Isolating the Gouy phase shift in a full physical-optics solution to the propagation problem

Area of Science:

• Optics
• Electromagnetism
• Wave Propagation

Background:

• The Gouy phase shift, discovered in the late 19th century, remains a topic of significant scientific interest.
• This phenomenon exists at the intersection of geometrical optics and diffractive behavior.
• Understanding the Gouy effect is crucial for a complete picture of light propagation.

Purpose of the Study:

• To derive a unified mathematical formula for the Gouy phase shift using a full electromagnetic solution.
• To reconcile the predictions of geometrical optics with the principles of physical optics in the context of the Gouy phenomenon.
• To provide a clear explanation of the physical effects contributing to the Gouy phase shift.

Main Methods:

• Employing purely mathematical arguments within a complete electromagnetic solution for light propagation.
• Deriving a formula that explicitly reveals all relevant physical effects, including the Gouy phase shift.
• Comparing the derived formula's results with traditional ray-tracing methods.

Main Results:

• A comprehensive formula was derived from electromagnetic theory, encompassing the Gouy phase shift.
• Discarding field information from the formula successfully reproduced ray-tracing results.
• The study validates geometrical optics predictions like ray mapping and optical path length accretion.

Conclusions:

• The derived formula offers a unified understanding of the Gouy phenomenon, bridging geometrical and physical optics.
• This work helps to resolve the dichotomy between geometrical and physical optics in explaining the Gouy effect.
• The findings provide a more complete theoretical framework for analyzing light propagation and phase shifts.