计算脉冲在非线性耦合器中演化的Matlab 程序 +P YX . &/)2P# u % This Matlab script file solves the coupled nonlinear Schrodinger equations of
5eS0
B{,c % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
{yFCGCs % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Ik W 8$> % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
V?pqK QL0 hc#Lni R3$ %fid=fopen('e21.dat','w');
5,Rxc= N = 128; % Number of Fourier modes (Time domain sampling points)
|qe[`x;
% M1 =3000; % Total number of space steps
ePF)wl;m J =100; % Steps between output of space
t @=*k9 T =10; % length of time windows:T*T0
Xm#rkF[, T0=0.1; % input pulse width
|7XPu MN1=0; % initial value for the space output location
k2]fUP dt = T/N; % time step
Jc8 ^m0_ n = [-N/2:1:N/2-1]'; % Index
b 2rlj6d t = n.*dt;
_"nzo4e0 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
~@Yiwp\ " u20=u10.*0.0; % input to waveguide 2
)T2V< 3l u1=u10; u2=u20;
P D,s,A U1 = u1;
ha Tmfh_| U2 = u2; % Compute initial condition; save it in U
5D 9n>K4| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
{nQ?+o3 w=2*pi*n./T;
<V?csx/eRd g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
lQ5d.}O& L=4; % length of evoluation to compare with S. Trillo's paper
K9z 1'k QH dz=L/M1; % space step, make sure nonlinear<0.05
OO$YwOKS for m1 = 1:1:M1 % Start space evolution
V c 2 (R^ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
]Q8[,HTG u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
|j2b=0Rpk ca1 = fftshift(fft(u1)); % Take Fourier transform
Mk=M)d` ca2 = fftshift(fft(u2));
(3. B\8s c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
p"l GR&b c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
C_5o& O8Bc u2 = ifft(fftshift(c2)); % Return to physical space
w ? ;j5[j u1 = ifft(fftshift(c1));
10gh4,z[ if rem(m1,J) == 0 % Save output every J steps.
,1|Qm8O U1 = [U1 u1]; % put solutions in U array
ORCG(N U2=[U2 u2];
As}3VBd MN1=[MN1 m1];
e^ Aw%t z1=dz*MN1'; % output location
0R21"]L_M end
}Mv$Up end
| XGj97#M hg=abs(U1').*abs(U1'); % for data write to excel
@XJzM]*w& ha=[z1 hg]; % for data write to excel
=\ek;d0Tqb t1=[0 t'];
l.>3gjr hh=[t1' ha']; % for data write to excel file
v~B
"Il %dlmwrite('aa',hh,'\t'); % save data in the excel format
U))2?# figure(1)
]cmq waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
;L`N F" figure(2)
f*%Y]XL; % waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
&eA!h w %2|Po5 非线性超快脉冲耦合的数值方法的Matlab程序 /s~(? =qYH 4{v ?<x8 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。
1#w'<}h#U 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
XI5TVxo(q Jc=~BT_G O)FkpZc@9c >2^|r8l5 % This Matlab script file solves the nonlinear Schrodinger equations
8MZ:= % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
( ah^</ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
&_1x-@oI2: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-J&
b~t@ 7*MjQzg-P C=1;
eaWK 2%v M1=120, % integer for amplitude
)k~{p;Ke M3=5000; % integer for length of coupler
6Zx'$F.iqK N = 512; % Number of Fourier modes (Time domain sampling points)
EYy|JT]B dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
p=T6Ix'_2e T =40; % length of time:T*T0.
F 2 ^qf dt = T/N; % time step
e~1$x`DH n = [-N/2:1:N/2-1]'; % Index
Ib}~Q@ ?2 t = n.*dt;
1nZ7xCDK98 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9Od|R"aS| w=2*pi*n./T;
By;{Y[@rS g1=-i*ww./2;
)e?6 Ncy g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
V9\y*6#Y, g3=-i*ww./2;
Rq[ VP# P1=0;
?l?_8y/ww P2=0;
lHc|: vG? P3=1;
+ab#2~,) P=0;
5T-CAkR{n for m1=1:M1
8(@ Y@`/ p=0.032*m1; %input amplitude
dXMO{*MF{H s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
@wTRoMHPQ s1=s10;
Yw6d-5=: s20=0.*s10; %input in waveguide 2
s $?u'}G3 s30=0.*s10; %input in waveguide 3
aU yJi s2=s20;
Fu*Qci1Z s3=s30;
XJguw/[wm p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
m^%Xl@V:c- %energy in waveguide 1
R-]i BL p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
52v@zDY %energy in waveguide 2
=| O ><O| p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
#+SdX[ N %energy in waveguide 3
r34 GO1d for m3 = 1:1:M3 % Start space evolution
+ V,Ld&r s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
}Zp5d7(@w s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
V5up/ 6b,1 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
MngfXm sca1 = fftshift(fft(s1)); % Take Fourier transform
"S Fs\] Z sca2 = fftshift(fft(s2));
wpepi8w, sca3 = fftshift(fft(s3));
`XK+Y sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
G&,2>qxK R sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
`\Hs{t] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
)A*Sl2ew s3 = ifft(fftshift(sc3));
*OR(8; s2 = ifft(fftshift(sc2)); % Return to physical space
-z?O^:e#x s1 = ifft(fftshift(sc1));
?{KC@c*c end
vy{YGT p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
mP+rPDGp p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
t Rzo}_+N p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
H\RuYCn2G P1=[P1 p1/p10];
fu d Lm P2=[P2 p2/p10];
gt:O t0\7 P3=[P3 p3/p10];
Xb5 $ijH P=[P p*p];
mqv!"rk'w end
pNzpT!}H> figure(1)
s[tFaB 1 plot(P,P1, P,P2, P,P3);
nyr)d% I{ MnT+p[. 转自：
http://blog.163.com/opto_wang/
