Beam pulse shapes

We do not consider here the dependence of the group velocity on the beam divergence and the related spatiotemporal effeets in the nonlinear medium leading to additional changes in the pulse shape. In the region of the core, these effects are small, and the radiation field power for the levels of the input pulse power considered here is low. 

As described in the section on nonlinear absorption, the transmission of a pulse which is short compared to the various molecular relaxation times is determined by its energy content. A measurement of the energy transmission ratio will then give the peak intensity of the pulse when its pulse shape is known 44>. In fact, the temporal and spatial pulse shape is of relatively little importance. Fig. 11 gives the energy transmission as a function of the peak intensity I [W/cm2] for the saturable dye Kodak 9860 with the pulse halfwidth as a parameter. It is seen that this method is useful in the intensity region between 10 and 1010 MW/cm2 for pulses with halfwidths greater than 5 to 10 psec. Since one can easily manipulate the cross-section and hence the intensity of a laser beam with a telescope, this method is almost universally applicable. 

Experiments were performed using a titanium sapphire laser oscillator capable of producing pulses with bandwidths up to 80 nm FWHM. The output of the oscillator was evaluated to make sure there were no changes in the spectrum across the beam and was compressed with a double prism pair arrangement. The pulse shaper uses prisms as the dispersive elements, two cylindrical concave mirrors, and a spatial light modulator (CRI Inc. SLM-256), composed of two 128-pixel liquid crystal masks in series. The SLM was placed at the Fourier plane [5]. After compression and pulse shaping, 200 pJ pulses were used to interrogate the samples. 

As a method to control wavepackets, alternative to the use of ultra-short pulses, I would like to propose use of frequency-modulated light. Since it is very difficult to obtain a well-controlled pulse shape without any chirp, it is even easier to control the frequency by the electro-optic effect and also by appropriate superposition of several continuous-wave tunable laser light beams. 

The femtosecond laser pulses shaped by the AOPDF are amplified by the CPA up to 0.5mJ/pulse. Ethanol vapor is continuously flow into the vacuum chamber through a micro-syringe (70 pm) with stagnation pressure of 7 Torr at room temperature. The laser pulses are focused on a skimmed molecular beam of the ethanol vapor with an achromatic lens (/ = 145 mm). The focal spot size of the laser beam is 20 pm(j>. The peak intensity of the transform-limited laser pulse is calculated to 4 x 1015 W/cm2. The fragment ions are mass-separated with Wiley-McLaren type time-of-flight (TOF) mass spectrometer, and are detected with a microchannel plate (MCP) detector. 

Figure 8 shows the results now the NO scattered pulse shows clearly a demodulation that proves that the residence time of the NO molecules is larger than the rise time of the pulse. In addition N2 is present but no other products (like N20, N02, 02) were detected. The measurable stay time of NO comes from the chemisorption of NO on the Pd clusters. The angular distribution (Fig. 8b, solid circles) shows a clear increase of the cosine component due to chemisorption of NO on the Pd particles. From the pulse shape (Fig. 8a) we see that when the NO beam is turned on, the NO signal increases abruptly then more slowly. The first part called fast component corresponds to NO scattered or desorbed from the clean MgO, while the slow component is associated to NO desorbing (from a chemisorbed state) from the Pd clusters. Then, it is possible to measure the intensity of the two components as a function... 

SFG using femtosecond lasers allows all the resonances within the broad (-200 cm" ) bandwidth of the IR pulse to be probed simultaneously, without scanning the infrared source. To obtain spectral resolution in an SFG spectrum, the IR polarization is upconverted with a narrowband (-8 cm" ) visible beam, which is prepared by pulse shaping the output of a femtosecond laser. Only the frequency components of the pulse that interact resonantly with the vibrational modes are enhanced, resulting in an SFG spectrum [28, 29]. Owing to the use of femtosecond... 

Here a denotes the maximum field amplitude, rj is the ellipticity together with the pulse-shape function g(rj), which depends on the phase rj = (ot — k r. The laser beam is characterized by the frequency co and the wave vector k with ck = co. The transversality condition implies k A — 0. For a charged point particle interacting with this external electromagnetic field, the Hamilton-Jacobi equation reads... 

For all X-ray diffraction results, we assumed an X-ray beam of 8 keV photon energy with a sin2-pulse shape, and a half-width of 100 fs, which should roughly correspond to the situation at the Linear Coherent Light Source (LCLS) including timing jitter [6]. 

Besides spatial deflection of the laser beam, temporal pulse shaping can be applied in order to influence the efficiency and quality of the ablation process during laser beam drilling. Figure 7 shows an example for the influence of temporal pulse shaping on the laser ablation process. 

In the first scheme it is not necessary to use two different lasers if a femtosecond pulse with a broad spectral range is used for excitation. The different spectral components in the pulse give rise to many different excitation paths. In order to achieve optimum population in the excited state, the relative phases of these different spectral components have to be optimized. This can be realized by the pulse-shaping techniques discussed in Sect. 6.1.11 (Fig. 10.11). Here a plate of many liquid crystal pixels are placed in the laser beam, which changes the phases of the lightwave by orientation of the molecules where a feedback loop with a learning algorithm is used to maximize or minimize the wanted decay channel of the excited state [1402,1403]. 

Autocorrelation, background-free Method of measuring mode-locked laser pulse lengths, in which the pulse train is split into two beams, one of which is delayed, and in which the two beams are focused to overlap in a crystal whose phase-matching conditions permit frequency summing only when one photon is taken from each beam. The summed or doubled power, versus path delay, is proportional to the autocorrelation in time of the pulse with itself and so gives the pulse length, if the functional form of the pulse shape is known. 

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