计算脉冲在非线性耦合器中演化的Matlab 程序 u QH] sXEIC #rq % This Matlab script file solves the coupled nonlinear Schrodinger equations of
0 cKsGD m % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
m-4#s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
&iw,||# % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Wjq 9f; J \|~k2~ %fid=fopen('e21.dat','w');
Epp>L.?r N = 128; % Number of Fourier modes (Time domain sampling points)
;6R9k]5P% M1 =3000; % Total number of space steps
r=3`Eb"t J =100; % Steps between output of space
%[KnpJ{\ T =10; % length of time windows:T*T0
d+)L K~ T0=0.1; % input pulse width
N KgEs MN1=0; % initial value for the space output location
\y?*} L dt = T/N; % time step
9^g8VlQdT n = [-N/2:1:N/2-1]'; % Index
BMO ,eQcB t = n.*dt;
&Qda | u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
5'f_~>1Wt u20=u10.*0.0; % input to waveguide 2
_+P*XY5 u1=u10; u2=u20;
%8I^&~E1 U1 = u1;
3HXeBW U2 = u2; % Compute initial condition; save it in U
^_v94!a 9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
{J1rjrPo w=2*pi*n./T;
9\?&u_ U" g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
R5QW4i9 L=4; % length of evoluation to compare with S. Trillo's paper
xib}E[-l# dz=L/M1; % space step, make sure nonlinear<0.05
!]s =9(O for m1 = 1:1:M1 % Start space evolution
V^FM-bg%9 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
7Fpa%N/WL u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
YIW9z{rrs ca1 = fftshift(fft(u1)); % Take Fourier transform
<H] PP6_g: ca2 = fftshift(fft(u2));
/Z*$k{qIR& c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
=>PX~/o c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
ynra%"sd u2 = ifft(fftshift(c2)); % Return to physical space
* Ib DA u1 = ifft(fftshift(c1));
z5({A2q if rem(m1,J) == 0 % Save output every J steps.
}P%gwgPK U1 = [U1 u1]; % put solutions in U array
wT+60X' U2=[U2 u2];
)?&mCI* MN1=[MN1 m1];
w7~]c,$y. z1=dz*MN1'; % output location
PT,*KYF_O" end
} %0 w25 end
yg}L,JJU< hg=abs(U1').*abs(U1'); % for data write to excel
m8L %!6o ha=[z1 hg]; % for data write to excel
exSwx-zxI t1=[0 t'];
o"RE4s\G~r hh=[t1' ha']; % for data write to excel file
oIOeX1$V %dlmwrite('aa',hh,'\t'); % save data in the excel format
! weYOOu figure(1)
7Y~5gn waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
JYjc^m figure(2)
!^L}LtqHI waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
(*eX'^Q)d .Sw4{m[g 非线性超快脉冲耦合的数值方法的Matlab程序 ; QuxTmWp^ GPAC0K^p 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
fU.hb%m)Q\ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
>/.jB /q myXGMN$ i 0j;|IU\ 2\$<&]q % This Matlab script file solves the nonlinear Schrodinger equations
.-s!} P" % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
PTpCiiA@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
~:!& }e5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
gDfM} 2]/ 6"?#s/fk C=1;
-{eiV0<^ M1=120, % integer for amplitude
+A,cdi9z M3=5000; % integer for length of coupler
ZKI` ; N = 512; % Number of Fourier modes (Time domain sampling points)
vA*NJ%&` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
jvd3_L-@E< T =40; % length of time:T*T0.
hhjsg?4uL dt = T/N; % time step
2s 9U& n = [-N/2:1:N/2-1]'; % Index
cP/( h t = n.*dt;
,V4pFQzL ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
*qMj o P, w=2*pi*n./T;
6*ZZ) W< g1=-i*ww./2;
Rx%kAt2X g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
N9 )ERW2`* g3=-i*ww./2;
QIN# \ P1=0;
jAt6 5a P2=0;
K1<l/
s P3=1;
$[=`*m P=0;
DML0paOm5 for m1=1:M1
wL0"1Y a p=0.032*m1; %input amplitude
gJOswN;([ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
jT QN(a9Y s1=s10;
jaux:fU s20=0.*s10; %input in waveguide 2
n |,} s30=0.*s10; %input in waveguide 3
S;vZXgyN? s2=s20;
>273V+dy s3=s30;
9*|A n p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
)>=|oY3 %energy in waveguide 1
x~yd/ R p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
HZ2 zL17 %energy in waveguide 2
kS7T ' [d p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
.fW`/BXE %energy in waveguide 3
|4Q><6 "G for m3 = 1:1:M3 % Start space evolution
>y q L s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
uqy~hY s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
P |)SXR s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
~u-`L+G"6 sca1 = fftshift(fft(s1)); % Take Fourier transform
|om3* ]7 sca2 = fftshift(fft(s2));
KQqQ@D&n sca3 = fftshift(fft(s3));
@1[LD[ < sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
b}q,cm sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
}KkH7XksF sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
wY}+d0Ch s3 = ifft(fftshift(sc3));
{la ^useg[ s2 = ifft(fftshift(sc2)); % Return to physical space
&9g#Vq% s1 = ifft(fftshift(sc1));
t,P +~ A end
gzdgnF2 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
C{S 6Ri p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Z=sAR(n}~ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
eZJOI1wNp P1=[P1 p1/p10];
>"nk}@ P2=[P2 p2/p10];
y.oJzU[p% P3=[P3 p3/p10];
,>jm|BTD { P=[P p*p];
C,z]q$4 end
@' ,;/j80 figure(1)
ZmHl~MR@ plot(P,P1, P,P2, P,P3);
:3Jh f$ 3 \WdA$Wx 转自：
http://blog.163.com/opto_wang/
