%?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
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（r3（r）））^2;?%power?reflection?coefficient
%of?single?grating
PHI?=?2*pi*nef*dzo/w;?%phase?difference?between?gratings
Fp?=?[exp（-i*PHI）?0;?0?exp（i*PHI）];
Ffp?=?F*Fp*F;
t3（r）?=?1/Ffp（11）;?%amplitude?transmission?coefficient
T3（r）?=?（abs（t3（r）））^2;?%power?transmission?coefficient?of
%Fabry-Perot?filter
end
%==================================================================
%Calculate?Delay?and?Dispersion?of?Fabry-Perot?Filter
theta?=?phase（r3）;
dtheta1?=?gradient（theta?h）;
dtheta2?=?gradient（dtheta1?h）;
DELAY3?=?-（（wal.^2）./（2*pi*c））.*dtheta1;
DELAYu3?=?DELAY3*1e12;?%delay?in?（ps）
DISPERSION3?=?（2*DELAY3./wal）?-?（（wal.^2）./（2*pi*c））.*dtheta2;
DISPERSIONu3?=?DISPERSION3*（1e12/1e9）;?%dispersion?in?（ps/nm）
%=====================================================================
%Plots?for?reflection?and?transmission?spectra?for?Bragg?reflector?and
%Fabry-Perot?filter?respectively
figure?（1）
plot（wal*1e9?R3?‘k‘）
grid
axis（[1549?1551.5?0?0.2]）
title（‘Reflection?Spectrum?of?Bragg?Reflector‘）
xlabel（‘Wavelength?（nm）‘）
ylabel（‘Power?（p.u）‘）
figure?（2）
plot（wal*1e9?T3?‘k‘）
grid
axis（[1549?1551.5?0.4?1]）
title（‘Transmission?Spectrum?of?the?Fabry-Perot?Filter‘）
xlabel（‘Wavelength?（nm）‘）
ylabel（‘Power?（p.u）‘）
figure?（3）
plot（wal*1e9?DELAYu3?‘k‘）
grid
axis（[1549?1551.5?0.4?1]

?屬性????????????大小?????日期????時間???名稱
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?????文件????????3361??2010-05-04?15:21??tmmcoupling.m