Pulse shaped

A sine-shape has side lobes which impair the excitation of a distinct slice. Other pulse envelopes are therefore more commonly used. Ideally, one would like a rectangular excitation profile which results from a sine-shaped pulse with an infinite number of side lobes. In practice, a finite pulse duration is required and therefore the pulse has to be truncated, which causes oscillations in the excitation profile. Another frequently used pulse envelope is a Gaussian frmction ... 

Gaussian pulses are frequently applied as soft pulses in modern ID, 2D, and 3D NMR experiments. The power in such pulses is adjusted in milliwatts. Hard" pulses, on the other hand, are short-duration pulses (duration in microseconds), with their power adjusted in the 1-100 W range. Figures 1.15 and 1.16 illustrate schematically the excitation profiles of hard and soft pulses, respectively. Readers wishing to know more about the use of shaped pulses for frequency-selective excitation in modern NMR experiments are referred to an excellent review on the subject (Kessler et ai, 1991). 

Soft-pulse multiple irradiation In this method, pre-saturation is done using shaped pulses having a broader excitation profile. Therefore, it is a more suitable method for the suppression of multiplets. This technique is very effective, easy to apply and easy to implement within most NMR experiments. In aqueous solutions, however, slowly exchanging protons would be detectable due to the occurrence of transfer of saturation. In addition, the spins with resonances close to the solvent frequency will also be saturated. 

Next, bi(t) was Laplace transformed into B(s), and then multiplied by the Laplace transformation U(s) of the step function u(t). The result B(s)U(s) is displayed in Figure 23B. In this example, the step response y(t) was measured for the 1H channel of a Varian 3.2 mm T3 probe tuned at 400.244 MHz with a time resolution of 25 ns, and Laplace transformed into Y(s). By dividing B(s)U(s) by Y(s), the function plotted in Figure 23C was obtained, from which, by performing inverse Laplace transformation, the programming pulse shape v(t) was finally obtained, as shown in Figure 23D. The amplitude and the phase of the complex function v(t) give the intensity and the phase of the transient-compensated shaped pulse. 

Frequency-selective REDOR (fsREDOR) is a very powerful technique developed for the study of 13C and 15N uniformly labeled peptides or proteins [92]. The basic idea of this technique is to combine REDOR and soft n pulses to recouple a selected 13C-15N dipole-dipole interaction in a multiple-spin system. Usually one could use Gaussian shaped pulses to achieve the required selective n inversions. Other band selective shaped pulses have been developed for a more uniform excitation profile [93]. In its original implementation, fsREDOR was used to extract the intemuclear distances of several model crystalline compounds [92], In the past few years, this technique has proven to be very useful for the study of amyloid fibrils as well. For the Ure2p10 39 fibril samples containing 13C and 15N uniformly... 

In this chapter, we have reviewed the experimental researches on the coherent optical phonons detected by novel nonoptical techniques, as well as on their optical control using shaped pulses. TRXRD can separate atomic displacements from collective motions of charges, while TR-THz and TRPE spectroscopies can visualize the ultrafast development of strong interaction... 

The idea of using the linear phase increments to achieve frequency-shifted excitation can be adopted almost to any pulses, such as hard (amplitude fixed) pulses, shaped pulses, and even adiabatic inversion pulses. Unlike any other pulses, the adiabatic pulses have already used non-linear phase increments for tilting the effective RF field slowly compared with the Larmor frequency of the spins in the rotating frame in order to fulfill the adiabatic condition. 

In general, a periodic pulse is composed of multiple identical shaped pulses and each shaped pulse is in turn composed of a number of back-to-back hard pulses with same or different strengths. The periodic pulse can be described by its x and y components of the RF field, i.e.,/lx(t) and /lv(/) with a period of T and a pulsewidth r. These two components satisfy the periodic conditions o(flx(t+T)=flx(t) and fly(t + T) =/jv(/), respectively. 

It is worth mentioning that Eq. (118), derived from the PIPs, is actually rather general and can be used for any pulse sequences with or without PIPs. If Aq> of a PIP equals zero, the PIPA/( 0, A

normal shaped pulse. If, on the other hand, f = 0 (correspondingly, (p0 = 0... 

Fig. 14.4 Pulse sequences used for the experiments described in this chapter. A [ N HJ-HSQC with water flip back and PFGs. The shaped pulse on the proton channel is a sine-shaped, 1.5 ms soft pulse all other pulses are hard pulses. Gradients are applied as square or sine-shaped pulses. The sign of the last gradient is reversed for anti-echo selection together with the sign of phase 6. B CPMG sequence. C bpPFGLED sequence. The delay T denotes the diffusion delay. Typically, r is set to 1 ms, T to 50-100 ms and Te to 1.2 ms.

