计算脉冲在非线性耦合器中演化的Matlab 程序 >z2 {D 7 V}( "8L % This Matlab script file solves the coupled nonlinear Schrodinger equations of
mEA w^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
,AJd2i x % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
S"dQ@r9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5v]xk?Eb +CACs7tV %fid=fopen('e21.dat','w');
JO$0Z N = 128; % Number of Fourier modes (Time domain sampling points)
0
[s1!Cm!i M1 =3000; % Total number of space steps
+1rJ ;G J =100; % Steps between output of space
g$+ 3IVq& T =10; % length of time windows:T*T0
:s f ;Fq T0=0.1; % input pulse width
(mzyA%;W MN1=0; % initial value for the space output location
/w| YNDA]j dt = T/N; % time step
*]rV,\ z: n = [-N/2:1:N/2-1]'; % Index
"/q6E t = n.*dt;
\"Np '$4eu u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
It4F ;Ah u20=u10.*0.0; % input to waveguide 2
?VJ Fp^Ra u1=u10; u2=u20;
Tb}b* d 3 U1 = u1;
V{8mx70 U2 = u2; % Compute initial condition; save it in U
:%0Z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
35ng_,t $ w=2*pi*n./T;
_C##U; e! g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
z\ \MLyS L=4; % length of evoluation to compare with S. Trillo's paper
%T&kK2d; dz=L/M1; % space step, make sure nonlinear<0.05
H;v*/~zl for m1 = 1:1:M1 % Start space evolution
G#csN &|, u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
g ,.iM8 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
jWm<!< ~ ca1 = fftshift(fft(u1)); % Take Fourier transform
p4/D%*G^` ca2 = fftshift(fft(u2));
/rquI y^ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
J[^-k!9M c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
CkOd> Kn u2 = ifft(fftshift(c2)); % Return to physical space
\X(.%5xC u1 = ifft(fftshift(c1));
m$U2|5un& if rem(m1,J) == 0 % Save output every J steps.
{3l] / X3 U1 = [U1 u1]; % put solutions in U array
8garRB { U2=[U2 u2];
S -im
o MN1=[MN1 m1];
gG#M-2 P z1=dz*MN1'; % output location
ec{pWzAe end
\=w|Zeu{l end
V%"aU}
hg=abs(U1').*abs(U1'); % for data write to excel
VlK W WQj ha=[z1 hg]; % for data write to excel
M]oaWQu t1=[0 t'];
?@tp1?) hh=[t1' ha']; % for data write to excel file
-ohqw+D %dlmwrite('aa',hh,'\t'); % save data in the excel format
q$\KE4v " figure(1)
gg<lWeS/3 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Wu: evaZ:i figure(2)
5B a e HzI waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
f-
_~rQ LnLuWr<;} 非线性超快脉冲耦合的数值方法的Matlab程序 #Hq XC\~n Ug/b;( dJ' 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。
Qax=_[r 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
0DGXMO$; :X+7}!Wlo _/hWzj=q ) !3sB{ H % This Matlab script file solves the nonlinear Schrodinger equations
'v?Z~"w= % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
3d[fP#NY7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
:
x W.(^(d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
BjSLbw-C Uh{|@D C=1;
L\o-z NY M1=120, % integer for amplitude
g%Eb{~v M3=5000; % integer for length of coupler
rxt)l N = 512; % Number of Fourier modes (Time domain sampling points)
t}+P |$[ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
af.yC[ T =40; % length of time:T*T0.
nzU^G) dt = T/N; % time step
9[T}cN=| n = [-N/2:1:N/2-1]'; % Index
L2+~I<|> t = n.*dt;
|%Pd*y ZA ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
',~,h J0 w=2*pi*n./T;
`i;f g1=-i*ww./2;
ji5 c0WH g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
p4[cPt ~C g3=-i*ww./2;
U 8 '}( P1=0;
Y$ ZZ0m P2=0;
:hC+r=!I P3=1;
> <^
, P=0;
uS;N&6;: for m1=1:M1
)k$ +T% p=0.032*m1; %input amplitude
/d*d '3{c s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
E {*d `n s1=s10;
OF-$* s20=0.*s10; %input in waveguide 2
^z)p@sk# s30=0.*s10; %input in waveguide 3
^- Bx zOp s2=s20;
q-}q r g s3=s30;
B^nE^"b p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
d#NG]V/
%energy in waveguide 1
^\KZE|^3@ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
WS6'R %energy in waveguide 2
j"1#n? 0 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
<*oTVl4fS %energy in waveguide 3
l$
^LY)i for m3 = 1:1:M3 % Start space evolution
>cJf D9-<h s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
6fY-D qF! s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
0o7*5| T4 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
c&X2k\ sca1 = fftshift(fft(s1)); % Take Fourier transform
+VT/ c sca2 = fftshift(fft(s2));
@L0xU??"| sca3 = fftshift(fft(s3));
ZW7z[,tk<. sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
~>SqJ&-moo sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
qjDt6B^RO sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
stQ Rl_(' s3 = ifft(fftshift(sc3));
%\$~B?At s2 = ifft(fftshift(sc2)); % Return to physical space
:J6 xY y$ s1 = ifft(fftshift(sc1));
FLUvFD end
(X zy~l< p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Rq B 8g p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
zi%Ql|zI~ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
{#y~ Qk;T P1=[P1 p1/p10];
Dk%+|c P2=[P2 p2/p10];
/x q^]0xy P3=[P3 p3/p10];
37<^Oly! P=[P p*p];
*be"$ Q end
h>k[ figure(1)
XSHK7vpMf plot(P,P1, P,P2, P,P3);
'- X[T} SFJ"(ey$ 转自：
http://blog.163.com/opto_wang/
