Pulse autocorrelation

Figure 8-13. Field-induced differential transmission (-A7ZT)a - a 1-91 (solid line) and 2.53 eV (dots) as a function of pump-probe delay. In the upper panel we also show, as a dashed line, the pump-pulse autocorrelation (from Ref. [40] with permission).

The transient emission in DSB under the conditions of laser action was measured by the technique of gated upconversion with 150-fs time resolution [233]. The transient laser emission is shown in Figure 22.47 together with the pulse autocorrelation function that determines the time t = 0 as well as the time resolution in our measurements. It can be seen that the laser emission in DSB has a delayed peak formed at about 5 ps after the pulsed excitation, followed by several oscillation ringing that last for -100 ps this is typical for SF emission process [113-115]. The transient oscillatory emission response was studied at several stripe illumination lengths, temperature, and polari2ation and was found to be in agreement with the model of transient SF dynamics. 

FIGURE 1. Anisotropic photobleaching transients for PSI-200 particles at 665 and 675 nm. Continuous curves are optimized convolutions of Eqs. 1 with the laser pulse autocorrelation functions. 

In the off-resonant regime at 760 nm, the Ufetime is about 0.5 ps, rising to more than 2 ps at 680 nm (Fig. 9.50). As with DFWM measurements, the lifetime can not be seen as an exponential signal decay, but as a broadening of the laser pulse autocorrelation signal. The lifetime... 

The frill width at half maximum of the autocorrelation signal, 21 fs, corresponds to a pulse width of 13.5 fs if a sech shape for the l(t) fiinction is assumed. The corresponding output spectrum shown in fignre B2.1.3(T)) exhibits a width at half maximum of approximately 700 cm The time-bandwidth product A i A v is close to 0.3. This result implies that the pulse was compressed nearly to the Heisenberg indetenninacy (or Fourier transfonn) limit [53] by the double-passed prism pair placed in the beam path prior to the autocorrelator. 

The intensity autocorrelation measurement is comparable to all of the spectroscopic experunents discussed in the sections that follow because it exploits the use of a variably delayed, gating pulse in the measurement. In the autocorrelation experiment, the gating pulse is just a replica of the time-fixed pulse. In the spectroscopic experiments, the gating pulse is used to mterrogate the populations and coherences established by the time-fixed pulse. 

An interferometric method was first used by Porter and Topp [1, 92] to perfonn a time-resolved absorption experiment with a -switched ruby laser in the 1960s. The nonlinear crystal in the autocorrelation apparatus shown in figure B2.T2 is replaced by an absorbing sample, and then tlie transmission of the variably delayed pulse of light is measured as a fiinction of the delay This approach is known today as a pump-probe experiment the first pulse to arrive at the sample transfers (pumps) molecules to an excited energy level and the delayed pulse probes the population (and, possibly, the coherence) so prepared as a fiinction of time. 

Figure 8.1 (a) Block diagram of the femtosecond near-infrared laser microscope system, (b) Spectrum ofthe light pulse from the Cr F laser, (c) Interferometric autocorrelation trace of SHG signal with envelope curve calculated assuming a chirp-free Gaussian pulse with 35 fs fwhm. 

Figure 8.3 Interferometric autocorrelation traces of the fluorescence intensities of perylene (a) and anthracene (b) microcrystals irradiated by two NIR Cr F laser pulses centered at 1.26 Xm with the same intensity.

The characterization of the laser pulse widths can be done with commercial autocorrelators or by a variety of other methods that can be found in the ultrafast laser literature. " For example, we have found it convenient to find time zero delay between the pump and probe laser beams in picosecond TR experiments by using fluorescence depletion of trans-stilbene. In this method, the time zero was ascertained by varying the optical delay between the pump and probe beams to a position where the depletion of the stilbene fluorescence was halfway to the maximum fluorescence depletion by the probe laser. The accuracy of the time zero measurement was estimated to be +0.5ps for 1.5ps laser pulses. A typical cross correlation time between the pump and probe pulses can also be measured by the fluorescence depletion method. 

The auto correlator is an important tool in the detection of nltrashort pulses in the femtosecond-picosecond range. The basic operational scheme of an autocorrelator is shown in Figure 3.28. 

Figure 3.29 The intensity of the second harmonic wave generated in an autocorrelator as a function of the displacement of the moving mirrors system. The insets show the intensity versus time curves for pulses A and B of Figure 3.28 (solid and dashed lines, respectively).

