Simulation of Light Diffraction Phenomena

Light diffraction refers to the bending phenomenon of light waves when encountering obstacles or passing through slits, with its specific patterns primarily determined by propagation distance. In MATLAB, we can visualize this physical process through numerical simulation using computational wave optics methods.

### Relationship Between Diffraction Types and Propagation Distance Diffraction is mainly classified into two types based on light propagation distance:

Fresnel Diffraction (Near-Field Diffraction) Occurs when the observation screen is relatively close to the obstacle. In this regime, the curvature of the wavefront cannot be neglected, resulting in complex patterns of bright and dark fringes with blurred edges and non-uniform intensity distribution.

Fraunhofer Diffraction (Far-Field Diffraction) Occurs when the observation screen is sufficiently far from the obstacle (satisfying the far-field condition), where light wavefronts approximate plane waves. The diffraction patterns become stable, displaying characteristic features like single-slit interference fringes or Airy disks for circular apertures.

### MATLAB Implementation Approach Modeling Obstacles Create a 2D matrix representing the aperture (e.g., single slit, circular hole) where transparent regions are set to 1 and opaque regions to 0. This binary mask can be generated using logical operations or geometric shape functions.

Calculating Diffraction Fields Near-field (Fresnel Diffraction): Implement using angular spectrum propagation method or Fresnel integral, accounting for spherical wave phase variations through complex exponent calculations. Far-field (Fraunhofer Diffraction): Utilize Fast Fourier Transform (FFT) to convert the optical field to frequency domain, effectively computing the Fourier transform of the aperture function with fft2() function.

Visualization Results By adjusting propagation distance parameters, compare intensity distribution patterns at different distances. Far-field diffraction exhibits more uniform fringe spacing, while near-field diffraction shows significant edge distortion and intensity fluctuations. Use imagesc() or surf() functions for 2D/3D visualization of diffraction patterns.

### Extended Applications Parameterizing propagation distance enables dynamic demonstration of the transition from Fresnel to Fraunhofer regions. For instance, when simulating laser propagation through apertures of varying sizes, the propagation distance proves decisive for diffraction pattern formation. This methodology finds applications in optical system design and educational demonstrations, particularly when combined with interactive GUI components for real-time parameter adjustment.