Beam Expansion: Distance between 2 lenses in a Keplerian beam expander

  • #1
tanhanhbi
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Homework Statement
Determine the optical distance d between the lenses such that the distance z′ to the waist of the final beam is as large as possible.
Relevant Equations
Gaussian beam
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Basically this is the Exercise In Fundamentals of Photonics book.
We also need to use these two equation (1) and (2)
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As we all know, in order to make the z' as far as possible, we must place 2 lens with this distance
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I already figure that thank to the initial condition of the first lens position
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So that the z1 must equal to f1
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For the z2, I tried to replace zo in (2) onto (1), then take the derivative of z' with respect to z2. My initial though that let the derivative of z' equal to 0, we can find the maximal of z'. But actually after finish the derivative thing, z' do not have maximal and I already always infinity ?
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So I am not sure what wrong with my thinking. If someone could give me a clue, I really appreciate it.
 

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FAQ: Beam Expansion: Distance between 2 lenses in a Keplerian beam expander

What is a Keplerian beam expander?

A Keplerian beam expander is an optical device that uses two lenses to increase the diameter of a laser beam. It consists of a converging lens (objective) followed by a diverging lens (eyepiece), arranged in such a way that the beam passing through is magnified.

How do you determine the distance between the two lenses in a Keplerian beam expander?

The distance between the two lenses in a Keplerian beam expander is equal to the sum of their focal lengths. If the focal lengths of the objective and eyepiece lenses are f1 and f2, respectively, then the distance d between the lenses is given by d = f1 + f2.

What happens if the lenses are not placed at the correct distance in a Keplerian beam expander?

If the lenses are not placed at the correct distance, the beam expander will not function properly. The beam may not be collimated correctly, leading to a distorted or unfocused output. Proper alignment is crucial to ensure that the expanded beam remains parallel and well-defined.

Can the magnification factor of a Keplerian beam expander be adjusted?

The magnification factor of a Keplerian beam expander is determined by the ratio of the focal lengths of the two lenses. Specifically, the magnification M is given by M = f2 / f1. To adjust the magnification, you would need to change one or both of the lenses to ones with different focal lengths.

What are the advantages of using a Keplerian beam expander?

Keplerian beam expanders offer several advantages, including a high degree of magnification and the ability to produce a collimated output beam. They are also relatively simple to design and can be used to improve the beam quality for various applications, such as in laser optics and scientific research.

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