计算脉冲在非线性耦合器中演化的Matlab 程序 jUI'F4.5x- vM 1f-I- % This Matlab script file solves the coupled nonlinear Schrodinger equations of
[[Qu|?KEa % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
@FdtM<X % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
m+"?;;s % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
d*3k]Ie%5f :JxShF :M %fid=fopen('e21.dat','w');
*s S7^OZ* N = 128; % Number of Fourier modes (Time domain sampling points)
*Jmy:C<> M1 =3000; % Total number of space steps
ygWo 9? J =100; % Steps between output of space
2^E. sf$f T =10; % length of time windows:T*T0
LylB3BM T0=0.1; % input pulse width
#fRhG^QKp MN1=0; % initial value for the space output location
+0;6.PK dt = T/N; % time step
/F4rbL^: n = [-N/2:1:N/2-1]'; % Index
3/@7$ nV t = n.*dt;
L#M9 ! u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
,L6d~>=41 u20=u10.*0.0; % input to waveguide 2
b{b2L . u1=u10; u2=u20;
M`9qo8zCi U1 = u1;
JC_Y#kN@z U2 = u2; % Compute initial condition; save it in U
KArR.o } ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
4T{+R{_Y1 w=2*pi*n./T;
tUDO L-Tv g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
i"r&CS)sT L=4; % length of evoluation to compare with S. Trillo's paper
_ohZTT%l dz=L/M1; % space step, make sure nonlinear<0.05
$ [by) for m1 = 1:1:M1 % Start space evolution
/![S 3Ol u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
k>FMy#N|@ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
k BS;SDl) ca1 = fftshift(fft(u1)); % Take Fourier transform
o6 'I%Gs ca2 = fftshift(fft(u2));
#Ne<=ayS c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
gah3d*d7 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
<_dyUiT$J u2 = ifft(fftshift(c2)); % Return to physical space
4h@jJm
u1 = ifft(fftshift(c1));
q?nXhUD if rem(m1,J) == 0 % Save output every J steps.
Q&opn vN U1 = [U1 u1]; % put solutions in U array
<%8j#@OdZ U2=[U2 u2];
_[<R<&jG MN1=[MN1 m1];
j #f+0 z1=dz*MN1'; % output location
/!=uM . end
j\B]>PP5 end
rr>QG<i;G hg=abs(U1').*abs(U1'); % for data write to excel
X};m \Bz ha=[z1 hg]; % for data write to excel
8V`NQS$ t1=[0 t'];
[2pp)wq hh=[t1' ha']; % for data write to excel file
D^baXp8 %dlmwrite('aa',hh,'\t'); % save data in the excel format
Kyt.[" p figure(1)
puF'w:I ( waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
XZ EawJ0 figure(2)
W2D^%;mw waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
3l _Ko %qS gPSUxE `O. 非线性超快脉冲耦合的数值方法的Matlab程序 0&mo1 k_U y>Zvos e 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。
s :'M[xI 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
vIF=kKl9, 4v_?i @,L /;-KWu+5= \V
/s % This Matlab script file solves the nonlinear Schrodinger equations
% 6+J]U % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
4EQ7 OGU % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
W $B&asO % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
q#:, 6HDd 8c(}*,O/ C=1;
R7;SZo M1=120, % integer for amplitude
P~Q5d&1SO M3=5000; % integer for length of coupler
uSLO"\zysX N = 512; % Number of Fourier modes (Time domain sampling points)
)xX(Et6+` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
6&M $S$y T =40; % length of time:T*T0.
%jdV8D#Q dt = T/N; % time step
9 yH95uaDF n = [-N/2:1:N/2-1]'; % Index
7}OzTup t = n.*dt;
J~eY,n.6] ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
o,[~7N w=2*pi*n./T;
w$n\`rQ g1=-i*ww./2;
Fh9%5-t:J g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
' @>FtF[Gu g3=-i*ww./2;
e4p:Zb: P1=0;
)8kcOBG^L P2=0;
]:i
:QiYD P3=1;
,Xs%Cg_Ig P=0;
)X@Obg for m1=1:M1
*vc=>AEc p=0.032*m1; %input amplitude
)A:2y + s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
W{O:j s1=s10;
b#bdz1@s s20=0.*s10; %input in waveguide 2
[_h HZMTH s30=0.*s10; %input in waveguide 3
A`v (hBM s2=s20;
%lNv?sWb s3=s30;
("0@_05O H p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
xB_F?d40T5 %energy in waveguide 1
W.iL!x.B@ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
xoF]r$sC8 %energy in waveguide 2
k@JDG]R<{ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
qg#TE-Y` %energy in waveguide 3
OSk:njyC[ for m3 = 1:1:M3 % Start space evolution
vZj^&/F$=g s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
";E Mu(IXb s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
u.*@ l GVW s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
g9|B-1[ sca1 = fftshift(fft(s1)); % Take Fourier transform
( mz5vzyw sca2 = fftshift(fft(s2));
NsJ t=~ sca3 = fftshift(fft(s3));
&o{I9MD sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Yr@_ X sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
ztf
VXmi' sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
CXks~b3SD s3 = ifft(fftshift(sc3));
lS]<~ s2 = ifft(fftshift(sc2)); % Return to physical space
WJ=DTO N s1 = ifft(fftshift(sc1));
1{4d)z UB end
LuY` mi p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
vA@K b3 , p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
T0s7aw[zm p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
]vJZ v"ACn P1=[P1 p1/p10];
rGuhYYvK P2=[P2 p2/p10];
8*kZ.-T
B P3=[P3 p3/p10];
vzJ69%E_ P=[P p*p];
e`k6YO end
Q W #]i figure(1)
C bm plot(P,P1, P,P2, P,P3);
jT"P$0sJAd ;ZX P*M9 转自：
http://blog.163.com/opto_wang/