Selective saturation (using shaped pulses) of all the aromatic ring CH resonances together since they show up generally in a short window of 6.5-8.5 ppm. The Q-matrix is easily set up for this case. 

Similarly to non-selective experiments, the first operation needed to perform experiments involving selective pulses is the transformation of longitudinal order (Zeeman polarization 1 ) into transverse magnetization or ly). This can be achieved by a selective excitation pulse. The first successful shaped pulse described in the literature is the Gaussian 90° pulse [1]. This analytical function has been chosen because its Fourier transform is also a Gaussian. In a first order approximation, the Fourier transform of a time-domain envelope can be considered to describe the frequency response of the shaped pulse. This amounts to say that the response of the spin system to a radio-frequency (rf) pulse is linear. An exact description of the... 

For selective irradiations with a flip angle of 180°, one can distinguish two groups of shaped pulses inversion pulses, which change the sign of Zeeman... 

To summarize the analysis of the various shaped pulses presented in this contribution, the following points can be formulated ... 

In this chapter, the discussion will be focused on the ID TOCSY (TO-tal Correlation SpectroscopY) [2] experiment, which, together with ID NOESY, is probably the most frequently and routinely used selective ID experiment for elucidating the spin-spin coupling network, and obtaining homonuclear coupling constants. We will first review the development of this technique and the essential features of the pulse sequence. In the second section, we will discuss the practical aspects of this experiment, including the choice of the selective (shaped) pulse, the phase difference of the hard and soft pulses, and the use of the z-filter. The application of the ID TOCSY pulse sequence will be illustrated by examples in oligosaccharides, peptides and mixtures in Section 3. Finally, modifications and extensions of the basic ID TOCSY experiment and their applications will be reviewed briefly in Section 4. 

When using the waveform generator to create the shaped pulses, the tmncation level should be kept low to reduce the spurious excitation due to the discontinuity. Usually, a 1% tmncation level (compared to the maximum amplitude of the shaped pulse) is recommended and is generally used. 

The double-selective TOCSY-ROESY and TOCSY-NOESY techniques are particularly useful. They allow one to measure NOE and ROE correlations in spectra with high degree of overlap as often found in carbohydrates. In addition to the DANTE, DANTE-Z [66], and Gaussian pulses as described earlier for selective excitation, self-refocusing shaped pulses such as BURP (EBURP and UBURP) [67] have also been used for this purpose [64]. 

The laser used to generate the pump and probe pulses must have appropriate characteristics in both the time and the frequency domains as well as suitable pulse power and repetition rates. The time and frequency domains are related through the Fourier transform relationship that hmits the shortness of the laser pulse time duration and the spectral resolution in reciprocal centimeters. The limitation has its basis in the Heisenberg uncertainty principle. The shorter pulse that has better time resolution has a broader band of wavelengths associated with it, and therefore a poorer spectral resolution. For a 1-ps, sech -shaped pulse, the minimum spectral width is 10.5 cm. The pulse width cannot be <10 ps for a spectral resolution of 1 cm . An optimal choice of time duration and spectral bandwidth are 3.2 ps and 3.5 cm. The pump pulse typically is in the UV region. The probe pulse may also be in the UV region if the signal/noise enhancements of resonance Raman... 

The CC pulse train experiments in Refs [63-65] utilize shaped pulses that use a transform-limited (TL) Gaussian pulse its phase is modulated in the frequency domain with a sine function, p ( ) = a sin( -I- c), while keeping the amplitude profile intact. The parameters a, b, and c are further varied to control molecular populations. In Reference [35], the effect of different values of these parameters on the IC dynamics of pyrazine and / -carotene is investigated and the significant role of overlapping resonances is exposed. 

Applications making use of the nonlinear absorption of dyes are passive Q-switching in solid-state lasers, pulse shaping, pulse intensity measurements of high-power ultrashort pulses, optical isolation between amplifier stages of high power solid-state lasers, and pulse width measurements of ultrashort pulses by the two-photon-fluorescence (TPF) method. 

X/Y coherence transfer steps as in the original HNCA experiment.41 As in the previous case, X nuclei are selectively irradiated by low power rectangular or shaped pulses, and coherence selection is accomplished by the matched pulsed field gradients Gb G2 and further assisted by a spoil gradient Gs. Owing to the need to avoid -pulses in the X-channel, the spectra are processed in magnitude mode in the fft dimension. 

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