Pulsed EPR experiments simulation

[Dmitry Akhmetzyanov]

Hello,
I have a very small question regarding one example from the easyspin web site. It is a simulation of the Hahn echo using the density matrix formalism. The question is about the pi-pulse. So, this the part of the script:

flipAngle = pi/2;
for p = 1:length(tp)
for k = 1:length(offset)
Ham0 = offset(k)*Sz;
Pulse = expm(-1i*(flipAngle*Sx+2*pi*tp(p)*Ham0));
TauEvol = expm(-2i*pi*tau*Ham0);
U = Pulse^2*TauEvol*Pulse;
signal(:,p) = signal(:,p) + ...
weights(k)*real(evolve(U*Sz*U',Sy,Ham0,n,dt));
end
end

The pi-pulse is reprented here as Pulse^2. So, the flipping angle is really pi, but also the static Hamiltonian part is influenced. Is it because the pi - pulse length is represented as a doubled length compared to pi/2 pulse but with the same B1? I am asking because the influence of the different lengths of the optimal pulses is ivestigated in this example, that is why it was not absolutely clear for me why the pi/2 and pi pulses have also different lengths here, instead of having the same lengths.
Thank you very much.

Best wishes,
Dmitry Akhmetzyanov

[Stefan Stoll]

Pulse^2 is a pulse that is twice as long as Pulse and has twice its flip angle. If you write it out using expm(A)^2 = expm(2*A), it should become clear.

[Dmitry Akhmetzyanov]

Thank you, Stefan