# Gaussian Beam propogation in a fiber

If we suppose that a Gaussian beam traveles in the fiber with diagonal end as it shown in the image, so I have several questions:

1- Do we get in the end of the fiber Evanescent field (Total reflection)?

2- If we get Evanescent field in the end of the fiber, what is the shape (intensity profile of the field) then?

3- I have question about also the traveling of Gaussain beam in the fiber, Does it hit always in the same position on the cladding in total reflection or it can be hit in another spots on the cladding as it shown in the following picture: (The red line is in case it just on path that can it take through the fiber, the gray line is in case it can take many paths through the fiber) which one is correct?!

• What core diameter and optical wavelength are we talking about here. The answer is very different if we are talking about 650 nm light with 1 mm core, vs 1550 nm light with 9 um core. – The Photon Jul 27 '19 at 15:57
• The wavelength that I use is 633nm the diameter of the core is 8 micrometer. – stdscience Jul 28 '19 at 10:21

We do not get total reflection at the end. These ends are used to couple fibers together, and the reason for the tilted end is to get rid of reflections in the backwards direction. These reflections would be evanescent and thus removed shortly after reflection.

Travelling waves in fibers do not always hit in the same spot, this is a simplified version to think of it as. Both ray-model and wave-model allows for propagation through fibers. The angle for TIR represents the cone through which light can enter the fiber and propagate without losses. I'd more of it think as the light as everywhere on the cladding as the light passes, each photon having different directions allowing for propagation.

• Thank you a lot for your answer :) .I didn't get the point about the reflection in the backwards direction. let's suppose that the light hits the surface in angle of 90 degree, does a reflection in the backwards occur?! why? And if so, Do these reflections cause to the evanescent field in the direction of the aperture, yes?! (Which fast removed right after) – stdscience Jul 27 '19 at 15:24
• @stdscience If it would arrive at an unslanted edge it would, due to the edge always being imperfect, encounter glass-air-glass interfaces at which reflections occur due to the differnet refractive indices. This means that there would be reflections in the backwards direction that would be able to propagate. Depending on the equipment on the other end this is not always desireable. I don't understand the last part of your comment? When you feel that you're satisfied with the answer, don't forget to mark it as answered. – DakkVader Jul 27 '19 at 16:14
• Thank you for your answer. Actually my whole interest is the evanescent field in the end of the fiber.. if I will get evanescent field or not... so do I get Evanescent field or not..?! There is another question in my mind, let's say we have flat straight end (normal one) so does the near field after the end of the fiber is containing evanescent field?! And how in this case the Near field is defined?! (And How do I mark it as answered?!) – stdscience Jul 28 '19 at 10:36
• If I can ask my question more clear, these reflections can cause for evanescent field as if it would be total internal reflection?! – stdscience Jul 28 '19 at 18:12
• Thank you a lot for your answers :), I think it gave me a picture that I can think further about that. I meant about the Evanescent field that if there will be Evanescent field in the medium (let say the other medium is air) which is the interface with the end of the fiber. Again thank you so much :) – stdscience Jul 28 '19 at 23:46

The wavelength that I use is 633 nm the diameter of the core is 8 micrometer.

IIRC, standard silica-glass 9-um fiber with ~0.5% index difference from core to cladding supports 3 or 4 propagating modes at 633 nm.

This means you have either single-mode fiber or something very close to it, unless the index contrast is much stronger than in standard fiber.

And this means your diagram showing many propagating rays, with dramatically different angles, is at best a gross simplification of the actual behavior, and likely to lead you to wrong conclusions about the physics.

To really understand the fiber behavior, you should consider a wave optics model rather than ray optics.

Do we get in the end of the fiber Evanescent field (Total reflection)?

Presence of an evanescent field does not imply total internal reflection.

There will always be an evanescent field present at a fiber end facet, if the modes profiles in the 2nd medium don't exactly match the mode profiles in the fiber.

There will not be total reflection when a fiber end is coupled to free space.

If we get Evanescent field in the end of the fiber, what is the shape (intensity profile of the field) then?

As far as I know, a complete 3-d EM simulation would be needed to answer this.

I have question about also the traveling of Gaussain beam in the fiber, Does it hit always in the same position on the cladding in total reflection or it can be hit in another spots on the cladding as it shown in the following picture

First, the mode profiles for (low mode-count) step-index fiber are not Gaussian. They are normally described by the Bessel functions. The difference between a Gaussian profile and a Bessel profile are pretty small, but they're enough to not allow perfect coupling from a fiber mode to a single free space mode.

Second, (here's where your ray optics model is leading you astray), the beam doesn't "hit" in specific locations along the cladding boundary. The beam propagates as a guided wave, with (for the main LP01 mode) nonzero energy anywhere in the core, and an evanescent component in the cladding, all along the length of the fiber.

• Thank you a lot for your answer :). Can you please explain more about the Evanescent field at the end of the fiber how it be there?! I didn't understand the statement "if the modes profiles in the 2nd medium don't exactly match the mode profiles in the fiber." What do you mean mode profile in the second medium? let's say the second medium is air so what that means?! And another question, do these Evanescent fields are much weaker than the Evanescent fields that we get in case of TIR (total internal reflection) ?! – stdscience Jul 28 '19 at 17:35