Exploring the limits of broadband excitation and inversion pulses

The design of broadband excitation and inversion pulses with compensation of B(1)-field inhomogeneity is a long standing goal in high resolution NMR spectroscopy. Most optimization procedures used so far have been restricted to particular pulse families to keep the scale of the problem within manageable limits. This restriction is unnecessary using efficient numerical algorithms based on optimal control theory. A systematic study of rf-limited broadband excitation by optimized pulses and broadband inversion by optimized pulses with respect to bandwidth and B(1)-field is presented. Upper limits on minimum pulse lengths are set for different degrees of pulse performance.     

Compensated adiabatic inversion pulses: broadband INEPT and HSQC

When adiabatic fast passage is used to flip nuclear spins, sites with different chemical shifts are inverted at different times, causing refocusing errors. By mapping the phase evolution diagrams, we show that these effects can be accurately compensated with matched pairs of adiabatic pulses, either opposed or in the same sense, depending on the application. Applied to well-known heteronuclear polarization transfer experiments such as INEPT and HSQC, the requisite evolution of J-vectors is achieved irrespective of chemical shift or the duration of the adiabatic sweeps. By replacing conventional 180 degrees pulses, these new adiabatic sequences offer an order of magnitude improvement in effective bandwidth for the X-spins. Alternatively the experiments can be carried out with significantly reduced radiofrequency power. One- and two-dimensional spectra of (13)C in 13-cis-retinal at 600MHz have been used to demonstrate these advantages.     

Optimal control design of constant amplitude phase-modulated pulses: application to calibration-free broadband excitation

An optimal control algorithm for generating purely phase-modulated pulses is derived. The methodology is applied to obtain broadband excitation with unprecedented tolerance to RF inhomogeneity. Design criteria were transformation of Iz-->Ix over resonance offsets of +/-25 kHz for constant RF amplitude anywhere in the range 10-20 kHz, with a pulse length of 1 ms. Simulations transform Iz to greater than 0.99 Ix over the targetted ranges of resonance offset and RF variability. Phase deviations in the final magnetization are less than 2-3 degrees over almost the entire range, with sporadic deviations of 6-9 degrees at a few offsets for the lowest RF (10 kHz) in the optimized range. Experimental performance of the new pulse is in excellent agreement with the simulations, and the robustness of the excitation pulse and a derived refocusing pulse are demonstrated by insertion into conventional HSQC and HMBC-type experiments.     

Broadband pulses for excitation and inversion in I = 1 systems

New composite pulses for exciting and inverting three-level systems are presented. The π/2 pulse is designed for use in quadrupole echo spectroscopy and has a bandwidth comparable to existing sequences and is slightly shorter. Two new broadband π pulses are presented which have bandwidths larger than other existing I = 1 inverting pulses without being significantly longer. Numerical calculations and experimental examples demonstrate the usefulness of the new sequences.     

Reducing the duration of broadband excitation pulses using optimal control with limited RF amplitude

Combining optimal control theory with a new RF limiting step produces pulses with significantly reduced duration and improved performance for a given maximum RF amplitude compared to previous broadband excitation by optimized pulses (BEBOP). The resulting pulses tolerate variations in RF homogeneity relevant for standard high-resolution NMR probes. Design criteria were transformation of Iz-->Ix over resonance offsets of +/-20kHz and RF variability of +/-5%, with a pulse length of 500 micros and peak RF amplitude equal to 17.5 kHz. Simulations transform Iz to greater than 0.995 Ix, with phase deviations of the final magnetization less than 2 degrees, over ranges of resonance offset and RF variability that exceed the design targets. Experimental performance of the pulse is in excellent agreement with the simulations. Performance tradeoffs for yet shorter pulses or pulses with decreased digitization are also investigated.     

