Explaining Gouy Phase Shift: Simple Explanation

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Gouy Phase Shift is a phenomenon that occurs at caustics, where the intensity of a wave increases significantly near a focal point. This shift in phase is attributed to the breakdown of the assumption that the wave behaves as a plane wave, which typically holds true except in the vicinity of caustics. The wave's intensity varies slowly on a scale of 1/k, but near the focal point, it becomes highly concentrated over a distance of approximately λ/2. A more detailed analysis can be conducted using the WKB approximation, which provides insights into the behavior of waves in this context. Understanding Gouy Phase Shift is essential for grasping the effects of focusing on wave propagation.
vivek91m
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Hello friends,
Could you please explain me Gouy Phase Shift, i have gone through the wikipedia article and i know that it occurs because of the focusing although i am not able to get a physical picture of the same, so it would be really nice if anyone can explain me in simple words about this phenomenon.

Regards,
Vivek.
 
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That's a general phenomenon occurring at caustics. Usually, it is a good approximation to assume that the wave is a plane wave with wavevector given as k=nw/c, where w is the frequency, n the refractive index and c the speed of light in vacuum. Usually the intensity of that wave A varies slowly on a scale 1/k. This assumption breaks down near a caustic or a focal point and the intensity becomes very large over a distance \Delta x\approx \lambda/2=\pi/k. This intensity bump thus shifts the phase of the wave after the focal point.
A more careful analysis starts from the short wavelength asymptotics of the wave equation (WKB approximation), see e.g.:

http://books.google.de/books?id=phb...wBzgo#v=onepage&q=caustic phase shift&f=false
 
Thank you for your reply.
 
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