EasySpin forum

I am trying to simulate EPR spectra recorded on a coplanar waveguide.

This is shown in the figure:

Here are shown the B0 (Zeeman) field from the magnet, and the microwave B1 field from the transmission line. The sample covers the entire area, so I there should be perpendicular- and some parallel-mode signals.

The "parallel-mode" signals should also give have a distribution of (B1,B0) angles due to the cylindrical symmetry of B1 around the transmission line.

From Easyspin's documentation there is no dedicated mode for transition lines for pepper. My approach is to carry out the calculation with an auxiliary function where I would calculate spectra from different modes.

Does that seem like a valid approach?I Is there something I overlook?

Thanks!

EasySpin does not have a built-in capability to average over an orientational distribution of B1. You can simulate parallel-mode and perpendicular mode spectra separately though, using Exp.Mode. That parameter also allows you to set an oblique angle. Here and here is a 2015 PRL paper we published that explains the theory behind this.

Thanks Stefan,

While I can see a scheme where a series of B1 orientations are simulated, I made a simpler thought:
Since all B1 vectors can be analyzed to three components B1x,y,z, with B1z // B0 and B1x,y _ | _ B0, wouldn't it be enough to calculate two different spectra (B1 // B0 and B1 _ | _ B0) and then add them up with a proper weighing factor for each.

Wouldn't this be enough to simulate any distribution of B1 orientations?

That is possibly correct, but best check it using a numerical simulation using Exp.Mode.

From a more general perspective, do you see any reason why the quantum mechanical transition probabilities and the spectral intensities (calculated with the Aasa–Vänngård correction), should be any different from those of field-swept CW spectra in regular cavities?

I expect pepper to be able to calculate them directly, at least for the simplest case of the perpendicular-mode contribution.

Do I overlook something obvious?

Upon carefully reading pepper's documentation, I have a question regarding the definition of the alpha angle in beam experiments.

According to the definition:

B0 is along the laboratory z axis (zL), [0; 0; 1] in the lab frame. Together, B0 and k define the zL-yL plane, where yL is the laboratory y axis.

However, in the Faraday configuration, B0 || k, so how can the zL-yL plane be defined? This subtle detail is not covered either in Fig 1 of the 2015 PRL.

Starting off from the above definition of zL, this is what I can make of the k-angle (poynting vector with B0) and the alpha angles.

Is that the correct convention?

Independent of the k tilt angle, a polarization angle of zero always means that the B1 vector has no xL component, and if the polarization angle is 90 degrees, then B1 is along the xL axis.

Here's the EasySpin code that sets up the B0, B1, and k vectors from the two angles given in Exp.Mode (called k_tilt and alpha_pol here):

nB0 = [0; 0; 1]; % unit vector along B0, in lab coordinates

sk = sin(k_tilt);
ck = cos(k_tilt);
nk = [0; sk; ck]; % unit vector along wave vector k, in lab coordinates

ca = cos(alpha_pol);
nB1 = [sin(alpha_pol); -ca*ck; ca*sk]; % unit vector along mw field vector B1, in lab coordinates

Hopefully this clarifies things.

Thanks for the clarification Stefan.

I have now corrected my scheme according to your code. It is always a right-handed reference frame with B0//z. Hopefully it captures the convention:

I think in the lower plot, the alpha angle is not correct. It should go towards the +xL axis, not -xL.