%?APPENDIX?A?:?Matlab?Code?for?Simulation?of
%?Gratings?using?the?Transfer
%?Matrix?Method
%THIS?M-FILE?USES?THE?TRANFER?MATRIX?METHOD?TO?EVALUATE?THE?COUPLED-MODE
%EQUATIONS.?THE?REFLECTION?SPECTRUM?OF?THE?GRATING?AND?THE?TRANSMISSION
%SPECTRUM?DELAY?AND?DISPERSION?OF?THE?FABRY-PEROT?FILTER?ARE?SIMULATED
clear?all
close?all
clc
%======================================================================
%?Fibre?simulation?parameters
walD?=?1.55e-6;?%design?wavelength
wal1?=?0.999*walD;
wal2?=?1.001*walD;
step?=?500;
wal?=?[wal1:（wal2-wal1）/step:wal2];
%======================================================================
%For?a?grating?of?maximun?reflectance?R?=?0.2
Rmax?=?0.2;?%required?maximum?reflectivity
rmax?=?sqrt（Rmax）;
kacL?=?atanh（rmax）;
c?=?2.99793e8;?%Speed?of?light
h?=?25e-9;
v?=?1;?%Fringe?visibilty
%======================================================================
%Implementation?of?the?transfer?matrix?method?for?solution?of
%coupled-mode?equations
nef?=?1.47;?%core?index?of?photosensitive?fibre
L?=?3000e-6;?%length?of?grating?in?micrometers
M?=?100;
dz?=?L/M;
dzo?=?-?L?+?10.69e-3;?%Distance?between?gratings
kac?=?kacL/L;?%“AC“?coupling?coefficient
kdc?=?2*kac/v;?%“DC“?coupling?coefficient
for?（r?=?1:step+1）
w?=?wal（r）;
F?=?[1?0;?0?1];
for（s?=?1:M）
det?=?2*pi*nef*（1/w?-?1/walD）;
gdc?=?det?+?kdc;
p1?=?sqrt（kac^2?-?gdc^2）;
p2?=?gdc^2/kac^2;
f11?=?cosh（p1*dz）?-?i*（gdc/p1）*sinh（p1*dz）;
f12?=?-i*（kac/p1）*sinh（p1*dz）;
f21?=?i*（kac/p1）*sinh（p1*dz）;
f22?=?cosh（p1*dz）?+?i*（gdc/p1）*sinh（p1*dz）;
ff?=?[f11?f12;?f21?f22];
F?=?ff*F;
end
r3（r）?=?F（21）/F（11）;?%amplitude?reflection?coefficient
R3（r）?=?（abs（