why am i recieving a "parse error" at m=2? how do i fix it?

function [E, x, y] = generate_hermite_gauss_beam(m, n, w0, lambda, gridSize, gridLength)
% Generate Hermite-Gauss beam
% Inputs:
% m, n: Hermite polynomial indices (m in x-direction, n in y-direction)
% w0: waist width of the beam
% lambda: wavelength of the beam
% gridSize: number of points in each dimension of the grid
% gridLength: total length of the grid in both x and y directions

% Create coordinate vectors for x and y
x = linspace(-gridLength/2, gridLength/2, gridSize);
y = linspace(-gridLength/2, gridLength/2, gridSize);

% Create a grid for x and y coordinates
[X, Y] = meshgrid(x, y);

% Calculate beam parameters
zR = pi * w0^2 / lambda; % Rayleigh range
w_z = w0 * sqrt(1 + (gridLength / zR)^2); % Beam waist at distance z
R_z = gridLength * (1 + (zR / gridLength)^2); % Radius of curvature

% Calculate Hermite-Gauss beam profile
u = X / w_z;
v = Y / w_z;
Hm = hermitePoly(round(m), u);
Hn = hermitePoly(round(n), v);
amplitude = 1 / (sqrt(2^round(m) * factorial(round(m)) * 2^round(n) * factorial(round(n)))) * ...
    exp(-(u.^2 + v.^2) / 2) .* Hm .* Hn;

% Calculate Gaussian phase profile
phase = exp(1i * pi * (X.^2 + Y.^2) / lambda / R_z);

% Calculate the final Hermite-Gauss beam
E = amplitude .* phase;

% Normalize the amplitude to 1
E = E / max(abs(E(:)));
end

function H = hermitePoly(n, x)
% Calculate the Hermite polynomial of order n at x
% using the recursive relation
if n == 0
    H = ones(size(x));
elseif n == 1
    H = 2 * x;
else
    H = 2 * x .* hermitePoly(n - 1, x) - 2 * (n - 1) * hermitePoly(n - 2, x);
end
end

% Define the parameters for the Hermite-Gauss beam
m = 2;            % Hermite polynomial index in x-direction
n = 3;            % Hermite polynomial index in y-direction
w0 = 1e-3;        % Waist width in meters
lambda = 632.8e-9;% Wavelength in meters (HeNe laser)
gridSize = 256;   % Number of points in each dimension of the grid
gridLength = 0.2; % Grid size in meters (total length in both x and y directions)

% Generate the Hermite-Gauss beam
[E, x, y] = generate_hermite_gauss_beam(m, n, w0, lambda, gridSize, gridLength);

% Display the amplitude and phase of the beam
figure;
subplot(1, 2, 1);
imagesc(x, y, abs(E).^2);
axis square;
title('Amplitude');
xlabel('x (m)');
ylabel('y (m)');

subplot(1, 2, 2);
imagesc(x, y, angle(E));
axis square;
title('Phase');
xlabel('x (m)');
ylabel('y (m)');
colormap(gca, 'hsv');
colorbar;

Answer 1

[Voss]

Function definitions in a script must appear at the end, like this:

% Define the parameters for the Hermite-Gauss beam
m = 2;            % Hermite polynomial index in x-direction
n = 3;            % Hermite polynomial index in y-direction
w0 = 1e-3;        % Waist width in meters
lambda = 632.8e-9;% Wavelength in meters (HeNe laser)
gridSize = 256;   % Number of points in each dimension of the grid
gridLength = 0.2; % Grid size in meters (total length in both x and y directions)
% Generate the Hermite-Gauss beam
[E, x, y] = generate_hermite_gauss_beam(m, n, w0, lambda, gridSize, gridLength);
% Display the amplitude and phase of the beam
figure;
subplot(1, 2, 1);
imagesc(x, y, abs(E).^2);
axis square;
title('Amplitude');
xlabel('x (m)');
ylabel('y (m)');
subplot(1, 2, 2);
imagesc(x, y, angle(E));
axis square;
title('Phase');
xlabel('x (m)');
ylabel('y (m)');
colormap(gca, 'hsv');
colorbar;


function [E, x, y] = generate_hermite_gauss_beam(m, n, w0, lambda, gridSize, gridLength)
    % Generate Hermite-Gauss beam
    % Inputs:
    % m, n: Hermite polynomial indices (m in x-direction, n in y-direction)
    % w0: waist width of the beam
    % lambda: wavelength of the beam
    % gridSize: number of points in each dimension of the grid
    % gridLength: total length of the grid in both x and y directions
    % Create coordinate vectors for x and y
    x = linspace(-gridLength/2, gridLength/2, gridSize);
    y = linspace(-gridLength/2, gridLength/2, gridSize);
    % Create a grid for x and y coordinates
    [X, Y] = meshgrid(x, y);
    % Calculate beam parameters
    zR = pi * w0^2 / lambda; % Rayleigh range
    w_z = w0 * sqrt(1 + (gridLength / zR)^2); % Beam waist at distance z
    R_z = gridLength * (1 + (zR / gridLength)^2); % Radius of curvature
    % Calculate Hermite-Gauss beam profile
    u = X / w_z;
    v = Y / w_z;
    Hm = hermitePoly(round(m), u);
    Hn = hermitePoly(round(n), v);
    amplitude = 1 / (sqrt(2^round(m) * factorial(round(m)) * 2^round(n) * factorial(round(n)))) * ...
                exp(-(u.^2 + v.^2) / 2) .* Hm .* Hn;
    
    % Calculate Gaussian phase profile
    phase = exp(1i * pi * (X.^2 + Y.^2) / lambda / R_z);
    
    % Calculate the final Hermite-Gauss beam
    E = amplitude .* phase;
    % Normalize the amplitude to 1
    E = E / max(abs(E(:)));
end


function H = hermitePoly(n, x)
    % Calculate the Hermite polynomial of order n at x
    % using the recursive relation
    if n == 0
        H = ones(size(x));
    elseif n == 1
        H = 2 * x;
    else
        H = 2 * x .* hermitePoly(n - 1, x) - 2 * (n - 1) * hermitePoly(n - 2, x);
    end
end

Reference: https://www.mathworks.com/help/matlab/matlab_prog/local-functions-in-scripts.html

[Voss]

@sai parayan: Did this answer work for you?