%% Physical Constants

PlanckConstant = 6.62606957e-34;
PlanckConstantReduced = PlanckConstant / (2 * pi);
FineStructureConstant = 7.2973525698e-3;
ElectronMass = 9.10938291e-31;
GravitationalConstant = 6.67384e-11;
ProtonMass = 1.672621777e-27;
AtomicMassUnit = 1.66053878283e-27;
BohrRadius = 0.52917721092e-10;
BohrMagneton = 927.400968e-26;
BoltzmannConstant = 1.3806488e-23;
StandardGravityAcceleration = 9.80665;
SpeedOfLight = 299792458;
StefanBoltzmannConstant = 5.670373e-8;
ElectronCharge = 1.602176565e-19;
VacuumPermeability = 4 * pi * 1e-7;
DielectricConstant = 1 / (SpeedOfLight^2 * VacuumPermeability);
ElectronGyromagneticFactor = -2.00231930436153;
AvogadroConstant = 6.02214129e23;

%% Parameters
syms x y z theta lambda P wo wx1 wz1 wx2 wz2 I gamma real

% Define constants
lambda_val = 0.532;  % µm
P_val      = 1;
wo_val     = 100;

% Set beam waists equal for simplicity
wx1 = wo; wz1 = wo;
wx2 = wo; wz2 = wo;
%% Rotation matrix and k-vectors
% Rotation matrix
R = @(theta) [1 0 0; 0 cos(theta) -sin(theta); 0 sin(theta) cos(theta)];

% Define rotated coordinates and k-vectors
k1 = @(theta) R(theta) * [0; 1; 0];
k2 = @(theta) R(-theta) * [0; 1; 0];

RotatedCoords1 = @(theta) R(theta) * [x; y; z];
RotatedCoords2 = @(theta) R(-theta) * [x; y; z];

%% Define E fields

k1vec = k1(theta);
coords = [x; y; z];
rot1 = RotatedCoords1(theta);
rot2 = RotatedCoords2(theta);

% Polarization vector
e_pol = cos(gamma)*[0; 0; 1] + sin(gamma)*[1; 0; 0];

E1 = sqrt((2 * P) / (pi * wx1 * wz1)) * ...
     e_pol .* exp(1i * (k1(theta).' * coords)) * ...
     exp(-(rot1(1)^2 / wx1^2) - (rot1(3)^2 / wz1^2));

E2 = sqrt((2 * P) / (pi * wx2 * wz2)) * ...
     e_pol .* exp(1i * (k2(theta).' * coords)) * ...
     exp(-(rot2(1)^2 / wx2^2) - (rot2(3)^2 / wz2^2));

Efield = simplify(E1 + E2);

%% Intensity expression
Intensity = simplify(1/2 * real(conj(Efield) .* Efield));  % 3-component

%% ================ Plot lattice =================== %%

% Define parameters
theta_val      = 10 * pi / 180;  % 10 degrees in radians
gamma_val      = pi/2.0;              % tilt of linear polarization

% Extract z-component of intensity at x = 0
Iplane_z       = simplify(subs(Intensity(3), x, 0));

% Convert to function
Iplane_func    = matlabFunction(Iplane_z, 'Vars', {y, z, theta, wo, lambda, P, gamma});

% Grid for y and z
[ygrid, zgrid] = meshgrid(linspace(-1000, 1000, 500), linspace(-100, 100, 300));

% Evaluate intensity
Ivals          = Iplane_func(ygrid, zgrid, theta_val, wo_val, lambda_val, P_val, gamma_val);

% Normalization
Ivals          = Ivals / max(Ivals(:));  

% Plotting
figure(1)
clf
set(gcf,'Position',[50 50 950 750])
contourf(ygrid, zgrid, Ivals, 200, 'LineColor', 'none');
colormap('turbo');
colorbar;
% Preserve physical aspect ratio
pbaspect([1 1 1]);  % Set plot box aspect ratio to 1:1:1
axis tight;
xlabel('y [µm]', 'FontSize', 12);
ylabel('z [µm]', 'FontSize', 12);
title(['I_{plane}(y, z) at x = 0, \theta = ' num2str(rad2deg(theta_val)) '^\circ'], 'FontSize', 14);
set(gca, 'FontSize', 12, 'Box', 'on');

%% ================ Plot Potentials of lattice =================== %%

% Find indices closest to zero in y and z grids:
[~, idx_y0] = min(abs(ygrid(1,:)));  % y=0 along columns
[~, idx_z0] = min(abs(zgrid(:,1)));  % z=0 along rows

% Cut along y at z=0: 
% z=0 corresponds to row idx_z0, extract entire column idx_z0 in y direction
Iprop_cut = Ivals(idx_z0, :);  % 1D array vs y

% Cut along z at y=0: 
% y=0 corresponds to column idx_y0, extract entire row idx_y0 in z direction
Ivert_cut = Ivals(:, idx_y0);  % 1D array vs z

% Extract corresponding y and z vectors
yvec = ygrid(1, :);
zvec = zgrid(:, 1);

% Plot -Iprop/2 along y
figure(2);
clf
set(gcf,'Position',[50 50 950 750])
plot(yvec, -Iprop_cut/2, 'LineWidth', 2);
title('Profile at x=0, z=0');
xlabel('y [\mum]');
ylabel('Depth');
grid on;
set(gca, 'FontSize', 12, 'Box', 'on');

% Plot -Ivert/2 along z
figure(3);
clf
set(gcf,'Position',[50 50 950 750])
plot(zvec, -Ivert_cut/2, 'LineWidth', 2);
title('Profile at x=0, y=0');
xlabel('z [\mum]');
ylabel('Depth');
grid on;
set(gca, 'FontSize', 12, 'Box', 'on');