Collimating light from Optical fibre problem

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SUMMARY

The discussion focuses on the optical principles involved in collimating light from two different optical fibres using a thin lens with a focal length f. For the first fibre with a small core diameter and numerical aperture NA, the optimal separation u between the lens and the fibre for best collimation is determined to be u = f. The divergence angle θ1 is calculated using the relationship NA = sin(θ1), and the diameter D of the collimated beam is approximated as D ≈ f NA. In contrast, the second fibre with a larger core diameter d results in a larger divergence angle θ2, which can be expressed as a function of f and d.

PREREQUISITES
  • Understanding of thin lens equations, specifically 1/u + 1/v = 1/f
  • Knowledge of numerical aperture (NA) and its relation to divergence angles
  • Familiarity with trigonometric approximations in optics
  • Basic principles of light propagation in optical fibres
NEXT STEPS
  • Study the derivation of the thin lens formula and its applications in optical systems
  • Explore the concept of numerical aperture and its impact on light propagation in optical fibres
  • Learn about diffraction limits in optical systems and how they affect beam divergence
  • Investigate the differences in light behaviour between small and large core optical fibres
USEFUL FOR

Optical engineers, physicists, and students studying optics or photonics who are interested in understanding light collimation techniques and the effects of fibre core diameter on beam divergence.

XCBRA
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Homework Statement



A thin lens of focal length f is used to collimate the light emerging from two different optical fibres.
When used with a first fibre of small core diameter and numerical aperture NA it acheives a diffraction limited divergence of θ1 for the collumated beam. Find the separation u between the lens and the fibre that provides the best collimation. Find θ1 and the diameter D of the collumated beam immediately behind the lens.

When used with a second fibre of a large core diameter d but the same numerical aperture, the beam diverges much faster than it did using the first fibre. Calculate this larger divergence angle 2 as a function of f and d


Homework Equations



NA = sin(θ1)

1/u+1/v=1/f

The Attempt at a Solution



I am not entirely sure how to approach this problem as it is not a point source. I would like to say that:

for best collimation u = f -- from lens equation
and then

D=f tan(θ1) ≈ fθ1 ≈ f NA -- from trigonometry

however I am not sure if this is correct. Any hints on how to approach this question would be greatly appreciated. Many thanks
 
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wow, so difficult to me!
 

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