Improving excitation and inversion accuracy by optimized RF pulse using genetic algorithm

In this study, a Genetic Algorithm (GA) is introduced to optimize the multidimensional spatial selective RF pulse to reduce the passband and stopband errors of excitation profile while limiting the transition width. This method is also used to diminish the nonlinearity effect of the Bloch equation for large tip angle excitation pulse design. The RF pulse is first designed by the k-space method and then coded into float strings to form an initial population. GA operators are then applied to this population to perform evolution, which is an optimization process. In this process, an evaluation function defined as the sum of the reciprocal of passband and stopband errors is used to assess the fitness value of each individual, so as to find the best individual in current generation. It is possible to optimize the RF pulse after a number of iterations. Simulation results of the Bloch equation show that in a 90 degrees excitation pulse design, compared with the k-space method, a GA-optimized RF pulse can reduce the passband and stopband error by 12% and 3%, respectively, while maintaining the transition width within 2 cm (about 12% of the whole 32 cm FOV). In a 180 degrees inversion pulse design, the passband error can be reduced by 43%, while the transition is also kept at 2 cm in a whole 32 cm FOV.     

Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR

Optimal control theory is considered as a methodology for pulse sequence design in NMR. It provides the flexibility for systematically imposing desirable constraints on spin system evolution and therefore has a wealth of applications. We have chosen an elementary example to illustrate the capabilities of the optimal control formalism: broadband, constant phase excitation which tolerates miscalibration of RF power and variations in RF homogeneity relevant for standard high-resolution probes. The chosen design criteria were transformation of I(z)-->I(x) over resonance offsets of +/- 20 kHz and RF variability of +/-5%, with a pulse length of 2 ms. Simulations of the resulting pulse transform I(z)-->0.995I(x) over the target ranges in resonance offset and RF variability. Acceptably uniform excitation is obtained over a much larger range of RF variability (approximately 45%) than the strict design limits. The pulse performs well in simulations that include homonuclear and heteronuclear J-couplings. Experimental spectra obtained from 100% 13C-labeled lysine show only minimal coupling effects, in excellent agreement with the simulations. By increasing pulse power and reducing pulse length, we demonstrate experimental excitation of 1H over +/-32 kHz, with phase variations in the spectra <8 degrees and peak amplitudes >93% of maximum. Further improvements in broadband excitation by optimized pulses (BEBOP) may be possible by applying more sophisticated implementations of the optimal control formalism.     

Design of phase-modulated broadband refocusing pulses

Broadband linear-phase refocusing pulses were designed with the Shinnar-Le Roux (SLR) transformation and verified experimentally. The design works in several steps: initially, a linear-phase B polynomial is created with the Parks-McClellan/Remez exchange algorithm. The complementary A polynomial required for the SLR transformation is generated with the Hilbert transformation, yielding the minimum-phase response. The phase response of the A polynomial is altered by zero-flipping, which changes the overall pulse shape while retaining its refocusing profile. Optimal pulses in terms of minimal B(1max) and hence broadest bandwidth were found with non-linear optimisation of the zero-flipping pattern. These pulses are generally phase modulated with a time-symmetric amplitude and anti-symmetric phase modulation. In this work, a whole range of pulses were designed to demonstrate the underlying relationships. Five exemplary pulses were implemented into a PRESS sequence and validated by acquiring images of a water-oil phantom and lactate spectra at TE = 144 ms.     

Tailoring the optimal control cost function to a desired output: application to minimizing phase errors in short broadband excitation pulses

The de facto standard cost function has been used heretofore to characterize the performance of pulses designed using optimal control theory. The freedom to choose new, creative quality factors designed for specific purposes is demonstrated. While the methodology has more general applicability, its utility is illustrated by comparison to a consistently chosen example--broadband excitation. The resulting pulses are limited to the same maximum RF amplitude used previously and tolerate the same variation in RF homogeneity deemed relevant for standard high-resolution NMR probes. Design criteria are unchanged: transformation of I(z)--> I(x) over resonance offsets of +/-20 kHz and RF variability of +/-5%, with a peak RF amplitude equal to 17.5 kHz. However, the new cost effectively trades a small increase in residual z magnetization for improved phase in the transverse plane. Compared to previous broadband excitation by optimized pulses (BEBOP), significantly shorter pulses are achievable, with only marginally reduced performance. Simulations transform I(z) to greater than 0.98 I(x), with phase deviations of the final magnetization less than 2 degrees, over the targeted ranges of resonance offset and RF variability. Experimental performance is in excellent agreement with the simulations.     

