计算脉冲在非线性耦合器中演化的Matlab 程序 v oxlo>: HChewrUAn % This Matlab script file solves the coupled nonlinear Schrodinger equations of
C@-JH\{\T# % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
^ytd~iK8 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
N_0O"" d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
2~)]E#9 ) 9 4R\f %fid=fopen('e21.dat','w');
e| LXH/H N = 128; % Number of Fourier modes (Time domain sampling points)
^9nM)[/C? M1 =3000; % Total number of space steps
o%.cQo=v* J =100; % Steps between output of space
rSk $]E ]Z T =10; % length of time windows:T*T0
"n:9Jq Pb T0=0.1; % input pulse width
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Rq&(R MN1=0; % initial value for the space output location
b/EvcN8 } dt = T/N; % time step
a #1X )ot n = [-N/2:1:N/2-1]'; % Index
F\e'z t = n.*dt;
^ =ikxZyO u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
, ]MX&] u20=u10.*0.0; % input to waveguide 2
dXj.e4,m u1=u10; u2=u20;
/d4xHt5a U1 = u1;
4$^=1a x U2 = u2; % Compute initial condition; save it in U
L 0Cf@~k ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
[Dhc9 w=2*pi*n./T;
TwN8|ibVmP g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
|F<aw?% L=4; % length of evoluation to compare with S. Trillo's paper
6 D O E6 dz=L/M1; % space step, make sure nonlinear<0.05
K^S#?T|[9 for m1 = 1:1:M1 % Start space evolution
Fi#t88+1 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
f
{
ueI< u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
2I7P}= ca1 = fftshift(fft(u1)); % Take Fourier transform
|z~?"F6 Y< ca2 = fftshift(fft(u2));
2g$ Wv :E3 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
NXx}KF c c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
&~& i > u2 = ifft(fftshift(c2)); % Return to physical space
FueJe/~t u1 = ifft(fftshift(c1));
dw-r}Qioe if rem(m1,J) == 0 % Save output every J steps.
^o 5q- ;a U1 = [U1 u1]; % put solutions in U array
,-b9:]{L U2=[U2 u2];
,P|PPx%@ MN1=[MN1 m1];
?aCR>AY5X z1=dz*MN1'; % output location
A9#2. 5 end
)mEF_ & end
4c% :?H@2 hg=abs(U1').*abs(U1'); % for data write to excel
S4 _Y^ ha=[z1 hg]; % for data write to excel
DXUI/C f t1=[0 t'];
h^s}8y hh=[t1' ha']; % for data write to excel file
n RGH58 %dlmwrite('aa',hh,'\t'); % save data in the excel format
s0 :1G
-I figure(1)
S("bN{7nE waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
S8y4 p0mV figure(2)
v=4TU \b% waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
"FU|I1Xz * <@ 非线性超快脉冲耦合的数值方法的Matlab程序 J 4gIkZD * +IUGR 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。
x83XJFPWL 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
^Z!W 3q Q ei5 S <n Q6BW ax| >Cf`F{X' U % This Matlab script file solves the nonlinear Schrodinger equations
%%_90t % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
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r9 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
84{<]y % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
UY+~xzm bHP-Z9riv C=1;
1/i| M1=120, % integer for amplitude
IV *}w"r M3=5000; % integer for length of coupler
BZj[C=#x N = 512; % Number of Fourier modes (Time domain sampling points)
MMf6QxYf dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
y`BLIEI T =40; % length of time:T*T0.
uPqPoI>N! dt = T/N; % time step
d+^;kse n = [-N/2:1:N/2-1]'; % Index
%:y-"m1\u$ t = n.*dt;
eAqQ~)8^ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
^v},Sa/ot] w=2*pi*n./T;
U*b SM8)L* g1=-i*ww./2;
@iaN@`5I6s g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
|\ ay^@N g3=-i*ww./2;
}Yj S v^ P1=0;
]}B&-Yp P2=0;
;gc 2vDMv P3=1;
,&k 5 Qq P=0;
[9L(4F20 for m1=1:M1
^R\blJQ<^ p=0.032*m1; %input amplitude
&K4o8Qz s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Ue% 0.G|<W s1=s10;
}O>IPRZ s20=0.*s10; %input in waveguide 2
Y7p#K<y]9 s30=0.*s10; %input in waveguide 3
?{[H+hzz0 s2=s20;
;?cUF78# s3=s30;
VcP#/&B| p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
P8EGd}2{8 %energy in waveguide 1
zL|^5p`K p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
k >MgrtJI %energy in waveguide 2
R|vF*0 )>W p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
9\ ;EX
%energy in waveguide 3
9qPP{K,Pq2 for m3 = 1:1:M3 % Start space evolution
c{ <3\ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
] * Hz' s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
vi2xonq^ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
qN) cB?+ sca1 = fftshift(fft(s1)); % Take Fourier transform
LgaJp_d>9* sca2 = fftshift(fft(s2));
N >z8\y sca3 = fftshift(fft(s3));
+VeLd+Q} sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
HP8pEo0Y sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
`+gF|o9 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
.{} t[U s3 = ifft(fftshift(sc3));
OU## A: gI s2 = ifft(fftshift(sc2)); % Return to physical space
M]2 c - s1 = ifft(fftshift(sc1));
$ D89|sy end
t EeMl =u p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
DXiD>1( q p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
8}0
D? p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
&a:aW;^A7 P1=[P1 p1/p10];
Fc]#\d6 P2=[P2 p2/p10];
R S1oPY
P3=[P3 p3/p10];
Yv; aQF"a P=[P p*p];
M}vPWW cl end
:K~7BJ(HO figure(1)
\<8!b {F plot(P,P1, P,P2, P,P3);
Hq g H\ w"e2}iE7 转自：
http://blog.163.com/opto_wang/
