Simulating Fresnel Diffraction Phenomena

Fresnel diffraction is a common optical diffraction phenomenon that occurs when there is a finite distance between the light source and observation screen, differing from Fraunhofer diffraction (far-field diffraction). MATLAB provides excellent capabilities for simulating this phenomenon, helping to understand the complex behavior of light wave propagation.

### Implementation Approach Wavefront Definition: First define the incident light's wavefront, which can be a plane wave or spherical wave. Complex numbers are typically used in simulations to represent both amplitude and phase of the light wave. Code implementation often involves creating a 2D matrix where each element contains complex values representing the wavefront at different spatial points. Diffraction Aperture Modeling: Set the shape of the diffraction screen (such as circular aperture, rectangular aperture, or custom shapes) and calculate the initial wavefront distribution after the light wave passes through the aperture. This can be implemented using logical indexing or custom mask functions to define the aperture geometry in the computational grid.

Fresnel Approximation: Utilize the Fresnel diffraction integral formula, calculating wavefront propagation to the observation screen through Fast Fourier Transform (FFT) or convolution methods. MATLAB's fft2() and ifft2() functions can efficiently handle these calculations. The angular spectrum method or direct integration approach can be implemented depending on the specific requirements.

Intensity Distribution Visualization: Finally calculate the intensity distribution on the observation screen (square of the amplitude) and display diffraction patterns through images or 3D plots. MATLAB's imagesc(), surf(), or pcolor() functions are commonly used for visualization, with proper colormap selection to enhance pattern recognition.

### Extended Considerations Parameter Effects: Adjust light source wavelength, aperture size, and propagation distance to observe changes in diffraction patterns. This can be implemented through parameter sweeps using for-loops or MATLAB's parameter study tools. Phase Modulation: Introduce phase objects (such as lens effects) on the diffraction screen to simulate more complex optical systems. This involves modifying the phase component of the wavefront using phase mask functions that represent optical elements. Dynamic Simulation: Generate diffraction process animations by iteratively changing propagation distances through loops, visually demonstrating the transition characteristics of Fresnel zones. MATLAB's getframe() and movie() functions can be used to create and display these animations.

This simulation approach is not only suitable for educational demonstrations but can also be used for preliminary verification in optical system design workflows.