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I could not get an answer if it is possible to select an arbitrary TEM (a single one) by using different optical fibres. Would it be for example possible, to choose a fibre that only supports TEM01 and another one that only supports TEM00 ?

I am asking because of the following reason: In the lab I am using a single mode (don't know which exactly, just got told it is a single mode fibre) and if I use a fibre tester which simply couples light through it I get the TEM01 mode (described by the Laguerre polynomials and Gaussian profile: https://en.wikipedia.org/wiki/Transverse_mode#Laser_modes) but I actually want the 00 mode.

Is it therefore possible that I was given the wrong fibre?

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It is not possible to have a fiber that supports TEM01 but not TEM00. If the fiber is radially symmetric, the lowest mode will be radially symmetric as well. If it is a single mode fiber, only the roundish mode will be guided. To be precice, the modes in a fiber are mostly called LP modes. See e.g. https://www.rp-photonics.com/modes.html (Fig. 3) The fundamental mode would be LP01. If you see an image which looks like TEM01 there are two possibilities:

  1. you're not having a single mode fiber and you see the higher order mode (LP11)
  2. your fiber end is broken or dirty such that it looks like you're having this mode.

So, first cleaning the fiber might help. You can then check for 1) by trying to change the coupling to the fiber while observing the mode image. If the intensity distribution changes, it should be a multi-mode fiber.

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