Calculates the steady-state solutions of the Bloch equations with field modulation.
blochsteady(g,T1,T2,deltaB0,B1,ModAmp,ModFreq); blochsteady(g,T1,T2,deltaB0,B1,ModAmp,ModFreq,Opt); [t,My] = blochsteady(...); [t,Mx,My,Mz] = blochsteady(...);
See also the user guide on how to use blochsteady
.
blochsteady
calculates the steady-state solution of the Bloch equations for a spin-1/2 in the presence of field modulation. This is a general solver. It correctly treats all passage and saturation regimes.
The function returns the three time-dependent components of the magnetization.
Mx
is the dispersion (transverse magnetization component in-phase with the microwave)
My
is the the absorption (transverse magnetization in quadrature with the microwave)
Mz
is the longitudinal magnetization Mz
.
The time t
spans one modulation period. For example, for a 100 kHz modulation frequency, the period is 10 μs.
If no outputs are requested, blochsteady
plots the result.
There are several inputs. Unlike other EasySpin functions, these are not grouped in spin system and experimental structure (although this will likely change in a future release).
The first few input parameters contain information from the spin system necessary for the calculation.
g
g
is the g value of the S=1/2 electron spin.
T1
T1
is the longitudinal relaxation time of the spin, in microseconds.
T2
T2
is the transverse relaxation time of the spin, in microseconds.
The next few input parameters provide experimental settings.
deltaB0
deltaB0
is the static field offset, in mT. This is the difference between the applied magnetic field and the resonance field of the spin.
B1
B1
is the amplitude of the oscillating microwave magnetic field, in mT.
ModAmp
ModAmp
is the peak-to-peak amplitude of the modulation field, in mT.
ModFreq
ModFreq
is the field modulation frequency, in kHz.
The structure Opt
collects calculation settings. Opt
need not be specified, in which case default values for all fields are used. The field names and their possible values are as follows.
nPoints
kmax
blochsteady
automatically sets it high enough such that the output is accurate.
Method
Opt.Method = 'td'
indicates time-domain evolution, which is straightforward, but slow. Opt.Method = 'fft'
indicates Fourier transform, which is faster and therefore the default.
Verbosity
blochsteady
prints to the command window. If Opt.Verbosity=0
, pepper
is silent. 1 logs relevant information, 2 gives more details.
Here is a simple example.
g = 2; % g factor T1 = 10; % longitudinal relaxation time, us T2 = 2; % transverse relaxation time, us deltaB0 = -0.05; % field offset, mT B1 = 0.002; % microwave field amplitude, mT ModAmp = 0.3; % peak-to-peak field modulation amplitude, mT ModFreq = 50; % field modulation frequency, kHz [t,My] = blochsteady(g,T1,T2,deltaB0,B1,ModAmp,ModFreq); plot(t,My);
blochsteady
sets up a linear system of equations in the Fourier coefficients of the magnetization components. blochsteady
automatically determines the maximum Fourier coefficient necessary to provide a converged solution.