Finite Pulse Length Effects Research Articles

DQ-DRENAR with back-to-back (BABA) excitation: Measuring homonuclear dipole–dipole interactions in multiple spin-1/2 systems

A new pulse sequence entitled DQ-DRENAR, (Double-Quantum based Dipolar Recoupling Effects Nuclear Alignment Reduction) was recently described for the quantitative measurement of magnetic dipole–dipole interactions in homonuclear spin-1/2 systems involving multiple nuclei. The double quantum coherences were created via a windowless symmetry-based pulse sequence (POST-C7). The present contribution evaluates the performance of the “Back-to-Back” excitation pulse scheme BABA-xy16 in such DRENAR experiments. Using SIMPSON simulations, special attention is given to finite pulse length effects, dipolar truncation, and chemical shift anisotropy interference. Experimental results on model compounds demonstrate good stability up to long mixing times (>10ms) as well as high accuracy. As its dipolar coupling efficiency is relatively high (the dipolar coupling scaling factor is 4.24 times as high as that of POST-C7), DQ-DRENAR-BABA-xy16 is most appropriate for the measurement of relatively weak dipolar coupling strengths (<400Hz). Different from POST-C7, for which the spinning rate is limited to 1/7 of the nutation frequency, DQ-DRENAR-BABA-xy16 experiments can take full advantage of ultrafast MAS experiments.

Dynamics of space-time self-focusing of a femtosecond relativistic laser pulse in an underdense plasma

The propagation of femtosecond, multiterawatt, relativistic laser pulses in a transparent plasma is studied. The spatio-temporal dynamics of ultrashort, high-power laser pulses in underdense plasmas differs dramatically from that of long laser beams. We present the results of numerical studies of these dynamics within a model which systematically incorporates finite pulse length effects (i.e., dispersion) along with diffraction and nonlinear refraction in a strongly nonlinear, relativistic regime. New space-time patterns of self-compression, self-focusing and self-phase-modulation, typical of ultrashort, high-intensity laser pulses, are analyzed. The parameters of our numerical simulations correspond to a new class of high-peak-power (> 100 TW), ultrashort-pulsed laser systems, producing pulses with a duration in the 10 - 20 femtosecond range. Spatiotemporal dynamics of these self-effects and underlying physical mechanisms are discussed.

Guiding and stability of short laser pulses in partially stripped ionizing plasmas

Laser pulse propagation can be strongly influenced by nonlinearity effects (relativistic and/or atomic electrons), ionization processes, and finite pulse length effects. In this paper these processes are included in the analysis of the propagation and stability of intense laser pulses in plasmas. An envelope equation, which includes ionization and nonlinear effects, is derived and the spot size is found to be unstable to an ionization–modulation instability. Introducing a quasiparaxial approximation to the wave equation, a pair of coupled envelope-power equations including finite pulse length effects, as well as nonlinearities, is derived and analyzed. In addition, short laser pulses propagating in plasma channels are found to undergo an envelope modulation that is always damped in the front and initially grows in the back of the pulse. Finite pulse length effects are also shown to modify nonlinear focusing processes. Finally, it is shown that, in a partially stripped plasma, the bound electrons can significantly alter the stability of laser pulses. In the presence of both free and bound electrons, an atomic modulation instability develops that can have a growth rate substantially higher than either the conventional relativistic modulational instability or the forward Raman instability. The filamentation instability is shown to be enhanced by bound electrons while the backward Raman instability is unaffected. An example of laser wakefield acceleration to electron energies greater than 2.5 GeV in a plasma channel is described.

Propagation of finite length laser pulses in plasma channels

Finite pulse length effects are shown to play a major role in the propagation, stability, and guiding of intense laser beams in plasmas. We present the quasiparaxial approximation (QPA) to the wave equation that takes finite pulse length effects into account. The QPA is an extension of the usual paraxial approximation. The laser field is shown to be significantly modified for pulses less than a few tens of wavelengths long. A pair of coupled envelope-power equations having finite pulse length effects, as well as relativistic and atomic electron nonlinearities, is derived and analyzed. Short laser pulses propagating in plasma channels are found to undergo an envelope oscillation in which the front of the pulse is always damped while the back initially grows. The modulation eventually damps due to frequency spread phase mixing. In addition, finite pulse length effects are shown to modify nonlinear focusing processes significantly. thinsp {copyright} {ital 1999} {ital The American Physical Society}

Nonparaxial propagation of ultrashort laser pulses in plasma channels

The propagation characteristics of an ultrashort laser pulse in a preformed plasma channel are analyzed. The plasma channel is assumed to be parabolic and unperturbed by the laser pulse. Solutions to the wave equation beyond the paraxial approximation are derived that include finite pulse length effects and group velocity dispersion. When the laser pulse is mismatched within the channel, betatron oscillations arise in the laser pulse envelope. A finite pulse length leads to a spread in the laser wave number and consequently a spread in betatron wave number. This results in phase mixing and damping of the betatron oscillation. The damping distance characterizing the phase mixing of the betatron oscillation is derived, as is the dispersion distance characterizing the longitudinal spreading of the pulse.

