Optical waveguide modes with different speed, what happens?

[ja!]

Hi, I'm new on the forum and I would like to start with a question. I've searched for a reply in old posts with no success. If you can help me to find an answer I'll be very glad.

Talking about optical modes inside a waveguide. If a waveguide support two different modes, say TM and TE mode, but one (suppose TE) has a faster propagation that the other, then what happens? Does the waveguide supports only the TE mode? Or both modes propagates? What happens to the transmitted signal? It has an higher TE component than a TM component?

Please help me on understanding this topic also adding your observations.

Thanks

 

[basik156]

Hello. Are you familiar with the idea of birefringence and the propagation of light in anisotropic media? For example if we take a crystal of calcite the two polarization states of the light will experience a different index of refraction due to the structure of the crystal provided the beam is propagating at some angle with respect to the optic axis. If this is not clear I suggest you pick up the book "Introduction to Modern Optics" by Fowles or just browse around online for notes on propagation in anisotropic media.

In the same spirit let us consider an optical fiber. If we take our waveguide to be just an optical fiber with some circular symmetry it will indeed be capable of propagating two modes with orthogonal polarization. If some anisotropy arises in the cross-section of our fiber it should be clear that these two modes will propagate at different speeds. If there is a definite phase relationship between these two modes and they propagate at an angle with the so called 'optic axis' of the fiber the resultant polarization will rotate through various states of elliptical polarization.

So let me ask you does the waveguide support only the TE mode? How can we preserve the polarization through the fiber? (It's okay if you don't get this second one but think about it)

 

[ja!]

Thanks for your reply. I'm trying to go deep in the argument, that's why I waited a bit before reply to you.

I would like to give you a scenario to discuss on:
I've got a waveguide that supports both TE and TM modes, but I put inside the waveguide just a TE mode.
Calling nTM the effective refractive index of the TM modes, and nTE the effective refractive index for the TE modes,
there are 3 possible situations:

1. nTM<nTE

2. nTM=nTE

3. nTM>nTE

what happens in the 3 cases?

In my opinion
I think that in both 3 cases, since the WG supports both TE and TM, even if I put inside just TE mode, I can have at the end of the WG also a percentage of TM mode, right?

CASE 1 and 3: TM, TE propagates with different speeds, so the polarization will change inside the waveguide and at the end I'll have an elliptical polarization depending on the length of the waveguide and with of the modes propagates faster.
CASE 2: TM, TE have got the same speed, and here I really don't know what should happen...

Could you help me on analyzing those situations or give me an hint for some reading about this stuff?
Thanks