# Problem with the number of phase fronts when attempting to generate OAM

Question asked by Harry.L on Aug 12, 2019

Problem with the number of phase fronts when attempting to generate OAM:

In brief, an OAM (Orbital Angular Momentum) beam with a specific mode l should present exactly l number of helical phase fronts in its radiation pattern:

(a) Propagating plane waves, (b) Propagating OAM waves of mode 3, (c) Wave front of plane waves and (d) Wave front of OAM waves of mode 3

To generate the OAM, we can use a uniform circular array. Corresponding to a number of equal finite azimuthal intervals, each antenna element is placed on a circle with equiangular spacing. All the antenna elements are fed by the same signal, but with an incremental phase shift of  , such that the  antenna element will have a phase of where N is the total number of the antenna elements and l is the OAM mode index.

So I try to implement the exact same logic in EMPro:

My geometry:

(The code used to generate the geometry is based on the phased array antenna example in EMPro. )

When plotting the result, the excitation of the ports are set as follows:

# Ntx: the number of port

# l: OAM mode, the number of expected phase fronts

exc = { p.name: 1/math.sqrt(Ntx)*complex(math.cos(2*math.pi*i*l/Ntx),math.sin(2*math.pi*i*l/Ntx)) for i, p in enumerate(empro.activeProject.circuitComponents()) if p.port }

# Load the far field result

farFieldResult = results.farField(excitation=exc, sensorName=SENSOR_NAME)

This way, for mode 1 and Ntx = 10, the excitation profile looks like this: (which is correct)

However, when I export the far-field data and plot it in MATLAB, the number of phase fronts is always doubled, as shown in the three following figures (for mode 1-3 respectively), while radiation magnitude pattern is correct (the angle of the main lobe matches the theoretical value)

Mode 1

Mode 2

Mode 3

Here is the code I used to plot these figures:

emproData  = zeros(height(FarField),4);

emproData(:,1) = FarField.RealEtheta + i*FarField.ImagEtheta;

emproData(:,2) = FarField.RealEphi + i*FarField.ImagEphi;

pat = sqrt(power(emproData(:,1),2) + power(emproData(:,2),2));

theta = emproData(:,3);

phi = emproData(:,4);

subplot(1,2,1)

patternCustom(abs(pat),theta,phi);

title(strcat('Efield Magnitude Pattern',{' '},str));

view(90,0);

subplot(1,2,2)