How to get b vs V plot for multimode optical fiber using matlab with using bessel's equation?

I want to plot b vs. V curve for different modes of optical waveguide(https://www.google.co.in/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjB-tTg3_rMAhVCGaYKHfpeBb4QjRwIBw&url=http%3A%2F%2Fwww.slideshare.net%2Ftossus%2Fwaveguiding-in-optical-fibers&psig=AFQjCNFhFM8YX_nSP2G-HHetH4b5GEB79A&ust=1464455430166614). There i need to solve bessel's equation with the help of numerical methods, specially by Newton Raphson Method. Can anyone please tell me the matlab code which uses Newton Raphson method for solving bessel's equation?

Answer 1

[AJEET KUMAR]

Hello,

The following code Implements the bV plot for optical waveguide.

% Matlab code for b-V plot in optical waveguide

% Author: Ajeet Kumar

% Feb 21, 2019

clc

close all

b = 0:0.01:1; % Value of b

c = 0.98; % Value of c

p = [0 1 10 100]; % Values of different a

% m = 0; % for m = 0;

% d = c-a*(1-c);

figure()

for m = 0:1:5 % For m = 0 to 5

for ii = 1:4

a = p(ii);

d = c-a*(1-c);

x1 = atan((1/d)*sqrt((a+b)./(1-b)));

x2 = atan((1/c)*sqrt(b./(1-b)));

v = (x1+x2+m*pi)./sqrt(1-b); % Expression of V, x1 and x2 are part of expression

plot(v,b);

% legend(['m = ',num2str(m)]);

axis([0 15 0 1]);

grid on

hold on

end

end

%% Separate plotting

% a = 1;

% m = 1;

% d = c-a*(1-c);

%

% x1 = atan((1/d)*sqrt((a+b)./(1-b)));

% x2 = atan((1/c)*sqrt(b./(1-b)));

% v = (x1+x2+m*pi)./sqrt(1-b);

% plot(v,b);

% hold on

%

% a = 10;

% m = 2;

% d = c-a*(1-c);

%

% x1 = atan((1/d)*sqrt((a+b)./(1-b)));

% x2 = atan((1/c)*sqrt(b./(1-b)));

% v = (x1+x2+m*pi)./sqrt(1-b);

% plot(v,b);

% hold on

%

% a = 100;

% m = 3;

% d = c-a*(1-c);

%

% x1 = atan((1/d)*sqrt((a+b)./(1-b)));

% x2 = atan((1/c)*sqrt(b./(1-b)));

% v = (x1+x2+m*pi)./sqrt(1-b);

% plot(v,b);

Hope this answers the question.

[saisree k]

what are a,c,d?

[Sachleen Singh]

2.405 value for LP11 mode is not there. Rather pointing at some different value around 1. Needs some modification.