# Modes of Optical Fiber propagation

• Super Sujan
In summary, modes are solutions to Maxwell's equations within a waveguide that satisfy boundary conditions. They can be visualized as rays which travel along the guide axis. There are many solutions, and they are usually classified according to the boundary conditions (e.g. TE, TM, or TEM). The physical interpretation of a mode depends on the type of waveguide used.
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?

Super Sujan said:
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'.

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.

Super Sujan said:
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

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.

Super Sujan said:
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).

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.

Last edited:
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.

## 1. What are the different modes of optical fiber propagation?

The different modes of optical fiber propagation are single mode and multimode. Single mode fibers allow only one mode of light to propagate, while multimode fibers allow multiple modes to propagate simultaneously.

## 2. How does light propagate through an optical fiber?

Light propagates through an optical fiber through the principle of total internal reflection. The light enters the fiber at an angle, and the refractive index of the core is higher than the cladding, causing the light to reflect and travel through the core of the fiber.

## 3. What is the difference between single mode and multimode fibers?

The main difference between single mode and multimode fibers is the diameter of their core. Single mode fibers have a smaller core diameter, typically around 9 microns, while multimode fibers have a larger core diameter, ranging from 50 to 100 microns. This difference affects the number of modes that can propagate through the fiber and the distance the light can travel without losing its signal.

## 4. What factors affect the propagation of light in optical fibers?

The main factors that affect the propagation of light in optical fibers are the fiber's core diameter, refractive index profile, and wavelength of light. These factors determine the number of modes that can propagate, the distance the light can travel, and the speed at which it travels.

## 5. What are the advantages of single mode fibers over multimode fibers?

Single mode fibers have several advantages over multimode fibers, including higher bandwidth, longer transmission distances, and lower attenuation (signal loss). They are also less prone to dispersion, which can cause signal distortion and decrease the quality of the transmitted data. However, single mode fibers are more expensive and require more precise alignment in their installation.

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