Tru Physics

Gouy Phase

—

by

Tru Physics
in

Introduction

The Gouy phase is a phase shift that occurs for a beam of light when it propagates through a focusing or defocusing element, like a lens. This phase shift, named after the French scientist Léon Gouy, is an essential aspect of Gaussian beams and wave optics.

Gaussian Beams

A Gaussian beam is a beam of monochromatic electromagnetic radiation whose amplitude (electric field) and intensity distributions are well described by Gaussian functions. The Gouy phase shift comes into play as the beam propagates and its width changes, typically through a lens or other focusing elements.

The complex amplitude of a Gaussian beam is given by:

U(r, z) = \dfrac{A}{w(z)} \cdot e^{\left(-\dfrac{r^2}{w^2(z)}\right)} e^{\left(-ikz - ik\dfrac{r^2}{2R(z)} + i \zeta(z)\right)}

where A is the peak amplitude, w(z) is the beam width, r is the radial distance from the center of the beam, k is the wave number, R(z) is the radius of curvature of the beam’s wavefronts, and \zeta(z) is the Gouy phase.

Gouy Phase

The Gouy phase itself is a function of the axial position z along the beam, and is given by the expression:

\zeta(z) = \arctan\left(\dfrac{z}{z_R}\right)

where z_R is the Rayleigh range, a parameter of the beam that describes the distance over which the beam’s cross-sectional area doubles.

Implications of Gouy Phase

The Gouy phase has several important implications in optics. It’s fundamental for the understanding of the propagation characteristics of Gaussian beams. It plays a critical role in nonlinear optics, the study of interactions between light and matter that occur at high light intensities. It is also crucial in the design of lasers, as the Gouy phase shift can affect the stability of laser cavities.

Gouy Phase in Mode-Locked Lasers

In mode-locked lasers, the Gouy phase shift can lead to a phenomenon known as “dispersive wave breaking,” which can limit the shortest achievable pulse duration. Understanding and managing the Gouy phase shift is therefore critical for achieving ultra-short pulse durations in mode-locked lasers.

Conclusion

The Gouy phase is an integral part of wave optics and the propagation of Gaussian beams. From laser design to nonlinear optics, a proper understanding of the Gouy phase shift is necessary to manipulate and control light for a variety of applications.

Do you prefer video lectures over reading a webpage? Follow us on YouTube to stay updated with the latest video content!

Want to study more? Visit our Index here!

Comments

Have something to add? Leave a comment!