Correlation of the code with itself (autocorrelation) yields only one correlation point in the time domain defined by the sequence and the unit code interval (see Figure 5c) and an otherwise clean baseline. Since the detector in our chromatogram just follows what the sample valve is doing, it also should be a pseudo random sequence and the cross-correlation of input and output is really an autocorrelation and thus yields the single pulse correlogram with an otherwise clean baseline. 

Figure 10. Photograph of ultra-compact, portable femtosecond infrared laser pumped by two inexpensive ( US 40) single-narrow-stripe AlGalnP diodes and powered by standard penlight (AA) batteries. An oscilloscope in the background records an intensity autocorrelation of the femtosecond pulses.

Using an experimentally-optimized focusing lens (/ = 15 mm spot radius, w = 4.3 pm) and a 3 mm KNbOj crystal (cut for NCPM at 22°C and 858 nm AR-coated), up to 11.8 mW of blue average power with a spectral width up to AIsh 1-4 nm at 429 nm was generated with only 44.6 mW of incident fundamental. The maximum observed SHG conversion efficiency was as high as 30 %. The overall efficiency of the electrical-to-blue process was over 1 %, and the blue pulses were measured by autocorrelation to be -500 fs in duration. ... 

Fittinghoff, D. N., der An, J. A., and Squier, J. 2005. Spatial and temporal characterizations of femtosecond pulses at high-numerical aperture using collinear, background-free, third-harmonic autocorrelation. Opt. Comm. 247 405-26. 

FIGURE 5.2 (a) Experimental (filled circles) wavelength tuning curve and accessible Raman freqnencies as a fnnction of the crystal temperatnre. The solid curves are a result of the calculations. (b) OPO output power versus pump power at the crystal facet (c) and (d) show the typical signal pulse spectrum and autocorrelation trace at the OPO cavity detuning of minus 36 (xm, respectively. 

Sacks Z, Mourou G, Danielius R (2001) Adjusting pulse-front tilt and pulse duration by use of a single-shot autocorrelator. Opt Lett 26 462-464... 

Abbreviations MD, molecular dynamics TST, transition state theory EM, energy minimization MSD, mean square displacement PFG-NMR, pulsed field gradient nuclear magnetic resonance VAF, velocity autocorrelation function RDF, radial distribution function MEP, minimum energy path MC, Monte Carlo GC-MC, grand canonical Monte Carlo CB-MC, configurational-bias Monte Carlo MM, molecular mechanics QM, quantum mechanics FLF, Hartree-Fock DFT, density functional theory BSSE, basis set superposition error DME, dimethyl ether MTG, methanol to gasoline. 

Fourier Transform-limited 100 fs, 800 nm, 1015 W cm 2 laser pulse and (b) the optimum result obtained by means of an 80-parameter unrestricted optimisation (dashed line) and a restricted 3-parameter optimisation (full line). The inset in (b) shows the evolution of the fitness value for the 80 parameter optimisation (full squares maximum fitness, open squares average fitness), (c) Autocorrelation trace of the optimal pulse corresponding to the 80 parameters optimisation. The pulse shapes consists of two pulses of 120 fs of equal amplitude separated by 500 fs. 

The results of two different optimisations of the production of charged states >11+ are presented in Fig. 2b. The dashed curve is the TOF distribution obtained when optimising 80 independent phases across the spectrum. By contrast with the Fourier Transform-limited pulse, ions up to 25+ are present in the TOF distribution The corresponding pulse shape (as determined from the autocorrelation in Fig. 2c) is a sequence of two pulses of equal amplitude and separated by 500 fs. To test the importance of the time delay between the two pulses, we performed restricted optimisations where a periodic phase was applied across the spectrum along with a quadratic term. In this case the period and amplitude of the oscillatory part... 

We have thus expressed the autocorrelation signals using the Wigner representation for both the external fields and the gate. The molecular properties are contained in the response function F(4). In the next section, we show how when the incoming external pulses and the detection gate are temporally well separated, we can use the Wigner representation for the material system as well. 

Although the preparation of the excited state has been described in terms of a delta function excitation, the same results should be obtained for the case of excitation by a broad-band, random, conventional light source. We have pointed out, in Section VI, that in the case of the non-radiative decay of an excited state, the same behavior is predicted to follow excitation by a light source characterized by a second-order autocorrelation function which describes random phases and excitation by a delta function pulse. A similar situation prevails when the radiative decay channel is also taken into account. 

We have seen that the limitations of the time characteristics of electronic devices requires the use of optical delays between the pump and probe pulses in ps flash photolysis. There are also indirect ways of using optical properties to measure the kinetics of laser pulses and of fluorescence, known as autocorrelation and up-conversion . These rely on the non-linear properties of certain materials or chemical systems, i.e. they are based on fast biphotonic processes. 

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