Selective excitation shaped pulses

The effect of a shaped pulse depends upon both the duration and the rf field intensity of the pulse. Normally the duration of a shaped pulse is adjusted to give the desired excitation range and then the rf field altered to obtain the desired tilt angle. As a rule of thumb the excitation range (selectivity) of shaped pulse in Hz is proportional to the reciprocal of the pulse duration. The RF field profile simulation can be used to study the effect of a shaped pulse and the rf field intensity of the pulse as function of the rf offset. Because of the correlation of pulse duration and tilt angle, the simulation does not accept normalized pulses instead the tilt angles of the individual magnetization vectors are calculated as a function of the rf field intensity of a specific rf offset. 

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). 

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... 

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... 

The peak rf amplitude required to achieve optimum excitation with a selective excitation pulse is given in comparison to the rf amplitude required to achieve an on-resonance 90° flip-angle with a selective rectangular pulse, the simplest conceivable shape. 

Fig. 1. Computer simulations of four selective excitation pulses. (Top) Pulse shapes. From left to right 90° rectangular pulse, 270° Gaussian truncated at 2.5%, Quaternion cascade Q, and E-BURP-1. The vertical axis shows the relative rf amplitudes, whereas the horizontal axis shows the time. (Middle) Trajectories of Cartesian operators in the rotating frame...

The principle of multiple selective excitation has been incorporated into a few ID and 2D experiments, the schemes of which are shown below (fig. 1). Depending on the experiment, either a DANTE pulse train (ID TOCSY [2]), frequency selective 180° pulses (ID NOE [3], ID INADEQUATE [4], ID C/H COSY [5] and 2D TOCSY-COSY [6]) or frequency selective 90° pulses (2D HMBC [11]) are applied to selectively perturb and uniquely label selected spins. Besides the DANTE pulse , composed itself of a series of non-selective rectangular pulses, Gaussian-shaped 180° and... 

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]. 

Lozovoy, V. V., Xu, B. W., Shane, J. C., and Danms, M. 2006. Selective nonlinear optical excitation with pulses shaped by pseudorandom Galois fields. Phys. Rev. A 74(4) 041805. 

Nymphaea caerulea, for seven natural anthocyanins stabilizing a DNA triplex, etc. Sequential analysis of the oligosaccharide structures of the flavonol tamarixetin-7-O-rutino-side has been performed by ID multistep-relayed COSY-ROESY experiments. Selective excitation was performed by Gaussian-shaped soft pulses. 

Fig. 3. Experimental demonstration of two-photon selective microscopy. The HPTS-labeled sample being imaged has acidic (bottom side) and a basic (top side) regions. Images were obtained with (A) 23-fs transform-limited pulses centered at 842 nm, and (B and C) phase shaped pulses optimized for selective excitation.

Recently, it has been shown that a Gaussian-shaped pulse can be used for selective excitation under the condition of MAS.34 This strategy has... 

In order to control elementary process (i), an effective scheme based on the concept of quadratic chirping has been proposed [12-17]. It has been demonstrated that this idea can be applied to process (i) and that fast and near-complete selective excitation of a wavepacket can be achieved without significant distortion of its shape through the utilization of specially designed quadratically chirped pulses [18,19]. This method is discussed in the first part... 

We will see that the major application of shaped pulses is to select a narrow region of the spectrum, thus displaying a narrow bandwidth. But there are also shaped pulses designed to do just the opposite — to give even excitation over a very wide range of frequencies. These broadband shaped pulses are specialized for inversion (Sz — S-) or refocusing... 

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