The Transition Amplitudes of Centerband and Sidebands in NMR Spectra of Rotating Solids

AbstractExpressions for the transition amplitudes of the centerband and sidebands of magic angle spinning (MAS) NMR spectra are derived by applying the Floquet theory. Signal amplitudes are defined in terms of transition amplitude operators, which are linear combinations of the Floquet operators. Two examples of the utilization of the Floquet approach for the evaluation of MAS signals are presented. In the first, the REDOR experiment on heteronuclear spin systems is discussed. The effects of finite pulse lengths on the REDOR signals are also derived. The second example deals with the MAS spectrum of a spin coupled to a heteronuclear spin that is irradiated by an rf field. Recoupled spectra are examined with the help of the Floquet theory and decoupled spectra are evaluated. In all cases the methodology of the Floquet approach is emphasized.

Displaying the results from NMR pulse sequence simulations as stereo diagrams

In some situations, it is so easy to simulate a pulse sequence that the simulation is done even before one has developed an experimental “feel” for the imperfections of a given pulse sequence. Recalling the pedagogical nature of Bloch diagrams, it is beneficial to display calculated spin magnetizations in a similar manner. However, for spin systems with the potential for dipolar or quadrupolar order, the length and the, orientation of the spin magnetization vectors are variable. To indicate both the length and the orientation of a vector on a 2D display, be it on paper or a computer screen, requires some three-dimensional visual cuing. Herein, the possibilities of stereo diagrams are explored. Stereo diagrams are most commonly seen by chemists as ORTEP diagrams of crystal structures ( 1). As is known to many chemists, stereo diagrams may be viewed with the aid of a low-cost stereo viewer (2) or without any aid whatsoever, using the technique of naked-eye stereopsis (3). Naked-eye stereopsis is an easily learned technique for many people. As an introduction to stereo diagrams, the evolution of the deuterium spin magnetization for a solution-state spin-echo pulse sequence, 90,” -~~-180,0T~-ACQ, with e2qz,Q/ h = 0 kHz, is shown in Fig. 1. As the off-resonance condition increases, finite pulse length effects reduce the refocusing efficiency of the spin-echo pulse sequence. Since the quadrupole coupling constant is zero, there can be no quadrupolar order; thus the length of the spin magnetization vector will be constant, in the absence of relaxation effects, and equal to the equilibrium magnetization, MO. The radius of the sphere is set equal to MO. “X” marks the spot on the trace where signal acquisition is to begin. In viewing the stereo diagram with naked-eye stereopsis, the instructions of J. C. Speakman are helpful (3): “look at the diagram from your normal reading distance, with spectacles if these be worn ordinarily; be careful to keep the horizontal line relating the pair parallel to a line connecting your eyes. To foster the illusion, at first, it may help to hold a piece of card (say, 20 cm X 8 cm) as an extension of the nose, so that the right eye sees only the right-hand picture, and ‘vice versa’. Be sure the diagram is well illuminated and free from unilateral shadows cast by the card. When

Finite pulse length effects in quadrupolar CPMG sequences

Finite pulse length effects in quadrupolar CPMG sequences

Obtaining high-fidelity [formula omitted] powder spectra in anisotropic media: Phase-cycled Hahn echo spectroscopy

In the spectroscopy of isolated spin-1 nuclei in anisotropic media, the spectral distortion resulting from the inability to record the initial part of the free-induction decay was eliminated by using the quadrupolar echo technique. Wideline spin- 1 2 spectroscopy is subject to the same problems associated with finite receiver recovery time as is spin-1 spectroscopy; however, these problems have been generally ignored in the past. Through the use of a very simple and well-known pulse sequence (90°-τ-180°) the chemical shift interaction, among others, can be refocused to generate a so-called Hahn echo. If magnetic dipolar interactions with like nuclei and fluctuating interactions with other nuclei may be neglected, then the refocusing of the magnetization will be complete and an undistorted spin- 1 2 powder spectrum can be obtained by Fourier transforming the signal starting at the peak of the echo. The practical aspects of implementing the Hahn echo technique are discussed. A phase-cycling scheme is proposed to prevent spectral distortion due to misset pulse lengths. The effects of finite pulse lengths are investigated, and the theoretical single pulse and echo distortion factors are demonstrated to differ from those which were determined for quadrupolar echo spectroscopy. Experimental verification of some of the theoretical predictions is provided.