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 state Potential 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 oscillators λ = 800 nm, Rep. rate = 80 MHz Low power ~10 nJ Pulses can be as short as ~10 fs

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

Regenerative amplifier

n(I) = n 0 + n 2 I + …. The electrical laser field is E(x,t) = E(t)cos(ωt-kx) φ = ωt-kx = ωt – ωnx/c = ω(t-n 0 z/c) – n 2 ωz/cI(t) ω = dφ/dt = ω – A dI/dt White light generation by Self Phase Modulation

Parametric generation or amplification The splitting of one photon in two: ω pump = ω signal + ω idler Conservation of momentum: k pump = k signal +k idler This can be done in nonlinear, birefringent crystals were the index of refraction depends on the polarization ω 1 +ω 2 ω1ω1 ω2ω2

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  3.7 o between pump and signal (Gale,Hache 1994)  large bandwidth The spatial walk-off (from the extraordinary pump beam) is 4.0 o, with P p farther from optical axis than k p. 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 ksks kpkp kiki idler angle α Optimize bandwidth by matching the signal and idler group velocities (=degeneracy for collinear beams): V S = V I cosΩ Expressed in terms of α and θ and solved for large bandwidths, one finds α = 3.7 o and θ = 32 o

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 ~6.4 o

NOPA

Amplified Ti:Sapphire Laser 0.5mJ 50 fs 1khz NOPA + Sapphire + Optical Delay Line Moving cell Grating Diode Array 1  m= 3 fs Oscillator-stretcher-amplifier-compressor

Amplified Ti:Sapphire Laser NOPA + Optical Delay Line Moving cell 1  m= 3 fs photodiode OPA

The instrument response function The cross- or auto correlation is given by

Stimulated emission Excited state aborption Ground state ES 1 ES 2

Ground State Absorption Excited State Absorption Difference Absorption Spectrum: A(t)-A(t=0) A or AA Stimulated Emission

Protochlorophyllide Oxido Reductase

Ultrafast Spectral Evolution in POR

Important experimental aspects: Repetition rate of laser must be slower than photocycle, or sample must be refreshed for every shot Excitation density must be low, only when less than 10% of complexes are excited you are in a linear regime -> annihilation, saturation due to stimulated emission, orientational saturation Population dynamics are measured under the ‘magic’ angle 54.7 o, at other angles orientational dynamics are measured anisotropy = r = (ΔDOD // -ΔDOD  ) / (ΔOD // + 2ΔOD  )

The probability to excite a complex is ~ (E.μ) 2 Since E 2 ~ I ~ n, n(Θ) = n cos 2 Θ Saturation

Pump Probe tt I || II Time-Resolved Polarized Absorption

Anisotropy:

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 induced P (3) (w,t) ~ Χ 3 E pr E* pu E pu This nonlinear polarization is the source of a new generated field (Maxwell equation + slowly varying envelop give) 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(ω s )c/4π |E lo (t) + E s (t)| 2 = I LO (t) + I S (t) + 2 n(ω s )c/4π Re[E* LO (t).E S (t)] And solve to get Here is used that Im[E* j (t)P(t)= |E(t)| 2 Im[P(t)/E(t)] The probe absorption is related to the out-of-phase component of the polarization Signal is quadratic in both pump and probe field: S~|E pu | 2.|E pr | 2 And linear rather than quadratic in the weak nonlinear polarization P absorption coefficient

Ground State Absorption Excited State Absorption Difference Absorption Spectrum: A(t)-A(t=0) A or AA Stimulated Emission

Fluorescence techniques I. Photon Counting Laser Spontaneous emission Monochromator or filter photomultiplier start stop Time to amplitude converter Instrument response ~30-50 ps High sensitivity, though mostly used with high rep rate systems, >100 KHz

II. Streak Camera Fluorescence Time resolution ~3 ps Whole spectrum at once Moderate sensitivity

III Fluorescence Upconversion Laser Spontaneous emission Very thin BBO crystal ~50  m ω laser +ω signal 1  m= 3 fs Mono chromator detector

‘ Slow’ Absorption difference spectroscopy Fast detector Relatively more probe light than in a fs-ps experiment, actinic?? Lampsample Ns laserpulse Monochromato r Photomultiplier or photodiode ΔOD

Step-scan FTIR Lamp IR detector MCT Cm -1 FFT