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)

Parameters

       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 initial condition

P - effective pulse propagator, expensive, and only available for

      the 'expm' method

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

The pulse is assumed to be piecewise-constant and should be supplied with sufficiently fine time discretisation to reproduce the waveform properly. Make certain that the frequency has the correct sign; a wrong sign makes the pulse hit far away from the intended location.

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