计算脉冲在非线性耦合器中演化的Matlab 程序 Xh?J"kjof TQL_K8k@_ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
0Qr|!B:+9) % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
/Z1>3=G by % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
O*lMIWx % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
BbG=vy8'l iezY+`x4 %fid=fopen('e21.dat','w');
H tx)MEZ N = 128; % Number of Fourier modes (Time domain sampling points)
c~)H" n M1 =3000; % Total number of space steps
M<K}H8? J =100; % Steps between output of space
70F(`; T =10; % length of time windows:T*T0
Iy;bzHXs T0=0.1; % input pulse width
dTVh{~/ MN1=0; % initial value for the space output location
gg?O0W{ dt = T/N; % time step
u`gY/]y! n = [-N/2:1:N/2-1]'; % Index
z{(c-7* t = n.*dt;
WqRaD=R->; u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
3J}/<&wv u20=u10.*0.0; % input to waveguide 2
OrRU$5Lo u1=u10; u2=u20;
AVO$R\1YR U1 = u1;
Tqm)- |[ U2 = u2; % Compute initial condition; save it in U
1Q!^%{Y; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
,R*YI w=2*pi*n./T;
4"et4Y7 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
F* _ytL L=4; % length of evoluation to compare with S. Trillo's paper
|>v8yS5 dz=L/M1; % space step, make sure nonlinear<0.05
l0BYv&tu for m1 = 1:1:M1 % Start space evolution
#eY?6Kjn u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
}kF*I@:g u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
!{S HlS ca1 = fftshift(fft(u1)); % Take Fourier transform
BDcA_=^R& ca2 = fftshift(fft(u2));
evE$$# 6R c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
!glGW[r/7 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
&\5%C\0Z< u2 = ifft(fftshift(c2)); % Return to physical space
l~#%j( Yo u1 = ifft(fftshift(c1));
1z-Q~m@@ if rem(m1,J) == 0 % Save output every J steps.
iX6'3\Q3A U1 = [U1 u1]; % put solutions in U array
qwvch^?>FQ U2=[U2 u2];
t@+z r3 MN1=[MN1 m1];
zuYz"-(L z1=dz*MN1'; % output location
pP*`b<| end
>mp"=Y end
`y*o-St3 hg=abs(U1').*abs(U1'); % for data write to excel
JU!vVA_ ha=[z1 hg]; % for data write to excel
mApl}I t1=[0 t'];
6B&ERdoX hh=[t1' ha']; % for data write to excel file
qVr?st %dlmwrite('aa',hh,'\t'); % save data in the excel format
(R^Ca7F figure(1)
p77 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
F(;95TB figure(2)
#TD0)C/ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
vFH1hm QmY1Bn?s 非线性超快脉冲耦合的数值方法的Matlab程序 cE7IHQ N6uKFQL:{ 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。
9RnXp&w 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
+*Pj,+;W 3sz?49tX . *c%A^> 11BfJvs: % This Matlab script file solves the nonlinear Schrodinger equations
#2Z\K>L % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
?gl[=N V % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
gB}UzEj^< % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$?dutbE 8BggK6X C=1;
[|dQZ M1=120, % integer for amplitude
Sj9NhtF]f M3=5000; % integer for length of coupler
{"@E_{\ N = 512; % Number of Fourier modes (Time domain sampling points)
['\u?m dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
{on+
;, T =40; % length of time:T*T0.
rEY5,'?YHv dt = T/N; % time step
z|WDqB%/I n = [-N/2:1:N/2-1]'; % Index
N-<m/RS t = n.*dt;
Z >F5rkJ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
{aYCrk1 w=2*pi*n./T;
YN($rAkL g1=-i*ww./2;
6^vHFJ$ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
>
@n?W" g3=-i*ww./2;
)+v'@]r P1=0;
TptXH? P2=0;
FX:'38-fk P3=1;
WoX,F1 o P=0;
(g#,AX for m1=1:M1
P'p5-l UK p=0.032*m1; %input amplitude
bT#re s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
X0Zr?$q
s1=s10;
"M4gl s20=0.*s10; %input in waveguide 2
_do(
s30=0.*s10; %input in waveguide 3
Wz-7oP%;I s2=s20;
=d`/BDD s3=s30;
X7{ h/^ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Kk<MS$Ov %energy in waveguide 1
5Q.z#]Lg p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
dT4e[4l %energy in waveguide 2
Hpq?I-g<^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
RlnJlY/ %energy in waveguide 3
u|uPvbM for m3 = 1:1:M3 % Start space evolution
@T8$/ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
.m
\y6 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
/%5X:*:H s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
z{ydP Ra sca1 = fftshift(fft(s1)); % Take Fourier transform
Th\t6K~ sca2 = fftshift(fft(s2));
+Rb0:r>kU sca3 = fftshift(fft(s3));
Tv`-h sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
#+6t| sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
4KCJ(<p| sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
a~"<lzu|$ s3 = ifft(fftshift(sc3));
0Rze9od]$ s2 = ifft(fftshift(sc2)); % Return to physical space
z8\;XR s1 = ifft(fftshift(sc1));
3f^~mTY9>] end
^VAvQ(b!:i p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
-|&5aH] p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
s5SKQ#,@P p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
L#X!. P1=[P1 p1/p10];
RmcQGQ P2=[P2 p2/p10];
Rr3<ln P3=[P3 p3/p10];
+7|Q d}\X P=[P p*p];
DV">9{"5'] end
LAfv1 figure(1)
Nw=mSW^E plot(P,P1, P,P2, P,P3);
cp\A
xWtUZ c<n <!!vi 转自:
http://blog.163.com/opto_wang/