计算脉冲在非线性耦合器中演化的Matlab 程序 !~9ASpqvPy hRX9Du`$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
m`-:j"]b$ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
|.$ B,cEd % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
\#]%S/_ A % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
l+F29_o# -%MXt %fid=fopen('e21.dat','w');
!9PA fi? N = 128; % Number of Fourier modes (Time domain sampling points)
%C,zR&]F M1 =3000; % Total number of space steps
"[~y u*
S J =100; % Steps between output of space
k1xx>=md|C T =10; % length of time windows:T*T0
.:}<4;Qz94 T0=0.1; % input pulse width
&? bsBqpN MN1=0; % initial value for the space output location
/kG ?I_z dt = T/N; % time step
iXo; e n = [-N/2:1:N/2-1]'; % Index
pP":,8 Q{ t = n.*dt;
i
/[{xRXiR u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
i*N2@Z[ u20=u10.*0.0; % input to waveguide 2
'uL$j=vB u1=u10; u2=u20;
i4D]> U1 = u1;
{U_ ,y(V U2 = u2; % Compute initial condition; save it in U
gPB =Z! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
e8 ]CB w=2*pi*n./T;
m<3. X"- g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
1 3/,^? L=4; % length of evoluation to compare with S. Trillo's paper
C('D]u$Hdk dz=L/M1; % space step, make sure nonlinear<0.05
eC"e
v5v for m1 = 1:1:M1 % Start space evolution
,jC~U s< u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
J&~I4ko] u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
ASoBa& vX ca1 = fftshift(fft(u1)); % Take Fourier transform
r hPv{6Z|7 ca2 = fftshift(fft(u2));
98 R/ ^\ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
02;'"EmP$ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
_VdJFjY?zc u2 = ifft(fftshift(c2)); % Return to physical space
jRC{8^98 u1 = ifft(fftshift(c1));
u->[ y1JY if rem(m1,J) == 0 % Save output every J steps.
7=fN vES2 U1 = [U1 u1]; % put solutions in U array
*(yw6(9% U2=[U2 u2];
[DjlkA/Zg MN1=[MN1 m1];
|+ Rx ) z1=dz*MN1'; % output location
2Xv}JPS2As end
yO7H!}y _ end
% IVM1 hg=abs(U1').*abs(U1'); % for data write to excel
l H_pG ~ ha=[z1 hg]; % for data write to excel
jG `PyIgw t1=[0 t'];
.jP|b~ hh=[t1' ha']; % for data write to excel file
1VFC K& %dlmwrite('aa',hh,'\t'); % save data in the excel format
+sn0bi/rG figure(1)
Szu @{lpP@ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
W#g!Usf:/ figure(2)
',[A KXJ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
5Xxdm-0 ?E!M%c@, 非线性超快脉冲耦合的数值方法的Matlab程序 >wqWIw.w> uaP5(hUI 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。
$ bMmyDw 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
V_$<^z| bvB7d` wx Mj>Q V(L8t x4kQG e( % This Matlab script file solves the nonlinear Schrodinger equations
'@KH@~OzRS % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
aO inD % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
#s\yO~F- % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
q m_r~j ux^rF C=1;
=jm\8sl~~ M1=120, % integer for amplitude
Y]6d Yq{k M3=5000; % integer for length of coupler
&k*oG: J3 N = 512; % Number of Fourier modes (Time domain sampling points)
8v/,< eARJ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
mnZ fk T =40; % length of time:T*T0.
b (H J| dt = T/N; % time step
bydI+pVMo n = [-N/2:1:N/2-1]'; % Index
GJU(1%- t = n.*dt;
au=@]n#<( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Zp{K_ec{ w=2*pi*n./T;
& $T7eOiZ g1=-i*ww./2;
Xajt][ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
KIY`3Fl09 g3=-i*ww./2;
um/F:rp P1=0;
mBye)q$ P2=0;
fS '` 9 P3=1;
W +GBSl P=0;
%b_0l<+
for m1=1:M1
2H8\ P+ p=0.032*m1; %input amplitude
} @3q;u ) s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
G,WLca[ s1=s10;
*@@dO_%6 s20=0.*s10; %input in waveguide 2
`N}V i6FG s30=0.*s10; %input in waveguide 3
H^o_B1 s2=s20;
#t Pc<p6m s3=s30;
FnOa hLS p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
6,1oLv U %energy in waveguide 1
x3 ( _fS p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
wLI1qoDM %energy in waveguide 2
2Gj)fMK38 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
QS4~":D/C %energy in waveguide 3
hDg" ?{ for m3 = 1:1:M3 % Start space evolution
\AI-x$5R * s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
c*<BU6y s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
qM3NQ8Rm s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
A ^hafBa sca1 = fftshift(fft(s1)); % Take Fourier transform
)iC@n8f7o sca2 = fftshift(fft(s2));
k=p[Mlic/ sca3 = fftshift(fft(s3));
b
~]v'|5[ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
D\J.6W sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
D8*6h)~ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
vqoK9 s3 = ifft(fftshift(sc3));
Z{
9Io/ s2 = ifft(fftshift(sc2)); % Return to physical space
-#4QY70H t s1 = ifft(fftshift(sc1));
G"L`9E<0V end
LtUw p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
&Vpr[S@:{ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
:YX5%6 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
;ioF'ov P1=[P1 p1/p10];
E}0g P2=[P2 p2/p10];
e=# D1 P3=[P3 p3/p10];
eMn'z]M&] P=[P p*p];
64"DT3: end
\v{HjqVkC figure(1)
I;?PDhDb plot(P,P1, P,P2, P,P3);
=l]
lwA - kQ2Wd pZ/ 转自：
http://blog.163.com/opto_wang/
