Note that, in contrast to third-order spectroscopy, the electric signal field is always generated with the sum or difference of the frequencies and k-vectors of the incoming pulses. Consider now propagation of the generated signal field through the nonlinear material inzdirection. For a description, the phase mismatch ∆k=kz−kz,1−kz,2needs to be taken into account. The Maxwell wave equation in the slowly varying envelope approximation is then given by
∂
∂zE(z, t) =e ikz
20Pe(z, t)e−i∆kz. (3.4)
Efficient conversion requires phase matching, i.e ∆k = 0. Since the wavenumber k is connected to the frequency byk=ω/(nc0) and the frequencies of the involved light fields are different, phase matching has to be achieved via the adjustment of the refractive index n. In practice, birefringent crystals are used, and phase matching is adjusted by tuning the angle of the optical axis. One of the most employed materials for light conversion in the UV-vis spectral range is β-BaB2O4 (BBO). It combines high conversion efficiency with a wide transparency range and high damage threshold.
By combination of the second-order processes in figure 3.1 pulses over the full range from the UV to the far infrared can be produced. Conversion with tunable output frequencies can be achieved with parametric amplification. In parametric generation (OPG) an incident pump pulse with frequency ω1 is split into two pulses: the signal with frequencyω2 and theidler with frequencyω1−ω2. The process can be stimulated by a seed pulse, thus defining the frequencies of the output pulses.
White light continuum can be generated by focusing ultrashort light pulses into a ma-terial like sapphire or CaF2. Spectral broadening is induced by a number of higher-order processes like self-phase modulation, stimulated Raman emission, and multi-photon ion-ization.[60,61]
3.3 Fluorescence Upconversion
The broadband fluorescence-upconversion was already described in references[62–64]. The setup is based on theFemtolasers sPro system. Measurements are recorded with ac-tinic excitation at two different wavelengths: pulses at 400 nm (4µJ, 40 fs) are generated by frequency-doubling part of the fundamental; 440–450 nm pulses (0.5 µJ, 50 fs) are provided by a TOPAS (Light Conversion) in combination with frequency mixing.
The pump beam is focused with the lens L1 to a diameter of 80 µm onto a 0.5 mm sample cell. The fluorescence is collected with an off-axis Schwarzschild objective (M2 and M3) and 1:7 imaged onto a KDP crystal (0.3 mm, 65◦). For gating the 1340 nm idler pulses from the TOPAS are used. Spatial separation of the upconverted beam is assured by overlapping fluorescence and gate beams at an angle of 20◦ on the KDP crys-tal. In this geometry, optimal time resolution is only reached if the wave fronts of the incident pulses are matched. In the setup the gate pulses are simultaneously compressed and have their pulse front tilted with a combination of the three prisms P1–P3 (SF59)
3 Experimental Section
Figure 3.2: The fluorescence upconversion setup
and a 140 mm lens, L2. The upconverted signal is imaged onto a fiber, dispersed in a prism or grating spectrograph, and detected with a CCD camera (ANDORNEWTON).
Recorded spectra are corrected for instrumental factors such that transient spectra at long delay times match the stationary fluorescence. The temporal apparatus function is limited by the pump and gate pulse durations, and the adjustment of the wave front tilt. Depending on the experimental conditions, it is described by a Gaussian of 80–350 fs width (FWHM).
3.4 Single-Shot Referencing in Transient Absorption and Raman Spectroscopy
Femtosecond transient-absorption and stimulated Raman spectroscopy are strongly re-lated from a conceptual point of view: it becomes possible to measure time-resolved Raman scattering in a pump-probe experiment by applying an additional narrow-band Raman pulse (although the experimental realization is not trivial). It is advantageous to use a common measurement setup, to achieve mutual improvements in both techniques.
The available spectroscopic information depends on the balance between spectral cov-erage and resolution. Vibronic bands in transient-absorption spectroscopy are usually broadened in solution, and a reliable distinction between different potential interme-diates requires broadband detection. An optical probe of up to 22000 cm−1 spectral width is provided here by multi-filament supercontinuum pulses, which are generated when focusing femtosecond pulses into a CaF2 crystal. When handling the resulting inhomogeneous and divergent beam, accurate imaging of the spot from the CaF2 crystal onto the sample cell and the detection array is necessary to avoid spectral and temporal
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3.4 Single-Shot Referencing in Transient Absorption and Raman Spectroscopy artefacts. For many Raman-spectroscopic applications, on the other hand, the most im-portant vibrations are found in the region 0-1700 cm−1relative to the Raman pulse. This range covers C=C and C=O stretch, as well as bending, deformation and torsion modes.
