Demonstration of Gaussian Beam Transformation through Lenses

When a Gaussian beam passes through a lens, its propagation characteristics undergo significant changes due to the focusing or diverging effects of the lens. This process involves modifications to key parameters including beam waist size, divergence angle, and wavefront curvature, which are crucial for laser optical system design.

Physical mechanism of Gaussian beam transformation by lenses: Beam waist position shift: The lens redefines the Gaussian beam's waist location, where the new waist position correlates with the lens focal length and incident beam parameters. Wavefront curvature adjustment: The lens modifies the incident beam's wavefront curvature, with the output beam's radius of curvature following the thin lens transformation formula. Waist size scaling: The output beam's waist diameter is inversely proportional to the lens focal length, which can be precisely calculated using ABCD matrix theory.

Parameterized implementation approach: The system can be designed with an interactive input interface supporting adjustment of initial beam parameters (wavelength, waist radius, lens focal length), enabling real-time visualization of transformed beam profiles and propagation characteristics. Core computations should be based on Gaussian beam complex parameter propagation laws combined with numerical simulation of the lens's phase modulation effects. Key functions would include q-parameter calculation using ABCD matrices and beam profile plotting using Gaussian field equations.

Application extensions: This model can be extended to multi-lens system analysis or practical scenarios like coupling efficiency optimization, serving as a theoretical pre-research tool for applications such as fiber coupling and laser processing. The code architecture could incorporate modular design for easy integration of multiple optical elements and efficiency calculation algorithms.