Computational Electromagnetics and Applications Professor Krish Sankaran Indian Institute of Technology Bombay Lab Tour 4

Transcription

1 Computational Electromagnetics and Applications Professor Krish Sankaran Indian Institute of Technology Bombay Lab Tour 4 So now we are going to do a different kind of experiment, now in a little bit in a higher frequency range. We are going to do optical devices experiment. So the kind of work what we are going to do in this particular lab tour is modelling the behaviour and the aspects of physical parameters of an optical fibre. So when I say optical fibre what I have in my hand is two different types of fibre the one which is in yellow colour what you see here is a single mode fibre. And the one which is in white colour is a multimode fibre. And they have been designed for 1300 to 1500 nanometres. This is the range in which they are being used. (Refer Slide Time: 01:23) So the single mode fibre is mainly used for the long range communication. And the multimode fibre is used for the short range communication. As I said it is in the range of 1300 to 1500 nanometres and what you see in this a very thin little thing is there are three things involved one is the core, and then there is a cladding, and then there is also a protective jacket on each of these in order to protect it from some damages. And these are very fine devices and for modelling these devices we have to use either analytical method or we can also use finite element method. So in this lab tour we are going to look at this two different types of material one is a single mode and the multi-mode fibre. And we are going to model it for their behaviours and characteristics and see it to using two methods. The first method what we will be doing is a kind of an analytical method. Which will explain us the characteristics, the modes what you are going to compute for this

2 particular fibres using some of the analytical techniques and then you will compare the analytical result with finite element method and we will compare how good the finite element method is compared to the analytical method itself. So there are going to be students who are going to work on this project. So the first part I will going to look into is the analytical method. So let us go and have a discussion with my student. (Refer Slide Time: 02:54) So Thomas is a student of mine was in the computational electromagnetic course and he is going to show us what he has done using analytical method for this particular problem. I have asked him to show some of the methods that we are used to analytical compute the most of this two types of fibres, one is the single mode and the multi-mode fibre. So let us discuss with him and see what he is doing. (Refer Slide Time: 03:18)

3 (Student Teacher Conversation starts) This is a, mainly we are modelling the modes of an optical fibre using finite element method. Ok. Actually we are comparing the finite element assess with an analytical results because analytical results are very common and we know that exact solutions of this fibre. So we are comparing the finite element results what we are getting and analytical results. Ok. So how are you doing the how the analytical method itself is placed is something we would like to know. (Refer Slide Time: 03:46) Ok. So problem statement is find out the possible modes in an optical fibre using analytical method and using FEM method also.

4 Ok. (Refer Slide Time: 03:54) So optical fibres can be divided in different ways. One is based on the number of modes propagating through a fibre and based on number of modes fibres can be divided into single mode fibre and multi-mode fibre, yellow one is the single mode fibre. In single mode fibre only one mode is operating and in multi-mode fibre many number of modes are propagating. And this is depends on the core diameter of the fibre. What is the core diameter of this particular fibre? In single mode fibre it is less than 10 micrometre, typically around 8 micrometre. And for multi-mode fibre there are two standards, old standard is 62.5 micrometres and new standard is 50 micrometre. (Refer Slide Time: 04:41)

5 So these are as we said before they are designed for certain frequency. These are mainly designed for 1300 nanometre. So you can go up with 1500 nanometres. Mainly there are three operating optical windows, one is 850 nanometre, the other one is 1300 nanometre and the third one is 1550 nanometre. This 1300 nanometre is one where the dispersion is very less but attenuation is very less in 1550 nanometre window. Ok. So we are mainly using this for last long distance communication, we are using 1300 or in fact any window can be used. So basically when we talk about dispersion what we are talking about the group velocity versus the phase velocity. So the dispersion error will be low in the 1300 whereas the wave decay itself, attenuation will be lower in the 1550 nanometre window. (Refer Slide Time: 05:36) So let us look at the And one classification of fibres is based on the profile, refractive index profile. One is stepindex profile and graded index fibre. In the step-index fibre the core refractive index is uniform and in graded index the refractive index is gradually changing, parabolically changing. Ok. So we can have basically different profiles. Yes. Typically you are using parabolic? Yes, typically parabolic because parabolic profile reduces the dispersion.

6 Ok. When you talk about the profile you are talking about the refractive index. But for simplicity we are using step-index profile for our simulation purpose. This is the refractive index profile of the fibre we are discussing. At the core the refractive index is n 1 and at the cladding it is n 2. So a is the diameter? a is the radius of the core. So the radius is a and when the radius is less than a you are having a refractive index n 1 and for the cladding and protective layer it is going to be n 2. And n 1 is greater than n 2 because the working principle for this is total internal reflection. So whatever is propagating gets totally reflected so that it travel can inside the core. (Refer Slide Time: 6:58) Then we are solving the Maxwell s equations for this fibre and I am getting the solution for the step-index fibre where A is the amplitude. There are two solutions cos dependent solutions and sine dependent solutions; and inside the core, the solution can be expressed as an index of Bessel s function of first kind and outside the core the solution can be expressed in terms of index of Bessel s function of second kind. Bessel s function of first kind are sinusoidal in nature and this is exponentially decaying. Since the power is propagating through the core, it will be sinusoidal in shape and outside the core, i.e., the cladding there is no power. Even if some power is leaking into the cladding it will exponentially decay. So that s how the solutions are coming. So tell us how.

7 Before that I will explained how it is solved. This is the solution when we are applying the boundary conditions we will get the mode solution. So how do you go ahead with that? At the core cladding boundary we are assuming the condition that the fields are contiguous. When we are taking the derivate. So, Thomas could you explain to us the analytical procedure for deriving the solution.