Coupled mode equations.txt

% ---------------------------------------------------------------
% MATLAB
% This .txt file is to calculate coupled mode theory.
% Written by Yuyang ZHUANG.
% Tanabe Lab at Keio University.
% 2018/10/23.
% ---------------------------------------------------------------

% The coupled differential equations are as follows (three modes)
% dA1(z)/dz=-j*b1*A1(z)+j*K12*A2(z)+j*K13*A3(z)
% dA2(z)/dz=-j*b2*A2(z)+j*K21*A1(z)+j*K32*A3(z)
% dA3(z)/dz=-j*b3*A3(z)+j*K13*A1(z)+j*K23*A2(z)
% K12=K21*=c1, K13=K31*=c2.
% Ignore the coupling between A2(z) and A3(z), means K23=K32*=0.

% The equations above can be simplified as
% dA1(z)/dz=-j*b1*A1(z)+j*c1*A2(z)+j*c2*A3(z)
% dA2(z)/dz=-j*b2*A2(z)+j*c1*A1(z)
% dA3(z)/dz=-j*b3*A3(z)+j*c2*A1(z)

% Assume that b1=b2=27μm-1, b3=27μm-1
% c1=c2=0.1μm-1

% Step 1: Set the coupled mode equations
A=[-27i,0.1i,0.1i;0.1i,-27i,0;0.1i,0,-27i];
Eqns=@(t,X) A*X;
% Step 2: Set the innitial condition A1(0)=1, A2(0)=0, A3(0)=0.
X0=[1;0;0];
options=odeset('RelTol',1E-8,'AbsTol',1E-8);
% Step 3: Calculate the equations using numerical solver ode45
[t,A]=ode45(Eqns,[0 20],X0,options);
% Step 4: Plot the power of A1(z), A2(z) and A3(z).
plot(t,abs(A(:,1)).^2);
hold on;
plot(t,abs(A(:,2)).^2,'r');
hold on;
plot(t,abs(A(:,3)).^2,'g--');

% End