Generalized eikonal treatment of the Gouy phase shift

Area of Science:

• Wave optics
• Physical optics
• Electromagnetic theory

Background:

• The Gouy phase shift is a fundamental phenomenon in wave optics, describing the phase accumulation of a light beam as it passes through a focus.
• Previous treatments often simplified the optical system, neglecting diffraction and phase distortion effects.
• Understanding the Gouy shift is crucial for applications involving focused light, such as optical trapping and microscopy.

Purpose of the Study:

• To generalize the understanding of the Gouy phase shift by incorporating diffraction effects.
• To provide a new perspective on the Gouy phase shift as an intensity-averaged optical path difference.
• To confirm the influence of transverse spatial confinement on the Gouy phase shift.

Main Methods:

• Development of a generalized refractive index that accounts for diffraction.
• Formulation of a generalized eikonal based on the generalized refractive index.
• Comparison between the generalized eikonal and the geometrical eikonal to calculate optical path differences.

Main Results:

• The Gouy phase shift is shown to be equivalent to an intensity-averaged optical path difference.
• The generalized approach successfully includes phase distortion effects.
• The role of transverse spatial confinement in the Gouy shift is quantitatively confirmed.

Conclusions:

• The generalized refractive index provides a unified framework for understanding the Gouy phase shift.
• This work offers a more comprehensive theoretical basis for analyzing focused light beams.
• The findings have implications for precise control and manipulation of light in various optical systems.