Orbital Angular Momentum Vertex Beam design based on 4 phase level

Hello Everyone,

I designed Orbital Angular Momentum (OAM) using the following MATLAB code

NUM = 100; 
x = linspace(-12,12,NUM); 
y = x;
[X,Y] = meshgrid(x,y); 
charge =1;
theta= charge*atan2(X,Y); 
Amp = ones(NUM);
OAM = Amp.*exp(1i*theta);

This code will generate OAM consisting of multi phase values. Whereas, I need an OAM which consist of only 4 phase values. Here, for the understanding I am attaching a picture of the OAM phase plate. A simple distribution like the following picture or generating such OAM distribution by formula both can help for my requirement.

[Siti Hasunah]

Hi, I tried to generate an OAM wave-front phase using MATLAB and want to see the results with different OAM mode. I managed to get wave-front for OAM mode = 0 and 1, but then the result doesn't differ for higher OAM mode more than 1. How can I get the different wave-front just like below attached picture of mode l = 2?

These are the codes I used to generate the wave front:

% Define parameters
desired_distance = 2.0;  % Desired transmission distance (2 meters)
wavelength = 1.551e-6;    % Wavelength (in meters)
num_points_x = 200;      % Number of points in the x-direction
num_points_y = 200;      % Number of points in the y-direction

x = linspace(-desired_distance/2, desired_distance/2, num_points_x);
y = x;
[X, Y] = meshgrid(x, y);

% OAM mode parameters
l = 1; % OAM mode order (change to the desired order)
k = 2 * pi / wavelength; % Wavenumber

% Calculate azimuthal angle theta
theta = atan2(Y,X);

% Calculate the OAM wave-front phase
phase = l * theta;

% Display the phase pattern
figure;
imagesc(x, y, phase);
axis equal;
title(['OAM Mode (l = ', num2str(l), ') Wave-Front Phase Pattern']);
xlabel('X (meters)');
ylabel('Y (meters)');
colorbar;

Answer 1

[Naeem]

Hi Siti Hasunah

For the higher order OAM you can use the following code. Jucst change the charge values and you will get the desired OAM.

clear;

clc;

NUM = 100;

x = linspace(-50,50,NUM);

y = x;

[X,Y] = meshgrid(x,y);

R = sqrt(X.^2+Y.^2);

charge =3;

theta = charge*atan2(X,Y);

%imagesc(theta)

Amp = ones(NUM);

Ex = Amp.*exp(1i*theta).*(R<50);

Ey = Amp.*exp(1i*theta).*exp(1i*pi/2).*(R<50);%

%Ey = Amp.*exp(1i*theta);

Exx = Amp.*exp(1i*theta);

figure;imagesc(x,y,angle(Ex));colorbar;daspect([1 1 1]);set(gca,'ydir','normal');

[Siti Hasunah]

Thank you for the help!

Answer 2

[Image Analyst]

How about this:

NUM = 100; 
x = linspace(-12,12,NUM); 
y = x;
[X,Y] = meshgrid(x,y); 
charge =1;
theta= charge*atan2d(X,Y); 
subplot(2, 1, 1);
imshow(theta, []);
impixelinfo
Amp = zeros(NUM);

% Top triangle.
mask = theta <= -135 | theta > 135;
Amp(mask) = pi/2;

% Right triangle.
mask = theta >= 45 & theta < 135;
Amp(mask) = 0

% Bottom triangle.
mask = theta >= -45 & theta < 45;
Amp(mask) = 3 * pi / 2

% Left triangle.
mask = theta <= -45 & theta > -135;
Amp(mask) = pi
subplot(2, 1, 2);
imshow(Amp, []);
impixelinfo
colorbar

[Naeem]

Dear Image Analyst,

Thank you so much for the prompt response and for your kind help. That’s exactly what I need it help me a lot and now I am utilizing it. Could you also please comment on generating OAM phase mask for l=2 (topological charge=2). I.e the phase mask in which the 4 phases are repeated twice, or the phase mask consist of 8 equally distributed phase values then I will use accordingly. Your help regarding this issue is appreciable thanks in advance.

[Image Analyst]

I don't know what that is. Do you have an example?

If you need 8 or more sectors, you can simply put my triangle code into a loop over all sector angles. Is that what you want to do? I think you're skilled enough to do that -- just make a for loop.