Graded Index Fiber - Basics, Mathematical Formula, Structure, Working, Basic Principle, Dispersion and Benefits in Graded Index Optical Fiber

We have already discussed step index fibers. The other type of optical fiber based on the refractive index profile is the graded index fibre.
As we know that step index fibres make step (sudden) change in the refractive index at the core-cladding interface. The core has a constant refractive index that changes to a lower (constant) refractive index in the cladding.

Step Index Vs Graded Index optical fiber (Read more)

Now let's discuss the graded index fibres-

What is Graded Index Optical Fibre?

In graded index fibre the core has maximum value of the refractive index at it's axis and this value decreases on radially moving away from the core axis and has a constant value of refractive index in the cladding. Now let's see the mathematical representation of the Graded index fiber- 

Mathematical representation of Graded Index Fibre

Graded index fibers refractive index formula

Refractive Index Profile Graph for Optical Fibers

Graded index fiber structure, working and refractive index profile graph

This graph shows how the refractive index of graded index fiber varies as we move away from the core axis.
This graph shows different kinds of refractive index profiles like- step index profile, triangular profile and parabolic profile.
Here we will use the refractive index profile (alpha= 2) for the graded index fibre.
The diagram above shows, how the light rays travel inside the graded index fibre-

🌓READ THIS ALSO:-
Optical Fiber Communication (Complete)

As you can see in this diagram, that the optical fiber has two layers, core (shown in blue colour) and cladding (shown in green colour).
The propagation of light rays inside the graded index fibers also, takes place by the Total Internal Reflection (TIR) phenomena like step index fibres. But the propagation path of light is not exactly same as in case of step index fibres.

🌓READ THIS ALSO:-
Structure and Working of optical Fiber

The graph given in this diagram also shows how the refractive index of the core and cladding changes as we move away from the core axis. You can observe here that the refractive index of the cladding is constant (n2) while that of core varies parabolically.
As you now know that the refractive index of the core in graded index fibre varies smoothly therefore the propagation path of light also has a smooth path.

Propagation of light inside Graded Index Fiber (Dispersion in optical Fibers)

By the following Diagram you will clearly and easily understand how the light ray moves inside the graded index fibre and why it has a smooth propagation path.

Propagation of light inside graded index optical fiber

The diagram shows only the core layer of the graded index fibre. As we know that as we move away from the core axis, the refractive index decreases until we reach the core-cladding interface. Therefore the refractive index has its maximum value at the core axis. So as the light ray moves from the core axis towards the core-cladding interface, it gets refracted continuously. As the light ray is moving continuously from a denser medium to rarer medium, it continuously deviates away from the normal when it goes away from the core axis and at some point this continuous deviation away from the normal causes the direction of the light ray turn back towards the core axis.
But when it returns back towards the core axis it continuously moves from rarer medium to denser medium and moves continuously towards the normal.

🌓READ THIS ALSO:-
Benefits of optical fibers

The light rays keep propagating in this way inside the core. This is known as the Total Internal Reflection (TIR). The total internal reflection is sharp (sudden) in case of step index fibre because the change in refractive index is sharp (sudden).

Benefits of graded index fiber and Dispersion

Observe the figure shown above. As the light rays travel slower in denser mediums (high refractive index) and we also know that refractive index in case of graded index fibers is maximum at the core axis and decreases as we move radially away from the core axis towards the core-cladding interface. 
We can transmit light rays at different angles into the optical fibre. So the light rays that travel near the core axis move slower in comparison to the light rays that travel near the core-cladding interfaces. 
You can easily understand this, that the light rays that travel near the core axis have to cover smaller distance in comparison to the rays that are close to the core-cladding interface. This creates a compensating effect in dispersion of light rays.

🌓READ THIS ALSO:-
Acceptance angle and Numerical Aperture (NA) in optical fibers

This phenomena is responsible for lower dispersion (broadening of light pulses) in case of graded index fibres in comparison to step index fibres because the light rays travelling at different angles reach at the receiving end almost at the same time. Because the light rays that need to travel longer distances (moving close to core-cladding interface) propagate at high speed because of lower refractive index (rarer medium) near the core-cladding interface. This reduces broadening (dispersion) of the light pulses.

Read More:

Go to home page
Optical fibers in communication: covers all important points
Optical fiber: structure and working principle
Optical fiber sources (desirable properties)
Advantages of optical fiber communication 
Step index optical fiber (multimode and single mode step index fibers)
Single-mode optical fiber advantages