Design of broadband RF pulses with polynomial-phase response

The achievable bandwidth of common linear-phase RF pulses is limited by the maximum feasible B1 amplitude of the MR system. It has been shown previously, that this limitation can be circumvented by overlaying a quadratic phase in the frequency domain, which spreads the power across the pulse duration. Quadratic-phase RF pulses are near optimal in terms of achieving minimal B1max. In this work, it is demonstrated that further B1max reduction can be achieved by combining quadratic with higher-order polynomial-phase functions. RF pulses with a phase response up to tenth order were designed using the Shinnar-Le Roux transformation, yielding considerable increases in bandwidth and selectivity as compared to pure quadratic-phase pulses. These benefits are studied for a range of pulse specifications and demonstrated experimentally. For B1max = 20 microT and a pulse duration of 2.1 ms, it was possible to increase the bandwidth from 3.1 kHz for linear and 3.8 kHz for a quadratic to 9.9 kHz for a polynomial-phase pulse.     

Nonlinear phase adjustment of selective excitation pulses

A continuous transformation of an RF waveform with a modified Korteweg-de Vries equation or generalization can be used to adjust the phase behavior of a selective excitation pulse while preserving the magnitude behavior of the spin response. This transformation has applications in removing or adding to the nonlinear phase properties of a selected region.     

Fully efficient adiabatic frequency conversion of broadband Ti:sapphire oscillator pulses

By adiabatic difference-frequency generation in an aperiodically poled nonlinear crystal-a nonlinear optical analog of rapid adiabatic passage in a two-level atomic system-we demonstrate the conversion of a 110?nm band from an octave-spanning Ti:sapphire oscillator to the infrared, spanning 1550 to 2450?nm, with near-100% internal conversion efficiency. The experiment proves the principle of complete Landau-Zener adiabatic transfer in nonlinear optical wave mixing. Our implementation is a practical approach to the seeding of high-energy ultrabroadband optical parametric chirped pulse amplifiers.     

Controlling the propagation of broadband light pulses by Electromagnetically Induced Transparency

We present an experimental and theoretical investigation, performed on hot sodium atoms in a ladder scheme, showing the control of the absorption and of the propagation velocity of a probe light pulse with a spectral bandwidth as large as 1.8 GHz. The predictions of the theoretical model compare favorably with the experimental results.     

混合加宽的宽带钕玻璃激光系统的放大特性研究

通过宽带激光脉冲放大的物理模型,以数值模拟为工具,研究分析了激光系统对不同带宽脉冲的放大能力,以及交叉弛豫时间对脉冲放大特性的影响.计算结果表明,随着带宽的增加,激光系统的输出能力逐渐降低,在其他条件相同时,宽带分别为2,5和10 nm时的输出能量比窄带输出（3000 J,1 ns脉宽）时分别减小了约2％,11％和27％;在带宽为几个纳米时完全非均匀加宽比完全均匀加宽的输出能量（3000 J,1 ns脉宽）降低了约20％;初步确定了交叉弛豫时间的范围为0—10 ns. 关键词： 激光系统 宽带激光 放大过程 交叉弛豫     

Interferometric technique for measuring broadband ultrashort pulses at the sampling limit

We present a new technique for measuring ultrashort optical pulses by use of spectral phase interferometry for direct electric-field reconstruction that is suitable for large bandwidth pulses. The method does not require generation of a replica of the pulse to be measured and encodes the spectral phase information in a spatial interference pattern. A major advantage of this method is that the spectral sampling saturates the Whittaker-Shannon bound. Moreover, the technique allows for the characterization of some types of space-time coupling. An experimental demonstration of the technique is presented.     

Generation of broadband similaritons for complete characterization of femtosecond pulses

Broadband nonlinear-dispersive similariton (50 THz bandwidth; > 100 nm at 800 nm central wavelength) is generated in passive uniform fiber and characterized experimentally through the chirp measurement technique of spectral compression and frequency tuning in the sum-frequency generation process. The potential of similariton applications to the signal synthesis and analysis problems on the femtosecond time scale, especially for similariton-induced temporal lensing and similariton-based spectral interferometry, is discussed on the basis of our experiments.