Meridional and Skew Rays (Optical Fiber Communication)

There are two types of light rays on the basis of propagation inside the optical fiber- 
#Meridional Rays and
#Skew Rays (Helical Rays)

Here we will discuss propagation of both types of rays-

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Optical Fiber Communication (Complete)

Meridional Rays

*Meridional rays enter into the optical fiber through it's axis. 
*These rays cross the fiber axis at each reflection.

Meridional Rays Propagation Inside Optical Fiber

The two diagrams given above show the propagation of meridional rays inside the optical fiber. The first diagram provides the ray path view along the fiber axis. It is clear from the diagram that the light ray is crossing the fiber axis at each reflection. These reflections are marked as 1, 2 and 3.

Meridional and Skew Rays Video

 

Another diagram is also of meridional ray propagation but with a different view. It is ray path view along the plane normal to the fiber axis.

Now let's discuss another kind of light ray propagation inside optical fibers i.e. Skew rays.

Skew Rays (Helical Rays)

*Skew rays are also known as helical rays as they move on helical path inside the optical fiber. 
*Skew rays do not cross the fibre axis and propagate around the optical fiber axis on zigzag path.
*Skew rays greatly outnumber the meridional rays. *Skew rays enter the optical fiber off the fiber axis.
It should be noted here that, in case of skew rays, the point of emergence from the fiber in air depends upon the number of reflections inside the optical fibre. It does not depend upon the input conditions to the fiber.

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This concept is made clear with the help of two diagrams given below. 

Skew Rays (Helical Rays) Propagation Inside Optical Fiber

The first diagram of skew ray shows the ray path view along the fiber axis and the second diagram shows the ray path view along the plane normal to the fiber axis.
It is clear from the second diagram that the skew ray (helical ray) is not crossing the optical fiber axis and propagating around the axis.

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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-

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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.

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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.

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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.

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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.

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ADVANTAGES OF OPTICAL FIBER COMMUNICATION

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PULSE MODULATION TECHNIQUES (PAM, PWM, PPM, PCM)

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PULSE AMPLITUDE MODULATION (PAM)

COMPARISON OF PAM, PWM, PPM MODULATION TECHNIQUES

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CONTINUOUS TIME AND DISCRETE TIME SIGNALS (C.T. AND D.T. SIGNALS)

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Step Index and Graded Index Fibre - Comparison between Step Index and Graded Index Fibre (Optical Fiber Cable)

Here is the comparison between step index and graded index fibres on the basis of various parameters like basic structure, working principle, types, refractive index profile, propagation of light inside fibers, dispersion in optical fibers, advantages and disadvantages-

1. In step index fibers, sudden (step) change takes place in the refractive index at the core-cladding interface. The refractive index of the core is uniform
While in case of graded index fibers, refractive index of the core is non-uniform. It is maximum at the core axis and then it decreases (generally parabolically) with increasing distance from the core axis.

2. Step index fibers are of two types on the basis of modes-
#Single mode step index fiber
#Multimode step index fiber

Multimode and Single Mode Step Index Fibers

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While on the basis of modes, only one type of graded index fibre is present i.e. Multimode graded index fibre.

Graded Index Fiber (Refractive Index Profile and Propagation of Light with TIR)

3. In step index fibres, light rays propagate in a zigzag manner (on zigzag path) inside the fiber Core. These rays travel as meridional rays. It means that the rays cross the axis of fibre for each reflection while propagating.

Step Index and Graded Index Fiber Video

 

But in case of graded index fibres, the light rays propagate as skew rays or helical rays. It means that while travelling inside the core these days do not cross the fibre axis.

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Optical fiber structure and working


4. In case of step index fibers the refractive index profile may be defined as-

Refractive Index Profile of Step Index Fiber

And in case of graded index fibers, the refractive index profile is defined as -

Refractive Index Profile of Graded Index Fiber

5. Modal dispersion is present that affects signal quality in case of step index fibres.
But the graded index fibres have very low or zero dispersion as the time taken by each mode to propagate is same. As the velocity of each mode is different due to change in refractive index.

Read More-

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Quadrature Amplitude Modulation (QAM)/ QAM Transmitter and QAM Receiver Block Diagram

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What are Microwaves and their Applications (Uses) in various fields

Microwaves Properties and Advantages (Benefits)

Basic Structure of Bipolar Junction Transistor (BJT) - BJT Transistor - Working and Properties

Polar Plots of Transfer Functions in Control Systems (How to Draw Nyquist Plot Examples)

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Acceptance Angle and Numerical Aperture (NA) (Optical Fiber Communication)

In this post we will discuss two important concepts of optical fibers, these are- Acceptance Angle and Numerical Aperture (NA).

Definition of Acceptance Angle

Acceptance angle is the maximum angle with the axis of the Optical Fiber at which the light can enter into the optical fiber in order to be propagated through it.

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Now let's understand this concept with the help of this diagram-

Acceptance Angle and Numerical Aperture (NA) in Optical Fiber

This diagram clearly illustrates the concept of the numerical aperture and acceptance angle. What we mean by Acceptance cone, is also explain here.

