Determine the intensity profile and fwhm for gaussian beam.

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Homework Help Overview

The problem involves determining the intensity profile and full width at half maximum (FWHM) of a Gaussian beam with a specified wavelength and initial FWHM, evaluated at a distance of 10 meters from the source. The context is within the field of optics.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the necessity of knowing the beam waist diameter or the distance to the beam waist to properly interpret the problem. Questions are raised about the meaning of "initially" in the context of the problem.

Discussion Status

The discussion is ongoing, with participants expressing uncertainty about the initial conditions required for a complete solution. Some suggest that further clarification from the problem setter may be necessary.

Contextual Notes

There is a lack of explicit information regarding the beam waist, which is critical for solving the problem. Participants note that without this information, any attempts to solve the problem may be speculative.

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Homework Statement



A beam of wavelength 600 nm has initially an intensity profile of Gaussian shape with a
fwhm of 1 mm. Determine the intensity profile and fwhm 10 meter away.

Homework Equations



FWHM = λ/(2NA√(1 + I/Is))

The Attempt at a Solution


[/B]
FWHM1 = 1mm = 600 nm/(2NA√(1 + I/Is))

(2NA√(1 + I/Is)) = 0.0006m
NA2(1+ I/Is) = 0.00015

10meters away :

NA2(1+ I/Is) = (0.00015)/10 = 0.000015
 
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Where is the initial information are given? Is it at the beam waist?
 
This is all the information given!
 
You have to know either the beam waist diameter or the distance between the initial plane and the beam waist. Without these information you can only guess what the question maker means with "initially" in the question's wording.
 
There must be a solution as it was on an exam?
 
If I were to face such a problem in an exam, exactly worded as you have written, I would be most likely not overwhelmed by shyness to ask the prof for a greater detail about the initial plane.
 

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