How do I plot spiral phase plate with staircase structure

I am trying to plot spiral phase plate with staircase structure like this:

I have coded this:

% Set the azimuthal index to 1
azimuthal_index = 1;
% Parameters
refractive_index_spiral_plate = 1.489;  % Refractive index of the spiral plate (n_o)
refractive_index_air = 1;  % Refractive index of air (n_air)
wavelength = 632.8e-9;  % Wavelength of He-Ne laser in meters
steps = 2 * pi / azimuthal_index;  % Number of steps
theta_step = 2 * pi / steps;  % Angle for each step
segments = 10; % Number of segments per step (assumed to be 10)
theta_segment = theta_step / segments;  % Angle for each segment
% Calculate the height for the spiral plate
height = (wavelength / (4 * pi * (refractive_index_spiral_plate - refractive_index_air))) * azimuthal_index;
% Initialize variables
total_height = height; % Total height for the spiral plate
segment_heights = zeros(1, segments); % Array to store heights for each segment
% Calculate the height increment for each segment
height_increment = total_height / segments;
% Calculate the height for each segment with increasing values
for i = 1:segments
    segment_heights(i) = i * height_increment;
end
% Define the transverse plane grid
[x, y] = meshgrid(linspace(-1, 1, 256), linspace(-1, 1, 256));
% Create the phase distribution on the transverse plane
phase = zeros(size(x));
for i = 1:segments
    phase = phase + segment_heights(i) * sin(azimuthal_index * atan2(y, x) + i * theta_segment);
end
% Create the complex field with the desired phase distribution
complex_field = exp(1i * phase);
% Plot the phase distribution in grayscale
figure;
imagesc(angle(complex_field));  % Display the phase
colormap('gray');  % Set the colormap to grayscale
colorbar;  % Add a color bar
axis equal;
title('Spiral Phase Pattern on Transverse Plane (Grayscale)');

That produces:

Now when i tried to do the staircase, it becomes like this:

% Create the 3D surface plot for the staircase structure
figure;
surf(x, y, phase_pattern, 'EdgeColor', 'none');

Unrecognized function or variable 'phase_pattern'.

xlabel('X-axis');
ylabel('Y-axis');
zlabel('Retardation (radians)');
title('Staircase Structure in Azimuthally Varying Retardation');
colormap('parula');  % Color anything
view(30, 30);  % Adjust plot

Appreciate any help!

[Mathieu NOE]

hello

1/ we cannot reproduce the second plot as phase_pattern is undefined

2/ I had a hard time to understand how your code is supposed to generate the "spiral plate". Have to admit I was not very good in optics at school !

[ILY]

1/ I will look again the phase_pattern~ thank you for the input!

Answer 1

[Altaïr]

Hey @ILY,

To create a spiral phase plot with a staircase pattern, the floor function can be employed. Here's an example that transforms a normal spiral plot into a spiral staircase plot using the floor function.

% Define grid size and range
n = 500; % Grid size
x = linspace(-1, 1, n);
y = linspace(-1, 1, n);
[X, Y] = meshgrid(x, y);

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

% Calculate the phase shift
phaseShift = mod(theta, 2*pi);

% Plot the surface
figure;
surf(X, Y, phaseShift, 'EdgeColor', 'none');
colorbar;
title('Spiral Phase Plate');
xlabel('X');
ylabel('Y');
zlabel('Phase Shift');

% Number of stairs
N = 20;

% Add staircase effect by adjusting the ZData
ZData = floor(phaseShift/(2*pi/N)) * (2*pi/N);

% Plot the surface
figure;
surf(X, Y, ZData, 'EdgeColor', 'none', 'FaceAlpha', 0.7);
colorbar;
title('Spiral Phase Plate with Staircase Surface');
xlabel('X');
ylabel('Y');
zlabel('Phase Shift');

The variable N represents the number of stairs. Increasing N will make the second plot resemble the first one more closely.

For more details on the floor function, please refer to the documentation page:

https://www.mathworks.com/help/releases/R2023b/matlab/ref/floor.html