Amplitude Modulated Pulses

The amplitude modulated pulses may require special equipment such as a waveform generator which, however, has become a standard constituent of the modem commercial spectrometers. The amplitude modulated pulses are usually windowless and the sidebands produced by these pulses, in most cases, are very weak and can be neglected. The simplest amplitude modulated pulses are Gaussian pulse, sine pulse or sine-square pulse [1]. The main drawback of these simple shapes is that they produce a phase gradient over the excitation bandwidth and their excitation profiles are non-uniform over the bandwidth of interest. The amplitude modulated pulses can easily be shifted off-resonance by applying a phase ramp over the pulse according to equation (4). 

Multisite excitation can be easily achieved by mixing together several frequency shifted pulses according to the principle of superposition, known from optics [6,7]  

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Assume a 180° PIP is applied at the centre of the 13CO in the middle of the 13C evolution time for homonuclear decoupling and at the same time a compensating PIP is applied on the other side of the l3C (Fig. 11) to minimize the disturbance to the 13C that may have a transverse or longitudinal magnetization. The two simultaneous PIPs become an amplitude modulated pulse described by 2/i cos (27iAft)Ix, where f is the pulse strength of each 180°... 

From equation (8) three modes of adiabatic spin inversion using RF pulses may be defined as (a) amplitude modulated pulses, e.g. I-BURP [13], G3[16], I-SNOB [17], (b) frequency modulated pulses, e.g. chirp [18,20], tangential sweep [20,21] and (c) both amplitude and frequency modulated pulses, e.g. the hyperbolic secant [22] or WURST (Wide band Uniform Rate Smooth Truncation) [23] pulse. 

Special pulses containing one or several notches in their excitation profiles have been designed for purposes of solvent suppression. Obviously such pulses could be used also for suppression of parent lines in applications involving isotopi-cally diluted nuclei. One of the simplest experiments of this kind is the jump and return experiment [24] and corresponding higher order binomial pulses with alternating phases. Similarly to binomial excitation pulses these constant amplitude solvent suppression pulses create sidebands and excitation sidelobes. Corresponding amplitude modulated pulses [25,26] provide a better alternative. 

Using fast amplitude modulation pulses it is possible to redistribute the population of the spin energy levels. This is the Rotor Assisted Population Transfer (RAPT) method introduced by Yao et al. [57]. It has been shown that enhancement by a factor of 1.5-2 is achieved in a MAS experiment of spin-3/2 nuclei when RAPT is applied before the excitation pulse. It is also possible to combine RAPT with MQMAS in an experiment which uses single-quantum coherences for the excitation of multiple-quantum coherences. Madhu and Levitt [58] have shown that a combination of RAPT and RIACT-FAM gives the best performance for MQMAS experiments of spin-3/2 systems. 

Interconversion of single- and triple-quantum coherences was first suggested by Vega and Naor, who demonstrated how application of amplitude-modulated pulses, having a modulation frequency equal to the 13/2) 11/2) satellite transition frequency t i/2,3/25... 

The maximum signal enhancement of 21 may be possible to achieve in the case of single-crystals, but in a spinning powder, especially with a large distribution of pq, amplitude-modulated pulses result in a mixture of inversion, saturation and partial... 

A rigorous examination of the various MQ MAS sequences has been carried out with reference to sensitivity enhancement in the isotropic dimension and the lineshapes of the corresponding MAS peaks in the anisotropic dimension. An echo efficiency parameter has been defined as an indicator of the performance aspects of the various sequences. A consequence of the systematic analysis has been the combination of a spin-lock pulse for excitation of MQ coherences and an amplitude-modulated pulse for their conversion into observable single-quantum coherences. This approach has resulted in an improved performance over other sequences with respect to both the anisotropic lineshapes and the isotropic intensities. 

Brauniger, T., Madhu, P.K., Pampel, A., and Reichert, D. 2004. Application of fast amplitude-modulated pulse trains for signal enhancement in static and magic-angle-spinning Ti-NMR spectra. Solid State Nucl. Magn. Reson. 26 114—120. 

T. Braimiger, P.K. Madhu, Fast amplitude-modulated pulse trains with frequency sweep (SW-FAM) in solid-state NMR of spin-7/2 nuclei, J. Magn. Reson. 193 (2008) 102-109. 

The integral describes the spatial amplitude modulation of the excited magnetization. It represents the excitation or slice profile, g(z), of the pulse in real space. As drops to zero for t outside the pulse, the integration limits can be extended to infinity whereupon it is seen that the excitation profile is the Fourier transfonn of the pulse shape envelope ... 

Luminescence lifetimes are measured by analyzing the rate of emission decay after pulsed excitation or by analyzing the phase shift and demodulation of emission from chromophores excited by an amplitude-modulated light source. Improvements in this type of instrumentation now allow luminescence lifetimes to be routinely measured accurately to nanosecond resolution, and there are increasing reports of picosecond resolution. In addition, several individual lifetimes can be resolved from a mixture of chromophores, allowing identification of different components that might have almost identical absorption and emission features. 

