计算脉冲在非线性耦合器中演化的Matlab 程序 M'X,7hZ V4Qy^nn1 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
/`#JM % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
vqoK9 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
h{\S '8 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
aS>cXJ;= >bmdu \j5R %fid=fopen('e21.dat','w');
;2 ?fz@KZ N = 128; % Number of Fourier modes (Time domain sampling points)
GKUjtPu M1 =3000; % Total number of space steps
4kV$JV.l J =100; % Steps between output of space
[\fwnS_1 T =10; % length of time windows:T*T0
7#Fcn T0=0.1; % input pulse width
BSr#;; \ MN1=0; % initial value for the space output location
e*I92 dt = T/N; % time step
c*R\fQd n = [-N/2:1:N/2-1]'; % Index
23ho uS t = n.*dt;
QAl 4w)F u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
ZcHIk{| u20=u10.*0.0; % input to waveguide 2
!"E/6z2&(k u1=u10; u2=u20;
77+3CME{' U1 = u1;
W"t^t|H'~ U2 = u2; % Compute initial condition; save it in U
\fvm6$ rZ^ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
5w~J"P6jg w=2*pi*n./T;
8090+ ( U g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
^,f^YL; L=4; % length of evoluation to compare with S. Trillo's paper
+l]> (k.2 dz=L/M1; % space step, make sure nonlinear<0.05
@a =jSB#B for m1 = 1:1:M1 % Start space evolution
96; gzG@1! u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Cd6th
F) u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
@S5HMJ2= ca1 = fftshift(fft(u1)); % Take Fourier transform
{od@S l ca2 = fftshift(fft(u2));
]j*uD317 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
-V" W c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
r Aq S;@]0 u2 = ifft(fftshift(c2)); % Return to physical space
9`^(M^ |c u1 = ifft(fftshift(c1));
= jxy4`oF if rem(m1,J) == 0 % Save output every J steps.
+RiI5.$=Z U1 = [U1 u1]; % put solutions in U array
VS7 U2=[U2 u2];
ru1^. (W2 MN1=[MN1 m1];
u35"oLV6}# z1=dz*MN1'; % output location
[yc7F0Aw end
el2<W=^M end
'9Q#%E!* hg=abs(U1').*abs(U1'); % for data write to excel
oe<@mz/ ha=[z1 hg]; % for data write to excel
BT$Oh4y4 t1=[0 t'];
zyP/'X_~: hh=[t1' ha']; % for data write to excel file
*L Y6hph" %dlmwrite('aa',hh,'\t'); % save data in the excel format
DH i@ ujr figure(1)
+nB0O/m'U waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
23'{{@30 figure(2)
Gfy9YH~ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
{(t R<z) /+ais 3 非线性超快脉冲耦合的数值方法的Matlab程序
MpJ\4D5G \;Q!}_ K 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。
5'`Dr TOA 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
2\#$::B9 -Oz! GX !\Cu J5U z/p^C~|} % This Matlab script file solves the nonlinear Schrodinger equations
ZnuRy: % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
MJH> rsTQ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7A$mZPKh % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
q['3M <q <y7Hy&&y- C=1;
nYv keT M1=120, % integer for amplitude
d@b2XCh< K M3=5000; % integer for length of coupler
B| M@o^Tf N = 512; % Number of Fourier modes (Time domain sampling points)
Dk2Z l dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
4N3 O<)C)@ T =40; % length of time:T*T0.
m*i,|{UZ dt = T/N; % time step
&t !f dti n = [-N/2:1:N/2-1]'; % Index
RjrQDh|(( t = n.*dt;
$GhL-sqm ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
@$%.iQ7A; w=2*pi*n./T;
;'[?H0Jw' g1=-i*ww./2;
%@ q2 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
.vi0D uD6 g3=-i*ww./2;
fwUF5Y P1=0;
F/:%YR; P2=0;
yB{1&S5 C P3=1;
_c:th{* P=0;
;/IX w>O(/ for m1=1:M1
m?8o\|i, p=0.032*m1; %input amplitude
X_Pbbx_j s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
s%5XBI s1=s10;
CkV -L4Jq s20=0.*s10; %input in waveguide 2
`@u9 fx. s30=0.*s10; %input in waveguide 3
"W9z>ezp s2=s20;
* {p:C s3=s30;
[`bK {Dq2 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
I9#l2<DYlX %energy in waveguide 1
:ee vc7 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
q$ j %energy in waveguide 2
Tn\{*A p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
OKu~Nb* %energy in waveguide 3
k!6m'} v for m3 = 1:1:M3 % Start space evolution
i`iR7UmHeR s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
iVmy|ewd s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
qc3,/JO1 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
?T|0"|\" ' sca1 = fftshift(fft(s1)); % Take Fourier transform
66_=bd(9 sca2 = fftshift(fft(s2));
I@#IXH?6 sca3 = fftshift(fft(s3));
X V) ctF4 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
[W3sveqj& sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
=fB"T+ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
!>kg:xV s3 = ifft(fftshift(sc3));
#2Iw%H 2q& s2 = ifft(fftshift(sc2)); % Return to physical space
Jv]$@># s1 = ifft(fftshift(sc1));
#nZPnc : end
@s, kx.S p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
$ma@z0%8} p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
P1$D[aF9$ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
)%8s t' P1=[P1 p1/p10];
qH d7C3 P2=[P2 p2/p10];
S5UQ
P3=[P3 p3/p10];
+u&3pK>f P=[P p*p];
gieso f end
C!6D /S figure(1)
3&+ nV1 plot(P,P1, P,P2, P,P3);
@zLyG#kHY n5tsaU; 转自：
http://blog.163.com/opto_wang/
