计算脉冲在非线性耦合器中演化的Matlab 程序 %cr]ZR ] b~2Dap % This Matlab script file solves the coupled nonlinear Schrodinger equations of
?J@?,rZQ^V % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
FX|lhwmc( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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GA0F9.U % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
H=o -ScA %Q sSR'` %fid=fopen('e21.dat','w');
WQLHjGehe N = 128; % Number of Fourier modes (Time domain sampling points)
d[ RWk k5 M1 =3000; % Total number of space steps
>,"D9! J =100; % Steps between output of space
v_ nBh,2 T =10; % length of time windows:T*T0
^Q)g sJY|I T0=0.1; % input pulse width
^8-~@01.`_ MN1=0; % initial value for the space output location
t1 :S!@ dt = T/N; % time step
/romTK4 n = [-N/2:1:N/2-1]'; % Index
>.O*gv/ _ t = n.*dt;
_KM $u>B8 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
{c\oOM<7 u20=u10.*0.0; % input to waveguide 2
,'1Olu{v[s u1=u10; u2=u20;
IGK_1@tq U1 = u1;
bDZ K Q& U2 = u2; % Compute initial condition; save it in U
l\sS? ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-0KbdHIKb' w=2*pi*n./T;
(| 36!-(iK g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
cJHABdK- L=4; % length of evoluation to compare with S. Trillo's paper
S QM(8*:X dz=L/M1; % space step, make sure nonlinear<0.05
17n+4J] for m1 = 1:1:M1 % Start space evolution
/ 8WpX u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
j""y2c1 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
}[KDE{,V ca1 = fftshift(fft(u1)); % Take Fourier transform
[aWDD[#j~ ca2 = fftshift(fft(u2));
p-i.ITRS c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
0x]OF8=J c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
){Ciu[h u2 = ifft(fftshift(c2)); % Return to physical space
g]==!!^<D u1 = ifft(fftshift(c1));
w `. T/ if rem(m1,J) == 0 % Save output every J steps.
N[a ljC-R U1 = [U1 u1]; % put solutions in U array
47C(\\ U2=[U2 u2];
*< $c
= MN1=[MN1 m1];
s}[A4`EWH z1=dz*MN1'; % output location
5!SoN}$ end
GTp?)nh^ end
q lz9&w hg=abs(U1').*abs(U1'); % for data write to excel
M|[@znzR< ha=[z1 hg]; % for data write to excel
jHu,u|e0>S t1=[0 t'];
1Es*=zg hh=[t1' ha']; % for data write to excel file
3X A p Y ' %dlmwrite('aa',hh,'\t'); % save data in the excel format
<m Ju v figure(1)
Mz/]D J8 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
9zoT6QP4 figure(2)
^)9MzD^_nV waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
B@"SOX f%Z;05 非线性超快脉冲耦合的数值方法的Matlab程序 T bKP8zw{ ~),;QQ, 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。
>bX-!<S 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
xZ.~:V03\t Q
SHx]* )
6m, KL5>W \A'|XdQ % This Matlab script file solves the nonlinear Schrodinger equations
(C-,ljY % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
z`emKFbv % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
97qtJ(ESI % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
J{Y6fHFi F,p`- m[q C=1;
e5qrQwU M1=120, % integer for amplitude
u%6Ird x M3=5000; % integer for length of coupler
c N02roQl N = 512; % Number of Fourier modes (Time domain sampling points)
0`VD!_` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
YVQ_ tCC_! T =40; % length of time:T*T0.
krQ l ^~@ dt = T/N; % time step
%sO Wg.0_ n = [-N/2:1:N/2-1]'; % Index
a )3O? Y t = n.*dt;
/<3;0~#){ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
~w
Zl2I w=2*pi*n./T;
_'! aj +{ g1=-i*ww./2;
?1G Y%- g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
'O.+6`& g3=-i*ww./2;
y-w2O] P1=0;
`ir&]jh.A P2=0;
ioB|*D<U2 P3=1;
T"L0Iy!k; P=0;
!cq=)xR for m1=1:M1
vKcl6bVT p=0.032*m1; %input amplitude
l,*yEkU s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
LYd}w(} s1=s10;
!1ML%}vvB, s20=0.*s10; %input in waveguide 2
SQq6X63 \ s30=0.*s10; %input in waveguide 3
G{@C"H[$< s2=s20;
q*~gWn>T s3=s30;
Uby,Tu p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
A)\>#Dv %energy in waveguide 1
[8, PO p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
H7{Q@D8 %energy in waveguide 2
DRH'A!r! p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
t9G}Yd[T %energy in waveguide 3
OJ v}kwV for m3 = 1:1:M3 % Start space evolution
|0tg:\. s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
M
(+.$uz s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
W[@i;f^g s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Gs+\D0o! sca1 = fftshift(fft(s1)); % Take Fourier transform
1*Sr5N[= sca2 = fftshift(fft(s2));
1|o$X sca3 = fftshift(fft(s3));
6exRS]BI sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
CD^CUbGk sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
q^Z~IZ8IT sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
%oAL s3 = ifft(fftshift(sc3));
:ar?0 s2 = ifft(fftshift(sc2)); % Return to physical space
z )5S^{( s1 = ifft(fftshift(sc1));
~_'0]P\ end
+IG1IF p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
NA+&jV p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
`'u Umyg p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
2< p{z P1=[P1 p1/p10];
>Y} 7[XK P2=[P2 p2/p10];
>4,{6<| P3=[P3 p3/p10];
OQ6sv/ P=[P p*p];
\;-qdV_JB end
>B0D/:R9 figure(1)
w|=gSC-o plot(P,P1, P,P2, P,P3);
'g]hmE bFSlf5* H 转自：
http://blog.163.com/opto_wang/