Fig. 10.12. Pulse sequence for amplitude modulated 2D J-resolved spectroscopy. The experiment is effectively a spin echo, with the 13C signal amplitude modulated by the heteronuclear coupling constant(s) during the second half of the evolution period when the decoupler is gated off. Fourier transformation of the 2D-data matrix displays 13C chemical shift information along the F2 axis of the processed data and heteronuclear coupling constant information, scaled by J/2, in the F1 dimension.

Fig. 10.13. 2D J-resolved NMR spectrum of santonin (4). The data were acquired using the pulse sequence shown in Fig. 10.12. Chemical shifts are sorted along the F2 axis with heteronuclear coupling constant information displayed orthogonally in F . Coupling constants are scaled as J/2, since they evolve only during the second half of the evolution period, t /2. 13C signals are amplitude modulated during the evolution period as opposed to being phase modulated as in other 13C-detected heteronuclear shift correlation experiments.

Similar to the PIP, the Hamiltonian [Eq. (52a)] of a periodic pulse shows an infinite number of effective RF fields with both x and y components of the scaling factors X a and the phases 0na. The periodic pulse, however, acquires a different symmetry as that of the PIP. From Eq. (52c) and = ana, it follows that the scaling factor Xm, is symmetric in respect to the sideband number n, while the phase 6na is anti-symmetric according to Eq. (51c). These symmetries seem to be a coincidence arising from the mathematical derivations. As a matter of fact, they are the intrinsic natures of the periodic pulse. Considering the term f x i)Ix for instance, any Iy component created by the rotating field denoted by a> must be compensated at any time t by its counter-component oj n in order to reserve the amplitude modulated RF field. 

The procedure to combine any two phase modulated pulses is straightforward and is going to be discussed below. For the kth step of the two pulses (denoted by the two indices a and b), their amplitudes and phases can be described by A a, Wka and A b, respectively. The vector sum (denoted... 

Prior to describing the possible applications of laser-diode fluorometry, it is important to understand the two methods now used to measure fluorescence lifetimes these being the time-domain (Tl)/4 5 24 and frequency-domain (FD) or phase-modulation methods.(25) In TD fluorometry, the sample is excited by a pulse of light followed by measurement of the time-dependent intensity. In FD fluorometry, the sample is excited with amplitude-modulated light. The lifetime can be found from the phase angle delay and demodulation of the emission relative to the modulated incident light. We do not wish to fuel the debate of TD versus FD methods, but it is clear that phase and modulation measurements can be performed with simple and low cost instrumentation, and can provide excellent accuracy with short data acquisition times. 

The phase delay A(nwE) and modulation ratio M(na>E) information of the high-frequency signals is transferred to low-frequency signals by amplitude modulation (cross-correlation) of r.(t) and Iff) with a periodic train of pulses C(f) given by Ref. 29. 

ESEEM is a pulsed EPR technique which is complementary to both conventional EPR and ENDOR spectroscopy(74.75). In the ESEEM experiment, one selects a field (effective g value) in the EPR spectrum and through a sequence of microwave pulses generates a spin echo whose intensity is monitored as a function of the delay time between the pulses. This resulting echo envelope decay pattern is amplitude modulated due to the magnetic interaction of nuclear spins that are coupled to the electron spin. Cosine Fourier transformation of this envelope yields an ENDOR-like spectrum from which nuclear hyperfine and quadrupole splittings can be determined. 

The quality of the profile pertaining to the selected region can be improved by a modulation of the pulse lengths within the pulse train, which mimics the amplitude modulation of a simple soft pulse [8]. Simple modulation schemes can be devised for attenuating or even suppressing the side-lobes in the vicinity of the selected region (as shown in fig. 3). Alternatively, more elaborated modulation schemes as those of the BURP family [9] can be run in the DANTE-Z mode [10]. This mode actually offers a... 

We have identified high-order dispersion as the main reason why ultrashort, 10 fs, pulses have rarely been used for nonlinear optical imaging. We discussed the MllPS method for automated measurement and elimination of high-order dispersion. We provided quantitative analysis for the advantage of high-order dispersion as compared with correction limited to SOD. This enhancement was confirmed experimentally in fixed and living cells, as well as in depth imaging. Finally, we demonstrated that the broad bandwidth of ultrashort pulses can be used for selective two-photon excitation when appropriate phase or amplitude modulation is used. 

In DFS, this is accomplished by applying an RF pulse with amplitude modulation so that, in the frequency domain, the RF frequency changes linearly and adiabatically as a function of time on both sides of the CT. This "DFS pulse" is applied at the beginning of the pulse sequence, being followed by a selective pulse applied solely to excite and detect the CT (or by a conventional spin-echo pulse sequence, also with CT-selective... 

P. K. Madhu, A. Goldburt, L. Frydman and S. Vega, Sensitivity enhancement of the MQMAS NMR experiment by fast amplitude modulation of the pulses. Chem. Phys. Lett, 1999, 307,41-47. 

Figure 6.3 Shaped femtosecond laser pulses from sinusoidal spectral phase modulation of an 800 nm, 20 fs FWHM input pulse. The left column shows the modulated pulses in the frequency domain, decomposed into spectral amplitude (gray line and background) and modulation...

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