Fourier-transform limited pulses

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... 

But the unadorned Eqs. (9.1.5) and (9.1.6) do not make sufficiently clear the physical significance of the nonstationary,initially-localized, f (O) states that are most easily created by a short, Fourier transform limited pulse of electromagnetic radiation. Short is not an absolute quality. For a sufficiently short pulse, the nature of the initial localization prepared and the specific dynamical processes sampled depend primarily on the duration of the preparation pulse and secondarily on its spectral content (Heller, et ai, 1982 Johnson, et ai, 1996). 

A short, smooth, Fourier-transform-limited pulse of electromagnetic radiation may be thought of as being composed of a sum of many longer pulses, each with its own center frequency, amplitude, and phase. By controlling the amplitudes and phases of each of these component pulses, the original short, smooth pulse can be converted into a series of temporally displaced, frequency-chirped sub-pulses (Kawashima, et al., 1995 Cao and Wilson, 1997). Such crafted pulses have been used to accomplish a variety of control and information storage objectives. 

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. 

Fig. 2a displays the ion time-of-flight (TOF) distribution obtained when (n) = 1.6 104 Xe clusters interacted with a Fourier Transform-limited 100 fs 800 nm, 1015 W cm 2 laser pulse. The TOF displays a number of peaks corresponding to ions up to Xe1,+. The peaks in the TOF are quite broad, and even display a double peak structure due to the fact that ions are emitted in forward-backward directions with respect to the detector. Both the charge state reached and the kinetic energy of the ions are signatures of collective effects in the cluster ionisation. For example, when only atoms were present in the atomic beam, the maximum charged state reached was 4+. 

The experimental configuration of the pump-probe experiment is similar to Ref. [5]. A home built non-collinear optical parametric amplifier (nc-OPA) was used as a pump, providing Fourier-transform-limited 30 fs pulses, which could be spectrally tuned between 480-560 nm. In all experiments white-light generated in a sapphire crystal using part of the fundamental laser (800 nm), was used as probe light. In the pump-probe experiments the pump was tuned to the S2 0-0 band for carotenoids with n>l 1. In the case of M9, it was not possible to tune the nc-OPA to its 0-0 transition, and hence another nc-OPA tuned to 900 nm was frequency doubled and used for excitation. In addition to conventional transient absorption pump-probe measurements, we introduce pump-deplete-probe spectroscopy, which is sensitive to the function of an absorbing state within the deactivation network. In this technique, we... 

Figures 6a-c show the population dynamics encountered in a three-level system (see Fig. 4) interacting resonantly with two Fourier-transform-limited laser pulses with three different delay times between the two pulses. The calculation was done assuming that the chosen Rabi frequencies fulfill the relation > 1/pulse duration) in all three cases. This relation ensures that the typical time for a Rabi oscillation of the population in an isolated two-level system is shorter than the pulse duration. Ionization from level 2 was introduced as a fast laser intensity-dependent decay of level 2 [6, 60], and resonant laser frequencies were assumed.

Figure 8. Scheme of the experimental setup of the CIS experiment. Two Fourier-transform-limited nanosecond laser pulses with different frequencies are interacting with cold molecules or van der Waals complexes in a skimmed supersonic molecular beam. 

We have presented a new technique for the investigation of intramolecular couplings in the electronic ground state 50. The new technique of CIS is based on the special population dynamics induced by the coherent excitation of a three-level system with two narrow-band Fourier-transform-limited laser pulses. It allows the investigation of high-lying intermolecular vibrational states in the electronic ground state of van der Waals complexes. These... 

It is important to have reliable laser diagnostics, preferably on a shot-to-shot basis this is possible for a 10 Hz system. To characterise the temporal profile of the pulses, single-shot spectra and autocorrelation data can establish whether the laser pulses are Fourier-transform limited. For lasers with a sech profile, a product AvAtxO.32 should be achieved. It is also important to monitor the focal spot, its Airy disc and average intensity. Alternatively, a reasonable measure of the focused intensity can be obtained using Xe gas and the known threshold intensities for producing the various stages of ionization [12]. 

Figure 5. Running fourier transforms of the linear cross-correlations taken for a series of laser pulses systematically truncated in the time domain. The entire pulse (a) is truncated in 500-fs intervals so that approximately half the pulse remains in panel (e). The center of a transform limited pulse was used to define the center (t = 0) of the optimized pulse.

This result implies that the pulse was compressed nearly to the Heisenberg indeterminacy (or Fourier transform) limit [53] by the double-passed prism pair placed in the beam path prior to the autocorrelator. 

In the case of coherent laser light, the pulses are characterized by well-defined phase relationships and slowly varying amplitudes (Haken, 1970). Such quasi-classical light pulses have spectral and temporal distributions that are also strictly related by a Fourier transformation, and are hence usually refered to as Fourier-transform-limited. They are required in the typical experiments of coherent optical spectroscopy, such as optical nutation, free induction decay, or photon echoes (Brewer, 1977). Here, the theoretical treatments generally adopt a semiclassical procedure, using a density matrix or Bloch formalism to describe the molecular system subject to a pulsed or continuous classical optical field, which generates a macroscopic sample polarization. In principle, a fully quantal description is possible if one represents the state of the field by the coherent or quasi-classical state vectors (Glauber, 1965 Freed and Villaeys, 1978). For our purpose, however. 

An intense coherent tunable Fourier-transform-limited narrow-band all-solid-state vacuum-ultraviolet (VUV) laser system has been developed by Merkt and coworkers [573]. Its bandwidth is less than 100MHz and the tuning range covers a wide spectral interval around 120,000 cm (15 eV). At a repetition rate of 20 Hz the output reaches 10 photons per pulse, which corresponds to an energy of 0.25 nJ per pulse, a peak power of 25 mW for a pulse length of 10 ns, and an average power of 5 nW. For these short VUV wavelengths of around A = 80 nm this is remarkable and is sufficient for many experiments in the VUV. 

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