Demonstration of Gaussian Beam Transformation Through Lenses

The transformation of Gaussian beams through lenses constitutes a fundamental topic in laser optics. Understanding this process provides direct guidance for laser system design and optical path alignment.

Typical Gaussian beam propagation characteristics are determined by the beam waist radius and Rayleigh length. When a beam passes through a lens, the lens' focal length modifies the beam wavefront curvature, thereby reshaping the beam's propagation properties. Based on ABCD matrix theory, we can derive that the new waist position after thin lens transformation satisfies the object-image relationship formula, while beam parameter changes can be precisely described through the transformation law of complex curvature radius.

Parametric analysis requires focus on three core variables: the incident beam's waist radius, the distance between incident plane and lens, and the lens focal length. These three parameters collectively determine the new waist position and size of the output beam. When the incident beam waist is located at the lens' front focal point, the output beam will form a new waist at the lens' rear focal point - this principle forms the basis for laser beam expander/reducer system design.

For optical simulation implementation, a step-by-step computational approach is recommended: first calculate the lens' modulation effect on wavefront phase, then compute the modulated beam propagation through Fresnel diffraction integration. This method accurately reproduces phenomena observed in practical optical systems, such as beam size oscillations and focal point shifts. In practical applications, non-ideal factors like lens aberrations and surface reflection losses must be considered for their impact on beam quality.