计算脉冲在非线性耦合器中演化的Matlab 程序 yk1syN_ =p 9d4smbn % This Matlab script file solves the coupled nonlinear Schrodinger equations of
k23*F0Dv % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
R8a4F^{* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
g bOd(ugH % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
R9X* R3nB &D, gKT~ %fid=fopen('e21.dat','w');
"V!y"yQ N = 128; % Number of Fourier modes (Time domain sampling points)
&?\ h[ 3 M1 =3000; % Total number of space steps
#wH<W5gSZ J =100; % Steps between output of space
{8Jr.&Y2 T =10; % length of time windows:T*T0
&]gw[
` T0=0.1; % input pulse width
7(<6+q2~ MN1=0; % initial value for the space output location
*k:Sg*neVq dt = T/N; % time step
/an$4?":~ n = [-N/2:1:N/2-1]'; % Index
ZSj^\JU t = n.*dt;
S siKuoxk u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
o:u *E u20=u10.*0.0; % input to waveguide 2
Y_n^6 ; u1=u10; u2=u20;
g6:S"Em U1 = u1;
0\f3L a U2 = u2; % Compute initial condition; save it in U
qSh^|;2?R ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
gR)T(%W w=2*pi*n./T;
E"7 iU g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
z-*/jFE L=4; % length of evoluation to compare with S. Trillo's paper
Nq|b$S [4 dz=L/M1; % space step, make sure nonlinear<0.05
zj.;O#hW for m1 = 1:1:M1 % Start space evolution
2
F3U,} u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
)h-Qi#{ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
swv 1>52{ ca1 = fftshift(fft(u1)); % Take Fourier transform
mF\r]ovVm ca2 = fftshift(fft(u2));
J%c4-'l c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
t(FI Bf3 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
|T : ' G u2 = ifft(fftshift(c2)); % Return to physical space
o@6:|X)7 u1 = ifft(fftshift(c1));
O p^r }7 if rem(m1,J) == 0 % Save output every J steps.
$Il?[4FF U1 = [U1 u1]; % put solutions in U array
0U'g2F>{ U2=[U2 u2];
c`
^I% i MN1=[MN1 m1];
ndEW$? W, z1=dz*MN1'; % output location
;C,D1_20Z end
< igsO end
{R b|"; hg=abs(U1').*abs(U1'); % for data write to excel
QGE)Xn#_bN ha=[z1 hg]; % for data write to excel
4 %do.D* t1=[0 t'];
NMYkEz(&R hh=[t1' ha']; % for data write to excel file
6j9P`#L t %dlmwrite('aa',hh,'\t'); % save data in the excel format
Ht.0ug figure(1)
cTf/B=yMi waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
,Q~C
F;qe figure(2)
.iFd waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
yM(zc/? :|i jCg+ 非线性超快脉冲耦合的数值方法的Matlab程序 6A$
\I44 :_ F$e 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
| ,k,X}gP Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
u`Kj s}F' l n}2 0^htwec! )r _zM~jI % This Matlab script file solves the nonlinear Schrodinger equations
wIT0A-Por4 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
9
z_9yT % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
i}mvKV?!|1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ghq#-N/t yj! 4L &A C=1;
J}IHQZS M1=120, % integer for amplitude
dY>oj<9 M3=5000; % integer for length of coupler
^b-o N = 512; % Number of Fourier modes (Time domain sampling points)
NbyVBl0= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Vm
NC knG T =40; % length of time:T*T0.
871taL= dt = T/N; % time step
qF!oP n = [-N/2:1:N/2-1]'; % Index
9(`d
h t = n.*dt;
x 5/O.5>f ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
^VCgc>x; w=2*pi*n./T;
78't"2> g1=-i*ww./2;
G2Zr (b') g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Ic_>[E?k g3=-i*ww./2;
QAiont ,! P1=0;
__Ei;%cV P2=0;
G[7Z5 )2B P3=1;
/DPD,bA P=0;
.H,v7L,~88 for m1=1:M1
VFLxxFJ p=0.032*m1; %input amplitude
RGrra< s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Cnp\2Fu/ s1=s10;
NEInro< s20=0.*s10; %input in waveguide 2
U#3Y 3EdF< s30=0.*s10; %input in waveguide 3
sBozz # s2=s20;
NijvFT$V1 s3=s30;
FOz7W p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
EMy Med_ %energy in waveguide 1
no_(J>p^& p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
5c*kgj:x %energy in waveguide 2
'urn5[i p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
dD _(MbTt %energy in waveguide 3
uh`W} n for m3 = 1:1:M3 % Start space evolution
\bJ,8J1C s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
L IM
cZh ; s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
58F jzW s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
} [a sca1 = fftshift(fft(s1)); % Take Fourier transform
yEm[C(gZ sca2 = fftshift(fft(s2));
3\J-=U sca3 = fftshift(fft(s3));
[gK (x% sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
c#l W ? sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
+k=BD s sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
i}C9 s3 = ifft(fftshift(sc3));
@ I{v s2 = ifft(fftshift(sc2)); % Return to physical space
FGzMbi<l#( s1 = ifft(fftshift(sc1));
CF|c4oY 82 end
fI:j @Wug p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
L`v7|! X p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
.qBL.b_` p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
}cDw9;~D P1=[P1 p1/p10];
m:EO}ws= P2=[P2 p2/p10];
yQ5F'.m9 e P3=[P3 p3/p10];
* !4r}h` P=[P p*p];
<w@z iUr end
j*u c$hC" figure(1)
wvH=4TT=w" plot(P,P1, P,P2, P,P3);
E A@p]+P J b.
V4 转自：
http://blog.163.com/opto_wang/
