计算脉冲在非线性耦合器中演化的Matlab 程序 @2 $Uk! V2 ;? % This Matlab script file solves the coupled nonlinear Schrodinger equations of
G&6`?1k % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
X1u\si%.4S % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
` v /p4/ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Y |-&= e5n"(s"G*[ %fid=fopen('e21.dat','w');
v] q"{c/ N = 128; % Number of Fourier modes (Time domain sampling points)
cft@s Y M1 =3000; % Total number of space steps
jR3 mV J =100; % Steps between output of space
-gb@BIV# T =10; % length of time windows:T*T0
YcS PU( T0=0.1; % input pulse width
eM7 F8j MN1=0; % initial value for the space output location
="g9> dt = T/N; % time step
#V[Os!ns n = [-N/2:1:N/2-1]'; % Index
Fl== k t = n.*dt;
1)-VlQK p u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Neew V=[% u20=u10.*0.0; % input to waveguide 2
7 $L*nf u1=u10; u2=u20;
`P;3,@
e U1 = u1;
.36]> 8 U2 = u2; % Compute initial condition; save it in U
R++w>5 5A ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
d=HD!
e w=2*pi*n./T;
[XA:pj;rg' g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
=AuxME g L=4; % length of evoluation to compare with S. Trillo's paper
?IiF Ffs dz=L/M1; % space step, make sure nonlinear<0.05
Zz T"u1, & for m1 = 1:1:M1 % Start space evolution
m \ @Q} u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
soB_j u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
[&p/7 ca1 = fftshift(fft(u1)); % Take Fourier transform
%W2
o`W$ ca2 = fftshift(fft(u2));
wI[J> 9Qn c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
[Z]CBEE c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
O3p<7`K<4 u2 = ifft(fftshift(c2)); % Return to physical space
kxY9[#:<fB u1 = ifft(fftshift(c1));
-ozcK if rem(m1,J) == 0 % Save output every J steps.
hi ),PfAV U1 = [U1 u1]; % put solutions in U array
gp^xl>E U2=[U2 u2];
R8j\CiV17 MN1=[MN1 m1];
g Yw=Z_z z1=dz*MN1'; % output location
1=jwJv.^/ end
'^:q|h end
pvM`j86 _ hg=abs(U1').*abs(U1'); % for data write to excel
h& Ezhv2 ha=[z1 hg]; % for data write to excel
9@
^*\s t1=[0 t'];
*Y ?&N 2@c hh=[t1' ha']; % for data write to excel file
ZP4y35&%y %dlmwrite('aa',hh,'\t'); % save data in the excel format
^QTkre figure(1)
RWG Axq`9f waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
L yjp figure(2)
"," to waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Rap_1o9#\ Q2t > E(S 非线性超快脉冲耦合的数值方法的Matlab程序 F:G
Vysy t)l^$j !h@ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
DV~g Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;.d{$SO g+ cH 9+frxD&pO ZX40-6#O % This Matlab script file solves the nonlinear Schrodinger equations
4~0 @(3 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
cq 1)b\ | % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
4AN(4"$N % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
a +`;:tX, D^H4]7wG@ C=1;
R lmeZy4.
M1=120, % integer for amplitude
V_ H0z M3=5000; % integer for length of coupler
@9h6D<? N = 512; % Number of Fourier modes (Time domain sampling points)
{mB &xz:b dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
[mG:PTK3 T =40; % length of time:T*T0.
/h K/t; dt = T/N; % time step
q>dERN& n = [-N/2:1:N/2-1]'; % Index
D~ f[ R g t = n.*dt;
HVM(LHm=: ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
A!_yZ|)$ T w=2*pi*n./T;
5[rA>g~ g1=-i*ww./2;
qoJ<e`h} g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
d>`s+B9K0 g3=-i*ww./2;
0d #jiG P1=0;
?~rz'Pu~ P2=0;
:stA]JB#
w P3=1;
axiP~t2 P=0;
T |h'"3' for m1=1:M1
\yA*)X+ p=0.032*m1; %input amplitude
`&o>7a; s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
:@sjOY s1=s10;
JA6#qlylL s20=0.*s10; %input in waveguide 2
Vg8c}>7 s30=0.*s10; %input in waveguide 3
N5@ l[F7I s2=s20;
JcI~8;Z@Z~ s3=s30;
7! #34ue p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
PQ4)kVT %energy in waveguide 1
Z oQPvs7_ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
#~;:i %energy in waveguide 2
E9PD1ADR p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
!wEz=
i %energy in waveguide 3
`Ez C'e for m3 = 1:1:M3 % Start space evolution
[X'u={ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
vo]$[Cp|4 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
vI+X9C? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
U: O&FE sca1 = fftshift(fft(s1)); % Take Fourier transform
2)+ddel<Z sca2 = fftshift(fft(s2));
&s_)|K sca3 = fftshift(fft(s3));
kZH IzU sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
!1Z rS sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
rsC^Re:*jr sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
_D~FwF&A s3 = ifft(fftshift(sc3));
Uk= L?t s2 = ifft(fftshift(sc2)); % Return to physical space
v
L!?4k s1 = ifft(fftshift(sc1));
cR/z; *wr7 end
Tyt1a>! qA p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
>Gi* BB p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
.V\: )\<| p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
$ 2PpG|q P1=[P1 p1/p10];
v[=TPfX 0 P2=[P2 p2/p10];
b0lZb' P3=[P3 p3/p10];
jij-pDQnv P=[P p*p];
Vh5Z'4 N end
s
N|7 figure(1)
" 2 J2za plot(P,P1, P,P2, P,P3);
\tZZn~ex W)m\q}]FYz 转自：
http://blog.163.com/opto_wang/
