FWHM Gaussian pulse

For the model system a 3-fs (FWHM) Gaussian pulse, resonant to the S0-S2 transition with moderate maximum electric field (100 GV/cm ) is used as pump pulse. The pump pulse should be resonant and its time duration short compared to the systems nuclear dynamics to produce a narrow and localized vibrational wavepacket on the excited state, which later can be efficiently coupled to the state. The MIR-control-field (3.0 p,m, 12 fs FWHM (100 GV/cm ), CEP = 0.1 n) has to follow at the right delay, here within 40 fs. 

When the full width at half maximum (fwhm) of a Gaussian pulse is 20 fs, its frequency width is 740 cm as the fwhm. Frequency components Ql and fis are present in the pulse and are used to generate the vibrational coherence, where Ql — iis is equal to the vibration frequency ox... 

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. 

Time evolution of c m(t) coefficients at different detunings from the center of far a Gaussian pulse with fall-width at half maximum (FWHM) of 120 cm-1. (a) <4(f), ( )] .(c) hn c m(t). [E is to be replaced by — co0)]. Note that Re denotes the real and Im denotes the imaginary part, of the argument that follows. 

The Radiation Boundary Model (RBM1-- The optical density of the Scheme 2 system at 435nm, produced by 35-40 psec (gaussian fwhm) laser pulses (0.5mJ per pulse at 354.7 nm), is due to the sum of the free and cage pair phenylthiyl radical concentrations. The expression for the time dependence of this sum [SR (t)], according to the RBM, is equation (9). This equation would be directly applicable if the temporal widths of the exciting and probing... 

The laser parameters We examine three different photon energies for the pmnp laser of 3.62, 3.68, and 3.70 eV resulting in a wavepacket on Vf. below the barrier, at the top of the barrier, and above the barrier, respectively. The electric field strength and the full width at half maximmn (FWHM) of the Gaussian pulses were taken to be 5.142 X 10 eV/m (0.001 au) and 100 fs, respectively. 

Fig. 3.12 Spectra of the electric fields in homogeneously broadened Gaussian pulses with widths FWHM) of 10, 20 and 50 fs (t = 6, 12 and 30 fs)...

A Gaussian pulse with t = 6 fs (a measured FWHM of 10 fs, the order of magnitude of the shortest pulses that can be generated by current Ti sapphire lasers) includes a span of about 6.25 x 10 Hz, which corresponds to an energy hv) band of 2.0 X 10 cm If the spectrum is centered at 800 nm (12,500 cm ), its FWHM is 274 nm. Figure 3.12 shows the energy distribution function for such a pulse and for pulses with FWHM s of 20 and 50 fs. 

Tp Pulse dmation at FWHM level (for Gaussian piflses)... 

In this expression, Erf denotes the error function, while M2 is the full width at half maximum (FWHM) of the Gaussian probe pulse. The calculation of the total ionization probability S(t) therefore only requires the knowledge of the excited state wavepacket x e(r,R, f) at time t = T. Note that the origin of time (t = 0) is chosen here as the peak intensity of the pump pulse, and consequently the quantity Tin Eq. (1) corresponds to the pump-probe delay. 

The time-dependent external field in the simulation comprises two laser pulses, an XUV pump pulse followed by an intense IR probe pulse, both with a Gaussian envelope. In order to consider a realistic case, we use parameters not too far from those used in experiments, compare with Ref. [154], but the XUV pulse is in our simulation centered around the first doubly excited states with 1P° symmetry ( 60 eV). The XUV-pump pulse is 385 ats long (full width at half maximum of the intensity), with the energy peaked at 60.69 eV, and an intensity of 2 1013 W/cm2 the probe is a Tirsapphire 800 nm (1.55 eV) pulse, 3.77 fs long (fwhm), with an intensity of 1012 W/cm2. 

Figure 2. Total energy (integrated intensity) of scattered signal versus incident pulse separation AT in units of incident pulse FWHM. The experimental data were plotted assuming Gaussian incident pulses.

The time dependent shape of this field is given by a cos-function with amplitude Eq enveloped by a Gaussian centered at the time t = 0 with full width at half maximum (FWHM) At representing the laser pulse length. 

The pulse risetime is essentially equal to the collection time. For the detector shown in Fig. 12.39a, the risetime will vary between 60 and 120 ns. For other detector geometries the variation in risetime is greater because the electrons and holes, following the electric field lines, may travel distances larger than the thickness of the detector core (Fig. 12.396). The variation in risetime for the detector of Fig. 12.396 will be between 60 and 200 ns. The distribution of pulse risetimes for commercial detectors is a bell-type curve, not exactly Gaussian, with a FWHM of less than 5 ns. 

Empirical measurements with near-Gaussian optical and electron pulses at 800 nm with 8.5 MeV electrons indicate that the FWHM response function broadening increases by 700 fs for every millimeter of travel through water [3]. Therefore, time resolution is ultimately limited by sample depth, the choice of which is affected by considerations such as detection sensitivity, signal strength and the ability of the sample to tolerate signal averaging. Because of this limitation, ultrafast in the context of accelerators refers to timescales from a few hundred femtoseconds to tens of picoseconds. 

Pulse-probe transient absorption data on the rise time of prompt species such as the aqueous electron can be used to measure the instrument response of the system and deduce the electron pulse width. Figure 7 shows the rise time of aqueous electron absorbance measured with the LEAF system at 800 nm in a 5 mm pathlength cell. Differentiation of the absorbance rise results in a Gaussian response function of 7.8 ps FWHM. Correcting for pathlength, the electron pulse width is 7.0 ps in this example. 

What is the actual time profile of mode-locked pulses from a cw argon laser if the gain profile is Gaussian with a halfwidth of 8 GHz (FWHM) ... 

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