Watch the Complete Video Here

 

Structure and Working of the Optical Fiber

Now observe this diagram carefully, two layers of the Optical Fiber- Core and Cladding can be seen in the diagram. These are drawn in pink color. The light rays propagate inside the core that has another layer over it, known as cladding.
Although other protective layers are also there over the cladding layer, But only core and cladding are shown in this image, which is enough to clear the concepts.

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The refractive index (the ratio of speed of light in vacuum and the speed of light in the medium) of the core is more than the refractive index of the cladding.
As we also know that, when a light ray propagates from a denser medium to the rarer medium, it deviates away from the normal. But when the angle of incidence is more than the critical angle then this light ray returns back into the same medium. This phenomena is called as the 'Total Internal Reflection' (TIR). 
Although it is a special case of refraction where the incidence angle is more than the critical angle, but here it seems like a reflection phenomena and the light ray is totally reflected back into the same medium. Therefore this phenomena is known as the Total Internal Reflection (TIR).

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The same phenomena of total internal reflection takes place in the optical fibre. Here the core acts as a denser medium while the cladding as a rarer medium. So the light rays propagate inside the core of the optical fiber with the total internal reflections.
But as we have already discussed that for the total internal reflection to take place, it is required that the incidence angle must be more than the critical angle. If this condition is satisfied then the light ray can propagate inside the core of The optical fiber with total internal reflection.

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Single-Mode Optical Fiber Advantages

Now again observe the image. This image shows two light rays. Focus on any one light ray. You will see that total internal reflection takes place inside the core every time at the core cladding interface. The reflected ray after total internal reflection acts as the incident ray for the next total internal reflection. As each time the incidence angle is more than the critical angle at the core cladding interface. Therefore the light ray propagates inside the core of The optical fibre with successive total internal reflections.

NOTE- For much better explanation, I suggest you to watch my video lecture given above on this page.

Acceptance Angle and Acceptance Cone

Now first we will understand the concept of acceptance cone. You can see this acceptance cone in the image given above. For the total internal reflection to take place, it is required that the light rays entering into the fibre must be confined to this cone.
It means that if there is any light ray that is entering into the fiber with an angle which is outside this cone, then the total internal reflection will not take place. Because in this case the incidence angle will be smaller than the critical angle (Visualize this condition by observing the image or you may watch the video given here). 

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Graded Index Fibers: Basics, Structure and Working

You can understand it easily with the help of this image also. According to this image, if the angle theta 1 reduces to a certain limit then this light ray goes out of the acceptance cone.
In other words we can say, if the light ray is out of the acceptance cone, then the incidence angle is smaller than the critical Angle and in this case total internal reflection will not take place.

Now you know the concept of acceptance cone. So it is very easy to understand, what is acceptance angle.
Acceptance angle is just the conical half angle of the acceptance cone. This acceptance angle is shown in the diagram here.

As already defined, "Acceptance angle is the maximum angle with the axis of the optical fiber at which light can enter the fiber, in order to be propagated through it".
The light rays that are outside this acceptance cone are not accepted by the optical fiber, that's why it is known as acceptance cone.

Let's now discuss what is Numerical Aperture...

Numerical Aperture (NA)

Numerical aperture in case of optical fiber communication can be defined as- "The light gathering (collecting) capacity of an optical fibre".

The numerical aperture provides important relationship between acceptance angle and the refractive index of the core and cladding.

These relationships are given here in the image below-

Formulas for Numerical Aperture (NA) and Acceptance Angle

Numerical Aperture and
Acceptance Angle Formulas

Read More-

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ADVANTAGES OF OPTICAL FIBER COMMUNICATION

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OPTICAL FIBER: STRUCTURE AND WORKING PRINCIPLE

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NEED AND BENEFITS OF MODULATION

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OPTICAL FIBERS IN COMMUNICATION: COVERS ALL IMPORTANT POINTS

OPTICAL FIBER SOURCES (DESIRABLE PROPERTIES)

AMPLITUDE MODULATION Vs FREQUENCY MODULATION (ADVANTAGES AND DISADVANTAGES)

PULSE CODE MODULATION (PCM) [ADVANTAGES AND DISADVANTAGES]

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SUPERPOSITION THEOREM (BASICS, SOLVED PROBLEMS, APPLICATIONS AND LIMITATIONS)

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Quadrature Amplitude Modulation (QAM)/ QAM Transmitter and QAM Receiver Block Diagram

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Microwaves Properties and Advantages (Benefits)

Basic Structure of Bipolar Junction Transistor (BJT) - BJT Transistor - Working and Properties

Polar Plots of Transfer Functions in Control Systems (How to Draw Nyquist Plot Examples)

Generation of Binary Phase Shift Keying (BPSK Generation) - Block Diagram of Binary Phase Shift Keying (BPSK)

Low Level and High Level Modulation Block Diagram (AM Transmitter Block Diagram)

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Slope Overload Distortion and Granular (Idle Noise), Quantization Noise in Delta Modulation

Frequency Translation/Frequency Mixing/Frequency Conversion/Heterodyning (Basic Concepts and Need)

Quadrature Phase Shift Keying Modulation (QPSK) Basics, Waveform and Benefits

Pulse Code Modulation (PCM) Vs Differential Pulse Code Modulation (DPCM)

Digital Modulation Techniques (Coherent and NonCoherent Digital Modulation Techniques)