Experimentally, such spectral width is already accessible directly with a non-collinear optical parametric amplifier. To discriminate between individual vibrational bands and capture subtle spectral shifts, the resolution should reach the order of 10 cm−1.
Small signal amplitudes make noise reduction an important issue in nonlinear spec-troscopy. Transient absorption depends to the third order on the incoming electric field, and the induced intensity changes in the probe pulse amount to only several percent at most. Femtosecond stimulated Raman spectroscopy is even a fifth-order experiment, and the signals are typically 100 times weaker than in pump-probe spectroscopy. The main source of noise are variations of the laser intensity and beam position, leading to continuum fluctuation of 1–10% between each shot. The corresponding noise may be reduced by monitoring the fluctuations in a reference experiment. Setups which were described recently,[65,66] use subsequent sample and reference pulses of the probe beam.
With this approach the correlation between two successive laser pulses is exploited.[67]
The signal/noise ratio can be further improved by extensive averaging. However, when working with biological samples, laser irradition, mechanical forces, and interaction with interfaces constantly expose the sample to stress, so that measurement is often a race against time. Single-shot referencing can significantly reduce the necessary number of sample averages, since high precision can be obtained even if successive probe pulses are uncorrelated. The measurement geometry is the result of constant improvement over a decade, and is further detailed in ref.[68].
Two identical setups are used. One is driven by the Femtolasers sPro system.
Pulses for continuum generation (20 µJ) are usually taken from the frequency-doubled beam. Pump pulses (0.6µJ) are conveniently generated at 400 nm or 267 nm, and other pump wavelengths are reached by parametric optical amplification (Light Conversion TOPAS). The other setup is driven by theClark-MXRCPA 2001 system. In this case, 30 fs probe pulses are generated at 520 nm in a 2-stage non-collinear optical parametric amplifier (Jobin Yvon NOPA). The 0.6 µJ pump pulses are generated in a 1-stage NOPA, followed by frequency doubling when necessary. The relative delay of the pump pulses is controlled by a delay stage (Physik Instrumente M-531.5IM).
The spectrograph setup is sketched schematically in Figure 3.3. Supercontinuum light is generated by focussing the probe pulses just before a 1 mm CaF2 plate with a fused silica lens (f = 200 mm). The plate remains stationary during an acquisition sequence, but it is translated in both directions orthogonal to the beam by about 100 µm whenever the delay stage moves to a new position. (Rotation of the plate is avoided because of an intensity dependence on rotation angle, due to nonlinear interactions.) The continuum extends a full angle of about 6◦, as found by an aperture stop before field mirror M1. Residual laser light close to the optical axis is absorbed by a central stop. Multifilament generation results in a speckle pattern of about 2–6 homogeneous zones at M1 which should be stable during the acquisition sequence. By optimizing the input beam diameter (~6 mm) and lens plate distance, measurement of transient optical density is possible from the near-IR to 270 nm. Optical relay of the supercontinuum is
3 Experimental Section
Figure 3.3: Setup for transient absorption and Raman spectroscopy. Multifilament supercontinuum generation extends the probe range from the visible into the UV to ~270 nm, but it requires optics for a 6◦ full solid angle at the source. For Raman spectroscopy alternatively the output of a non-collinear optical parametric amplifier is used directly.
Mirror objectives allow 50 µm spot size in the sample cell and upon entrance into two spectrographs. Apertures and slits are avoided after the beam splitter BS (for notations see text).
achieved by repeated use of a 1:1 objective in an off-axis Schwarzschild arrangement. All mirrors are aluminium coated with enhancement optimized around 300 nm. The first objective images the supercontinuum source 1 mm in front of beam splitter BS. About 20 mm before the beam splitter, the light passes through a color filter which is made with a flow cell (0.3 mm internal path length between 0.2 mm thick fused silica windows). BS has approximately 40% transmission and 40% reflection for the front surface of a fused silica substrate. Light reflected from the front surface is used for optical probing and transmitted light for reference, as shown in Figure 3.3. In this arrangement, a lateral displacement of the source leads to equivalent displacements on the entrance planes of the two spectrographs. A counter-wedge (CW) in the reference beam cancels the angular dispersion which is caused by BS, and its partial reflection balances the additional losses
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