Shaped pulse af.m

Shaped pulse in amplitude-frequency coordinates using Fokker-Planck formalism (Eqn. 33 in http://dx.doi.org/10.1016/j.jmr.2016.07.005).

Syntax

[rho,traj,P]=shaped_pulse_af(spin_system,L0,Lx,Ly,rho,rf_frq_list,rf_amp_list,rf_dur_list,rf_phi,max_rank,method)

Arguments

L0 - drift Liouvillian that continues

                     running in the background

       Lx          - X projection of the RF operator

       Ly          - Y projection of the RF operator

       rho         - initial state vector or a stack 
                     thereof

       rf_frq_list - a vector of RF frequencies at each
                     time slice, Hz

       rf_amp_list - a vector of RF amplitudes at each
                     time slice, rad/s

       rf_dur_list - a vector of time slice durations,
                     in seconds

       rf_phi      - RF phase of the first pulse slice

       max_rank    - maximum rank of the Fokker-Planck
                     theory, increase until the answer 
                     stops changing, 2 is a good start

       method      - propagation method, 'expv' for Krylov
                     propagation, 'expm' for exponential
                     propagation, 'evolution' for Spinach
                     evolution function

Outputs

rho - final state vector or a stack thereof

       traj        - system trajectory as a [1 x (nsteps+1)]
                     cell array, the first point is the ini-
                     tial condition

       P           - effective pulse propagator (expensive),
                     only available for the 'expm' method

Note: the pulse is assumed to be piecewise-constant and should be
      supplied with sufficiently fine time discretisation to pro-
      perly reproduce the waveform.

Note: make it dead certain that your freqiency has the correct
      sign; wrong sign means that the pulse hits very far away
      from your intended location. This is the principal source
      of bugs when using this function.

ilya.kuprov@weizmann.ac.il

Examples

An example of a chirped inversion pulse pulse applied to a system with 31 J-coupled protons (examples/nmr_liquids/shaped_pulse_3.m):

Note that only 100 time slices are required in the frequency-amplitude representation: considerably fewer than would be needed in the Cartesian representation used by shaped_pulse_xy.m function.

Notes

Of the three propagation methods, 'expv' is recommended because it runs Krylov propagation that avoids explicit matrix exponentiation. The 'expm' option forces the rather inefficient sparse matrix exponentiation path and should only be used when the effective propagator is required. In very anomalous cases (long pulses, large state vector stacks, very large state spaces), the 'evolution' option might become necessary.

See also

shaped_pulse_xy.m, read_wave.m, vg_pulse.m, pulse_shape.m, chirp_pulse.m

Shaped pulses and gradients

Version 2.2, authors: Ilya Kuprov