用matlab模拟光经过两层折射率不同的介质时p位置的点扩散函数强度轴向分布

这个问题需要利用光学传输理论和Fresnel公式来模拟光线在介质之间的传播和折射，并最终计算出扩散函数强度的轴向分布。

以下是一个可能的MATLAB代码实现，其中包括了基本的光学传输理论和Fresnel公式的应用：

% Define input parameters
n1 = 1.0; % Refractive index of medium 1 (e.g. air)
n2 = 1.5; % Refractive index of medium 2 (e.g. glass)
lambda = 0.5e-6; % Wavelength of light (in meters)
NA = 0.5; % Numerical aperture of the lens
z = 0:1e-6:2e-3; % Axial positions to calculate intensity (in meters)

% Calculate parameters for Gaussian beam
w0 = 2 * lambda / (pi * NA); % Beam waist
zR = pi * w0^2 / lambda; % Rayleigh range

% Calculate parameters for Fresnel reflection and transmission coefficients
theta1 = asin(NA / n1); % Angle of incidence
theta2 = asin(NA / n2); % Angle of refraction
Rs = (n1 * cos(theta1) - n2 * cos(theta2)) / (n1 * cos(theta1) + n2 * cos(theta2)); % Reflection coefficient (s-polarization)
Rp = (n2 * cos(theta1) - n1 * cos(theta2)) / (n2 * cos(theta1) + n1 * cos(theta2)); % Reflection coefficient (p-polarization)
Ts = 2 * n1 * cos(theta1) / (n1 * cos(theta1) + n2 * cos(theta2)); % Transmission coefficient (s-polarization)
Tp = 2 * n1 * cos(theta1) / (n2 * cos(theta1) + n1 * cos(theta2)); % Transmission coefficient (p-polarization)

% Calculate intensity distribution at each axial position
I = zeros(size(z));
for i = 1:length(z)
    % Calculate beam waist and divergence angle at this axial position
    w = w0 * sqrt(1 + (z(i) / zR)^2);
    theta = atan(z(i) / zR);
    
    % Calculate complex amplitude at the input plane
    A = exp(-r.^2 / w^2) .* exp(-1i * k * z(i)) .* exp(1i * k * r.^2 / (2 * z(i))) .* (r <= w);
    
    % Propagate complex amplitude through medium 1
    A = A .* exp(1i * k * n1 * z(i));
    
    % Calculate reflection and transmission coefficients at the interface between medium 1 and medium 2
    Rs = (n1 * cos(theta) - n2 * sqrt(1 - (n1 * sin(theta) / n2)^2)) / (n1 * cos(theta) + n2 * sqrt(1 - (n1 * sin(theta) / n2)^2));
    Rp = (n2 * cos(theta) - n1 * sqrt(1 - (n2 * sin(theta) / n1)^2)) / (n2 * cos(theta) + n1 * sqrt(1 - (n2 * sin(theta) / n1)^2));
    Ts = 2 * n1 * cos(theta) / (n1 * cos(theta) + n2 * sqrt(1 - (n1 * sin(theta) / n2)^2));
    Tp = 2 * n1 * cos(theta) / (n2 * cos(theta) + n1 * sqrt(1 - (n2 * sin(theta) / n1)^2));
    
    % Propagate complex amplitude through medium 2
    A = A .* Ts .* exp(1i * k * n2 * (z(i) - z(1))) + A .* Rp .* exp(-1i * k * n1 * (z(i) - z(1)));
    
    % Calculate intensity at this axial position
    I(i) = sum(abs(A).^2);
end

% Plot intensity distribution versus axial position
figure;
plot(z, I);
xlabel('Axial position (m)');
ylabel('Intensity');

这段代码首先定义了输入的一些光学参数，包括两种介质的折射率、光的波长、数值孔径和轴向位置。然后，它使用这些参数计算出高斯光束的一些参数（如束腰和瑞利范围），并计算出Fresnel反射和透射系数。接下来，它使用这些参数来模拟光线在两种介质之间的传播和折射，并计算出在每个轴向位置处的扩散函数强度。最后，它将强度与轴向位置绘制成图表。

需要注意的是，这只是一个简单的示例代码，仅用于说明如何使用MATLAB来模拟光线传输和计算扩散函数强度。实际上，真正的模拟可能需要更复杂的模型和算法，因此需要更多的参数和计算步骤。