Optikes_Mathima05

clc;
clear all;

% =========================================================================
% Given the fiber V-number solve for a specific mode of order (m,n) = (p,r)
% =========================================================================

m = 0;  % Azimuthial order (0 = fundamental), denoted as p in Lecture Notes
n = 1;  % Root order (1 = fundamental), denoted as r in Lecture Notes
V = 2.2;

[V b] = FibreScalar_FindRoots(m, n, V);

% =========================================================================
%                       Mode Profile F(x,y)
% =========================================================================

figure;
set(gcf, 'PaperPositionMode', 'auto', 'w');
FigSize = [400 400];    % Pixels
cccb = [ 1 1 1; LVCMv2( [0 0 0; 0 0 0.5; 0 0 1; 0 1 1; 1 1 0; 1 0 0] ) ];
set(gcf, 'Position', [100 100 FigSize]);

% Fiber Specs
a = 20  % radius in μm
% Define a Space (x, y) ----> (rho, theta)
x = 3 * a * linspace(-1, 1, 200);
y = 3 * a * linspace(-1, 1, 200);
[x y] = meshgrid(x, y);
ra = sqrt(x.^2 + y.^2);
% th = atan(x ./ y);
th = atan2(y, x);
is = ra <= a;
os = ra >= a;

options = optimset('Display', 'off');
bo = b;
Va =V;

% Calculate field mode on that
U = Va * sqrt(1-bo);
W = Va * sqrt(bo);
F = NaN * x;
Ain = 1;
Aot = Ain * besselj(m, U) / besselk(m, W);
F(is) = Ain * besselj(m, U * ra(is)/a) .* cos(m * th(is));
F(os) = Aot * besselj(m, W * ra(os)/a) .* cos(m * th(os));

% Plots
cla; hold on;
pcolor(x/a, y/a, (F));
plot(cos(2*pi*linspace(0,1,100)), sin(2*pi*linspace(0,1,100)), 'k-.', 'LineWidth');
plot(get(gca, 'XLim'), [0 0], 'k:', [0 0], get(gca, 'YLim'), 'k:');