Gouy Phase Shift: Definition, Formula, and Applications in Optics

Gouy phase shift refers to the phase shift that occurs in the transverse plane of a light beam as it propagates through an optical system, such as a lens or waveguide. This phase shift is caused by the variation of the optical path length of the beam across its transverse profile.

In particular, the Gouy phase shift is related to the focusing of the beam. As the beam converges towards a focus, the optical path length in the center of the beam is shorter than at the edges, leading to a phase shift between these regions. This phase shift is known as the Gouy phase shift and is given by:

Δϕ = arctan(z/zR)

where Δϕ is the Gouy phase shift, z is the distance from the focus, and zR is the Rayleigh range of the beam, which characterizes the degree of divergence of the beam.

The Gouy phase shift is important in the design and optimization of optical systems, as it affects the spatial and temporal properties of the beam. For example, it can influence the formation of interference patterns and the propagation of laser beams in nonlinear media.