计算脉冲在非线性耦合器中演化的Matlab 程序 ~i_ R%z:y 9OJ\n|,( % This Matlab script file solves the coupled nonlinear Schrodinger equations of
D^R! |K/ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
u):Rw % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
yQA"T? % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
6Nd_YX >* Qk~kv<% %fid=fopen('e21.dat','w');
vsr~[d= N = 128; % Number of Fourier modes (Time domain sampling points)
]zM9 0$6 M1 =3000; % Total number of space steps
3bI|X!j J =100; % Steps between output of space
dE9aE# o T =10; % length of time windows:T*T0
uwS'*5tU T0=0.1; % input pulse width
N(({ 2'Rr MN1=0; % initial value for the space output location
J<P/w%i2 dt = T/N; % time step
:#!F 7u n = [-N/2:1:N/2-1]'; % Index
cX =b q_ t = n.*dt;
/RULPd
PH u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
EpoQV ^ Ey u20=u10.*0.0; % input to waveguide 2
'?!<I u1=u10; u2=u20;
nrD=[kc!w U1 = u1;
C` 1\ $U~% U2 = u2; % Compute initial condition; save it in U
~zOU/8n
,F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
TXk"[>,:H w=2*pi*n./T;
fS$Yl ~-m? g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
pcxl2I L=4; % length of evoluation to compare with S. Trillo's paper
8'_
]gfF dz=L/M1; % space step, make sure nonlinear<0.05
1.OXkgh for m1 = 1:1:M1 % Start space evolution
o _,$`nEJ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
ABYW 1K= u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
c.me1fGn ca1 = fftshift(fft(u1)); % Take Fourier transform
LF,c-Cv!jL ca2 = fftshift(fft(u2));
~(doy@0M c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
nh.v?| c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Z Y O/'YW u2 = ifft(fftshift(c2)); % Return to physical space
V9 t:JY u1 = ifft(fftshift(c1));
h^,YYoA $ if rem(m1,J) == 0 % Save output every J steps.
"@<g'T0 U1 = [U1 u1]; % put solutions in U array
PT*@#:MA U2=[U2 u2];
O7_NX fh| MN1=[MN1 m1];
w\Eve: z1=dz*MN1'; % output location
E6IL,Iq9 end
1~iBzPU2 end
u^eC hg=abs(U1').*abs(U1'); % for data write to excel
). #D:eO[~ ha=[z1 hg]; % for data write to excel
T=KrT7 t1=[0 t'];
cngPc]?N hh=[t1' ha']; % for data write to excel file
Vh-h{ %dlmwrite('aa',hh,'\t'); % save data in the excel format
#S74C*'8 figure(1)
eMMiSO!3 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
:QY 9p T figure(2)
v?' k)B waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Mh B=+S[@ L1w4WFWO 非线性超快脉冲耦合的数值方法的Matlab程序 si4=C $fpDABf 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
j 3'/jk]\ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Iz=E8R g ov.rHVeI /u1zRw x~,?Zj)n?C % This Matlab script file solves the nonlinear Schrodinger equations
*>H'@gS % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
<5L` d } % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@?N LME % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
vb2O4%7tw y,eoTmaI C=1;
N9hWx()v M1=120, % integer for amplitude
~9 nrS9) M3=5000; % integer for length of coupler
-P uVI5L< N = 512; % Number of Fourier modes (Time domain sampling points)
[9H m][|Ph dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
:EAfD(D{) T =40; % length of time:T*T0.
j[
YTg] dt = T/N; % time step
5 `mVe0uI n = [-N/2:1:N/2-1]'; % Index
A)0m~+?{J t = n.*dt;
+K4v"7C
V ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
q:eAL'OkM w=2*pi*n./T;
j>=".^J g1=-i*ww./2;
C3 Z(k} g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
!: [`
V!{ g3=-i*ww./2;
m#(x D~V P1=0;
g5]DA.&( P2=0;
u9% :2$[ P3=1;
PltPIu)F P=0;
dNmX<WXG for m1=1:M1
5{=MUU=
p=0.032*m1; %input amplitude
~0 t'+. s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
0a;zT
O/"v s1=s10;
%[;KO&Ga s20=0.*s10; %input in waveguide 2
rJ*WxOoS{ s30=0.*s10; %input in waveguide 3
.j,&/y& s2=s20;
#_5+kBA+>' s3=s30;
KWkT
9[H p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
O~1p]j %energy in waveguide 1
LD "}$vfs p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
.h } D%Qa %energy in waveguide 2
<0MUn#7' p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
z#!Cg*K( %energy in waveguide 3
D {}\7qe for m3 = 1:1:M3 % Start space evolution
\p |!=H@ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
}jXUd=.Nu s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
m) 2U-3*iX s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
#@`^
. sca1 = fftshift(fft(s1)); % Take Fourier transform
vdM\scO: sca2 = fftshift(fft(s2));
~nlY8B( sca3 = fftshift(fft(s3));
27 gm_ * sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
3`I_ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
+{*&I DW sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
tt91)^GdYa s3 = ifft(fftshift(sc3));
q3:'
69 s2 = ifft(fftshift(sc2)); % Return to physical space
+d15a%^` s1 = ifft(fftshift(sc1));
g==^ioS}* end
L*38T\ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
3 s Nq3I p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Tj#XsD?J p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Gj?q+-d!(5 P1=[P1 p1/p10];
sJv n#cS P2=[P2 p2/p10];
su SIz 7:
P3=[P3 p3/p10];
[J#(k`@ P=[P p*p];
F3'G9Xf8Q= end
[Hf FC3U figure(1)
q5Mif\ plot(P,P1, P,P2, P,P3);
%stktVDAP O@$i 转自：
http://blog.163.com/opto_wang/
