38 lines
1.4 KiB
Mathematica
38 lines
1.4 KiB
Mathematica
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function U = generateModulatedSingleGaussianBeamPotential(positions, waists, P, options)
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alpha = options.Polarizability;
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wavelength = options.Wavelength;
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mod_amp = options.ModulationAmplitude;
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% Define constants
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eps0 = 8.854187817e-12; % Permittivity of free space (F/m)
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c = 299792458; % Speed of light in vacuum (m/s)
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a0 = 5.29177210903e-11; % Bohr radius (m)
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% Modulation amplitude
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mod_amp = mod_amp * waists(1);
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% Number of points in positions
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n_points = length(positions(1, :));
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% Calculate modulation function
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[dx, x_mod] = Helpers.calculateModulationFunction(mod_amp, n_points, 'arccos');
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% Calculate amplitude A
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A = 2 * P ./ (pi * Calculator.calculateWaist(positions(2, :), waists(1), wavelength) .* Calculator.calculateWaist(positions(2, :), waists(2), wavelength));
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% U_tilde constant term (same as before)
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U_tilde = (1 / (2 * eps0 * c)) * alpha * (4 * pi * eps0 * a0^3);
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% Initialize dU matrix
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dU = zeros(2 * n_points, n_points);
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% Compute dU values for each modulated x position
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for i = 1:length(x_mod)
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dU = [dU; exp(-2 * ((x_mod(i) - positions(1, :)) ./ Calculator.calculateWaist(positions(2, :), waists(1), wavelength)).^2)];
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end
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% Calculate the potential U using the trapezoidal rule for numerical integration
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U = - U_tilde * A .* (1 / (2 * mod_amp)) .* trapz(dx, dU, 1); % Integration along the first dimension (axis=0)
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end
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