1. Pulse Techniques

2. Off-Resonance Effects Initial magnetization along z x-pulse (  = 0) On-resonance: M z -> -M y Off-resonance: phase 

3. Off-Resonance Effects – 90º Pulse 90º hard pulse works well for  <  1 Phase shift  is approximately linear Effective flip angle  increases

4. Off-Resonance Effects – 90º Pulse Assume:  Close to resonance  90º pulse (   =  /2)  First-order approximation Phase angle is proportional to offset  First-order phase correction

5. Off-Resonance Effects – 90º Pulse Initial magnetization state is irrelevant Result:  z -  x -  z

6. Off-Resonance Effects - Compensation Not constant-time  Subtract 2  90 /  for each 90º pulse, or  Add a short echo Constant-time  No compensation needed if 90º pulses are identical Shaped 90º pulses?

7. Pulse calibration – 180º or 360º? 180º pulse:  Poor off-resonance performance M xy ~   Linear phase twist   Saturation in repeated experiments 360º pulse  Better off-resonance performance  < 0.1  1  Uniform phase  Minimal saturation

8. Off-Resonance Effects – 180º Pulse Inversion:  Poor off-resonance performance Refocusing:  Orthogonal better than parallel  Phase twist is the same Both work only for  < 0.2  1

9. Composite Pulses Trains of rectangular pulses instead of a single pulse  Off-resonance performance  Tolerance to B 1 inhomogeneity 90º – historic 180º inversion – most common

10. 90 x -180 y -90 x Composite Pulse 90 x -180 y -90 x replaces 180 x for inversion The middle 180º compensates for off- resonance behavior of the outer 90º pulses

11.  x -2  y -  x Composite Pulse 90 x -180 y -90 x has better broadband inversion performance   <  1 90 x -225 y -90 x has smoother, but narrower profile   < 0.7  1  x -2  y -  x composite pulse is less sensitive to mis- calibration of 90º pulse Cannot be used for refocusing

12. Selective Pulses Requirements:  Uniform excitation (inversion) profile  Minimal perturbation outside the target frequency range  Uniform resulting phase (for excitation)  Short pulse length  Low peak power  Easy to implement shape

13. Soft Rectangular Pulses Find  1, which produces a null in the excitation (inversion) profile at a certain offset off-resonance

14. Shaped Pulses Approximated by a series of short rectangular pulses Every point i :  Amplitude  i  Phase  i

15. Examples - Gaussian Pulse Truncated at 1% of max amplitude Excitation profile - gaussian

16. Examples - Sinc Pulse One-lobe of the sinc function Needs less power for the same length Similar excitation profile

17. Examples - SEDUCE-1 Essentially a gaussian, smoothed at both ends Used mostly for decoupling

18. Examples - Q5 Gaussian Cascade ~300  s pulse used as 90º 13C excitation pulse in Bruker pulse sequences Better than a soft rectangular 90º pulse For I y -> I z application needs to be time-reversed

19. Q5 Gaussian Cascade – Excitation Profile

20. Examples - Q3 Gaussian Cascade ~200  s pulse used as 180º 13C refocusing pulse in Bruker pulse sequences

21. Q3 Gaussian Cascade – Refocusing Profile

22. Q3 Gaussian Cascade – Inversion Profile It also provides good inversion

23. Examples - E-BURP2 Used in L-optimized experiments

24. E-BURP2 – Excitation Profile

25. Phase-Modulated Pulses – Frequency shifting Linear phase ramp  0 controls the phase of the resulting pulse:  90º ( I z -> I y ):  N = 0  90º ( I y -> I z ):  0 = 0  180º ( I y -> -I y ):  N/2 = 0  180º ( I z -> -I z ): arbitrary

26. Phase-Modulated Pulses – Resolution Issues Time resolution  More points = better shape approximation  Minimal pulse delay Phase resolution  More points = smaller phase steps  Minimal phase step

27. Phase-Modulated Pulses – Multi-band excitation Cosine modulation  10 kHz Needs 2x more power

28. Adiabatic Pulses “Conventional” pulses:  Stationary B eff orientation  Magnitude may be variable  Precession around B eff Adiabatic pulses:  Non-stationary B eff orientation  Magnetization follows B eff, while precessing around it

29. Adiabatic Pulses – Performance Conditions B eff magnitude should be changed gradually

30. Adiabatic Pulses – Performance Conditions A second rotating frame {x r, y r, z r } within the first rotating frame B eff magnitude should be tilted slowly

31. Adiabatic Pulses – Performance Conditions Adiabatic condition Adiabaticity factor

32. Adiabatic Pulses - Chirp 180 13C inversion on Bruker  60 kHz sweep  500 us  20% smoothing

33. Chirp – Inversion Profile Very broad inversion profile Low peak power  ~50% of high power

34. Adiabatic Pulses – Tolerance B 1 Inhomogeneity Power 3 dB higher than calibrated Power 3 dB lower than calibrated

35. Adiabatic Pulses - Wurst Smoothed ramp-up and ramp-down

36. Adiabatic Pulses - sech

37. Pseudo Bloch-Siegert Shifts Assume:  x-pulse (  = 0)  Very far off-resonance  Magnetization along y  Third order approximation

38. Pseudo Bloch-Siegert Shifts The result is a z-rotation by an angle  In the absence of  1 the rotation  =  p – the chemical shift evolution! Pulse phase and initial magnetization phase are irrelevant

39. Pseudo Bloch-Siegert Shifts An off-resonance pulse incurs a phase shift  PBS It is proportional to time- averaged square of  1  Also valid for shaped pulses Continuous application of  1 leads to a frequency shift  PBS  SEDUCE decoupling during chemical shift evolution

40. PBS Phase Shifts - Compensation Small-phase adjustment of a 90º pulse or phase correction in the frequency domain  Depends on whether there is chemical shift evolution  Works only for a narrow range of resonances far off-resonance  Partial compensation  Used in BioPack

41. PBS Phase Shifts - Compensation Using a second identical pulse and an echo  Perfect compensation over a broad spectral range  Limited by the broadband performance of refocusing 180º pulse  Default for Bruker sequences

42. PBS Phase Shifts - Compensation A second pulse with opposite offset  Must be far off- resonance  Imperfect compensation – first- order phase correction required  Not widely used Cosine modulation  Requires twice the power

43. PBS Frequency Shifts – SEDUCE decoupling Train of cosine modulated SEDUCE-1 shaped pulses  Modulation frequency  mod Signals of interest are near the carrier Decoupling is very far off resonance The result is a scaling of the spectrum by a factor  Compression around the center

44. PBS Frequency Shifts – SEDUCE decoupling 600 MHz example  15  s hard 13C pulse  252  s SEDUCE-1   1 max = 2.1 kHz  Scaling factor  = 0.36 For squared shapes, relative to a rectangle of the same amplitude   mod = 17.7 kHz For 80 ppm spectral width  0.2 ppm shift at edges Unsuitable for 15N-, 13C ali -, 13C aro -NOESY