计算脉冲在非线性耦合器中演化的Matlab 程序 QE=Cum
Q^b_+M % This Matlab script file solves the coupled nonlinear Schrodinger equations of
'g|%Ro/ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
f&7S ivS# % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
S%kE<M? % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
05=O5<l
J55K+ %fid=fopen('e21.dat','w');
f?2Y np=@ N = 128; % Number of Fourier modes (Time domain sampling points)
WFjNS'WI_ M1 =3000; % Total number of space steps
L!3{ASIN0 J =100; % Steps between output of space
"z=A=~~<{ T =10; % length of time windows:T*T0
+}I[l,,xy T0=0.1; % input pulse width
o3]B/ MN1=0; % initial value for the space output location
/-8v]nRB dt = T/N; % time step
;]i&AAbj n = [-N/2:1:N/2-1]'; % Index
s lDxsb t = n.*dt;
gt';_ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
V%<<Udu< u20=u10.*0.0; % input to waveguide 2
(|bMtT?"x u1=u10; u2=u20;
slOki|p; U1 = u1;
yodJ GGAzk U2 = u2; % Compute initial condition; save it in U
w4:n(.;HK ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
{5#P1jlT w=2*pi*n./T;
\-#~)LB]M g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
n&r- L=4; % length of evoluation to compare with S. Trillo's paper
TEh]-x`
dz=L/M1; % space step, make sure nonlinear<0.05
!|9$ for m1 = 1:1:M1 % Start space evolution
5w@ ;B u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
c^6v7wT5 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
gK-: t ca1 = fftshift(fft(u1)); % Take Fourier transform
_B 8e 1an ca2 = fftshift(fft(u2));
Q2Yv8q_}Uq c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
"SNsO f c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
PC.$&x4w1 u2 = ifft(fftshift(c2)); % Return to physical space
ed'}ReLK u1 = ifft(fftshift(c1));
-,TBUWg if rem(m1,J) == 0 % Save output every J steps.
X']>b U1 = [U1 u1]; % put solutions in U array
Mpk^e_9`< U2=[U2 u2];
SV<*qz MN1=[MN1 m1];
l0U 6eOx z1=dz*MN1'; % output location
5y(irbk7 end
;}A#ws_CD_ end
Av.(i2 hg=abs(U1').*abs(U1'); % for data write to excel
b v\V>s ha=[z1 hg]; % for data write to excel
tmRD$O%: t1=[0 t'];
e&OMW ,7 hh=[t1' ha']; % for data write to excel file
U`W^w% %dlmwrite('aa',hh,'\t'); % save data in the excel format
<^~Xnstl figure(1)
yD#w @yG waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
$a15
8 figure(2)
a_waLH/ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Eh!%Ne O _xl#1>G^J 非线性超快脉冲耦合的数值方法的Matlab程序 SjtGU47$! {;n?c$r 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。
9`4h"9dO 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
c5;YKON J}._v\Q7P :`:<JA3, / v5Pk.!o % This Matlab script file solves the nonlinear Schrodinger equations
**_VNDK+ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
%f6l" ~y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
D'fP2?3FK % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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yd u\t[rC=yd C=1;
^ n bze M1=120, % integer for amplitude
Jgtv i a M3=5000; % integer for length of coupler
z9w @-]) N = 512; % Number of Fourier modes (Time domain sampling points)
$rFv(Qc^= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
0a8nBo7A-X T =40; % length of time:T*T0.
4TwU0N+> dt = T/N; % time step
)tFFa*Z' n = [-N/2:1:N/2-1]'; % Index
Se0/ysVB t = n.*dt;
oq8~PTw ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
}K<;ygcWE@ w=2*pi*n./T;
` 3pe\s g1=-i*ww./2;
aCGPtA' g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
1Y}gki^F g3=-i*ww./2;
=!#D UfQf P1=0;
o<Y|N P2=0;
3C_g)5
_: P3=1;
}^ ` {YD
P=0;
t$l[ 4
R- for m1=1:M1
M#<x2ojW p=0.032*m1; %input amplitude
\M>AN
Z} s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
U?$v 1 || s1=s10;
)z/j5tnvm s20=0.*s10; %input in waveguide 2
Q l&P1|& s30=0.*s10; %input in waveguide 3
!c SD9q* s2=s20;
a.%]5%O;t s3=s30;
X){F^1CT{ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
\?3];+c9 %energy in waveguide 1
Tw!x* p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
2mU}"gf[ %energy in waveguide 2
u52; )"&=) p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Qbv)(&i# ~ %energy in waveguide 3
(]7@0d88 for m3 = 1:1:M3 % Start space evolution
p-*BB_ J" s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
M\`6H8aLn s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
|I OTW=> s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
3g- }k sca1 = fftshift(fft(s1)); % Take Fourier transform
D"^ogY#LK sca2 = fftshift(fft(s2));
V{d "cs>9 sca3 = fftshift(fft(s3));
1d\K{ 7i# sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
SCGQo .~, sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
; H:qDBH sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
)s6tj lf8 s3 = ifft(fftshift(sc3));
zR{ TWk] s2 = ifft(fftshift(sc2)); % Return to physical space
L"}@> &6 s1 = ifft(fftshift(sc1));
b]|7{yMV end
TS
UN(_XGW p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
\2N iI]t] p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Ym F`7W p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
E+~~d6nB P1=[P1 p1/p10];
E> 4
\9 P2=[P2 p2/p10];
>`oO(d}n[0 P3=[P3 p3/p10];
Pyyx/u+?@ P=[P p*p];
57[O)5u.+ end
JBoo7a1 figure(1)
X(WG:FP27 plot(P,P1, P,P2, P,P3);
\H" (*["& V KR6 i 转自：
http://blog.163.com/opto_wang/
