-2 =1000 times damage treshold most materials!

Regenerative amplifier

n(I) = n0 + n2I + ….

The electrical laser field is

E(x,t) = E(t)cos(ωt-kx)

φ = ωt-kx = ωt – ωnx/c = ω(t-n0z/c) – n2 ωz/cI(t)

ω = dφ/dt = ω – A dI/dt

White light generationby Self Phase Modulation

Parametric generation or amplification

The splitting of one photon in two:ωpump = ωsignal + ωidler

Conservation of momentum:kpump = ksignal +kidler

This can be done in nonlinear, birefringent crystals were the index of refraction depends on the polarization

ω1+ω2

ω1

ω2

Noncollinear optical parametric amplification

• When using a non-collinear phase matching angle in BBO pumped at 400 nm, the phase matching angle becomes independent of wavelength over a large part of the spectrum, for an angle of 3.7o between pump and signal (Gale,Hache 1994) large bandwidth

• The spatial walk-off (from the extraordinary pump beam) is 4.0o, with Pp farther from optical axis than kp. This is coincidently close to the noncollinear angle high gain

• Sub-10 fs with μJ energies can be obtained (efficiency 10-30%)

optic axis

signal angle

ks

kp

ki

idler angle

α

Optimize bandwidth by matching the signal and idler group velocities (=degeneracy for collinear beams):

VS = VI cosΩ

Expressed in terms of α and θ and solved for large bandwidths, one finds α = 3.7o and θ = 32o

Tune by

• changing delay since white light is dispersed

• phase matching angle and noncollinear angle

Shorter pulses by •minimizing dispersion of white light (no dispersive optics)•or even lengthening pump pulse•optimal compression (small apex angle prisms or gratings)

400 nm pump

white light seed

~6.4o

NOPA

Amplified Ti:Sapphire Laser0.5mJ50 fs1khz

NOPA

+Sapphire

+

OpticalDelayLine

Moving cell

Grating

Diode Array

1 m= 3 fs

Oscillator-stretcher-amplifier-compressor

Amplified Ti:Sapphire Laser

NOPA

+

OpticalDelayLine

Moving cell

1 m= 3 fs

photodiode

OPA

The instrument response functionThe cross- or auto correlationis given by

1

7.234003 103

puls t( )

200200 t200 0 200

0.5

1

0.999999

1.252241 106

A x( )

300300 x400 200 0 200 400

0

0.5

1

Stimulated emission

Excited stateaborption

Ground state

ES 1

ES 2

Ground State Absorption

Excited State Absorption

Difference Absorption Spectrum: A(t)-A(t=0)

Aor

A

Stimulated Emission

Protochlorophyllide Oxido Reductase

Ultrafast Spectral Evolution in POR

Important experimental aspects:

• Repetition rate of laser must be slower than photocycle, or samplemust be refreshed for every shot

• Excitation density must be low, only when less than 10% ofcomplexes are excited you are in a linear regime -> annihilation,saturation due to stimulated emission, orientational saturation

• Population dynamics are measured under the ‘magic’ angle54.7o, at other angles orientational dynamics are measuredanisotropy = r = (ΔDOD// -ΔDOD) / (ΔOD// + 2ΔOD)

The probability to excitea complex is ~ (E.μ)2

Since E2 ~ I ~ n, n(Θ) = n cos2 Θ

Saturation

Pump

Probe

t

I||

I

1cos32.0

2)(

2

||

||

t

II

IItr

Time-Resolved Polarized Absorption

Anisotropy:

0 500 1000 1500 2000 25000.0

0.1

0.2

0.3

exc.

= 880nm

855 nm 865 nm 890 nm

An

isot

rop

y

Delay time (fs)

Pu Pu Pr

t1

Time to absorb a photon, either determined by pulse length of pump, or by the dephasing time of the optical coherence i.e. ђ/absorption bandwidth

A third order polarization is inducedP(3)(w,t) ~ Χ3EprE*puEpu

This nonlinear polarization is the source of a new generated field (Maxwell equation + slowly varying envelop give)

|)(||)(| tPtPt ss

),()(

2),( tzP

cnitzE

z j

j

Stimulated emission

Pump-probe spectroscopy is a self-heterodyned third order spectroscopy:

Heterodyne detection, observation of superposition of ‘local oscillator’ field (= probe field) and signal field:

I(t) = n(ωs)c/4π |Elo(t) + Es(t)|2 = ILO(t) + IS(t) + 2 n(ωs)c/4π Re[E*LO(t).ES(t)]

And solve to get

Here is used that Im[E*j(t)P(t)= |E(t)|2Im[P(t)/E(t)]

The probe absorption is related to the out-of-phase component of the polarizationSignal is quadratic in both pump and probe field: S~|Epu|2.|Epr|2

And linear rather than quadratic in the weak nonlinear polarization P

absorption coefficient

),()(

2),( tzP

cnitzE

z j

j

),(/),(Im[)(

4tzEtzP

cnI

z

Ijj

j

j

Ground State Absorption

Excited State Absorption

Difference Absorption Spectrum: A(t)-A(t=0)

Aor

A

Stimulated Emission

Fluorescence techniquesI. Photon Counting

LaserSpontaneous emission

Monochromatoror filter

photomultiplier

start

stopTime to

amplitude converter

Instrument response~30-50 psHigh sensitivity, thoughmostly used with highrep rate systems, >100 KHz

II. Streak Camera Fluorescence

Time resolution ~3 psWhole spectrum at onceModerate sensitivity

III Fluorescence Upconversion

LaserSpontaneous emission

Very thin BBO crystal ~50 m

ωlaser+ωsignal

1 m= 3 fsMonochromator

detector

‘Slow’ Absorption difference spectroscopy

• Fast detector• Relatively more probe light than in a fs-ps experiment, actinic??

Lamp sample

Ns laserpulse

Monochromator

Photomultiplieror photodiode

ΔOD

Step-scan FTIR

Lamp

IR detectorMCT

3000 10002000Cm-1

FFT