Modes of Optical Fiber propagation

[Super Sujan]

What actually is a mode of optical fiber propagation?Is it similar to modes which correspond to various configurations as in standing waves on a string ? Also How correct is it to consider no. of rays as no of modes?

 

[Andy Resnick]

What actually is a mode of optical fiber propagation?Is it similar to modes which correspond to various configurations as in standing waves on a string ? Also How correct is it to consider no. of rays as no of modes?

Officially, a fiber mode is a subset of 'waveguide modes', stable solutions to Maxwell's equations within a waveguide. There are many solutions, so they are usually classified as 'TE', "TM', or 'TEM', depending on the boundary conditions. Specifically for optical fibers and lasers, the modes are often called 'LP modes', since the source generates linearly polarized light:

https://www.rp-photonics.com/lp_modes.html
https://www.rp-photonics.com/passive_fiber_optics2.html

I don't understand your second question 'How correct is it to consider no. of rays as no of modes'.

 

[Super Sujan]

Thank you Andy.
Can you also explain the physical interpretations of various modes ? I know that modes are solutions to the helmholtz equations of a waveguide (obtained by combining maxwell's equations and boundary counditions).I'm looking for a non or less mathematical answer.

 

[berkeman]

I'm looking for a non or less mathematical answer.

Have you read the Wikipedia article? It's a reasonable intro and discusses multi-mode versus single-mode fibers...

https://en.wikipedia.org/wiki/Optical_fiber

 

[Super Sujan]

Yes , I have read the article you have mentioned multiple times in the past. However the article doesn't provide a clear explanation of what a mode is or what distinguishes single mode from multi mode at the very basic level.

 

[Tom.G]

Try this one. Detailed explanations of modes.
https://en.wikipedia.org/wiki/Transverse_mode

 

[Andy Resnick]

Thank you Andy.
Can you also explain the physical interpretations of various modes ? I know that modes are solutions to the helmholtz equations of a waveguide (obtained by combining maxwell's equations and boundary counditions).I'm looking for a non or less mathematical answer.

Asking for a non-mathematical answer to a mathematical question doesn't make sense (to me).

 

[EmilyRuck]

There is of course a purely mathematical answer to this question (the Wikipedia pages can contain it), but it's not the only one.

As regards (metallic, dielectric, ...) waveguides: a mode is a field configuration which

• is a solution of Maxwell's equations and satisfies the boundary conditions of the waveguide;
  
• is able to keep a uniform magnitude along the direction of propagation;
• is self-consistent along the guide (that is: a field which behaves as if it were a plane wave in free space, but along the direction of propagation inside the waveguide). This implies that, after two consecutive reflections on the waveguide boundary, the field is able to be the same as before the reflections.

This is why it is a "stable" solution.
It is the structure of the waveguide, together with the boundary conditions, that determines what field configurations are allowed to meet the above features: for this reason, the modes are often considered as the eigenfunctions of the structure, with the related propagation constants being the eigenvalues. They represent the kind of waves that the waveguide structure can naturally host.

Maybe the main difference between a waveguide mode and the standing waves of a string is propagation: a mode is a field which travels along the waveguide axis; a standing wave is, by definition, not able to propagate. But yes, they can both be described by a fixed field structure.

IIRC, in the case of optical fibers, each mode has a related angle of incidence and it can be depicted as a ray, so yes, I think it is often correct to consider the number of rays equal to the number of currently active modes.

http://www.eecs.ucf.edu/~tomwu/course/eel6482/notes/19%20Parallel%20Plate%20and%20Rectangular%20Waveguides.pdf (page 3) is one of the simplest kind of modes you can obtain:

$$\mathbf{E}(z) = - \displaystyle \frac{V_0}{d} e^{-j k z} \mathbf{a}_y\\
\mathbf{H}(z) = \displaystyle \frac{V_0}{\eta d} e^{-j k z} \mathbf{a}_x$$

This is a field which is constant along $y$. The direction of propagation is $z$ and the magnitude of the Electric field $V_0 / d$ is constant for all $z$ (the magnitude of the Magnetic field is constant, too). It is also a TEM mode, because both the Electric and Magnetic fields are orthogonal to the direction of propagation.

 

[EmilyRuck]

If you are interested in modes, in this page the mode field expressions are obtained for a dielectric slab waveguide. It starts from Maxwell's equations and then uses boundary conditions (after introducing refraction and some basic concepts). Modes in optical fibers are obtained through a similar, if not equal, way (but, with dielectric waveguides, expressions are simpler).
The same site contains also some Matlab code to plot the field expressions.