计算脉冲在非线性耦合器中演化的Matlab 程序 *?rO@sQy] ^H`4BWc % This Matlab script file solves the coupled nonlinear Schrodinger equations of
aIo%~w % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
o k1-`c P % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
K1CgM1 v % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
45Lzq6 BG_6$9y %fid=fopen('e21.dat','w');
4w#:?Y
_\[ N = 128; % Number of Fourier modes (Time domain sampling points)
)(+q~KA} M1 =3000; % Total number of space steps
Ij2T h] J =100; % Steps between output of space
8lFYk`|g T =10; % length of time windows:T*T0
sB0 m^Y' T0=0.1; % input pulse width
m+QZ| MN1=0; % initial value for the space output location
nm,(Wdr dt = T/N; % time step
KGrYF n = [-N/2:1:N/2-1]'; % Index
d+p^fBz t = n.*dt;
z:oi @q u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
m:Fdgu9 u20=u10.*0.0; % input to waveguide 2
PIH KSAnq u1=u10; u2=u20;
eCjyx|:J U1 = u1;
L, 2; -b| U2 = u2; % Compute initial condition; save it in U
^B$cfs@* ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
j [4l'8Ek w=2*pi*n./T;
A "/|h]. g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
>02p,W6S> L=4; % length of evoluation to compare with S. Trillo's paper
8&SW Q dz=L/M1; % space step, make sure nonlinear<0.05
.UYhj8 for m1 = 1:1:M1 % Start space evolution
e)$a ;6 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
"u)L e6. u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
z\-/R9E/5- ca1 = fftshift(fft(u1)); % Take Fourier transform
'. ]<lh! ca2 = fftshift(fft(u2));
K=> j+a5$ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
9^E!2 CJ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
45 H9 pY w u2 = ifft(fftshift(c2)); % Return to physical space
]fSpG \yU u1 = ifft(fftshift(c1));
5!BW!-q if rem(m1,J) == 0 % Save output every J steps.
T0N6k acl U1 = [U1 u1]; % put solutions in U array
KG GJ\r6 U2=[U2 u2];
:xk+` ` T MN1=[MN1 m1];
ko"xR %Q z1=dz*MN1'; % output location
U6#9W}CE end
Ec&_& end
:qj7i( hg=abs(U1').*abs(U1'); % for data write to excel
n7.85p@ua ha=[z1 hg]; % for data write to excel
[U:P&) t1=[0 t'];
R`M@;9I.@ hh=[t1' ha']; % for data write to excel file
#'y& M t %dlmwrite('aa',hh,'\t'); % save data in the excel format
XB]>Z) figure(1)
Bm;:
cmB0e waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
y"k % Wa`* figure(2)
HGF&'@dn waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
3|%058bF I~4!8W-Y 非线性超快脉冲耦合的数值方法的Matlab程序 >z7 3uKA( ^ywDa^;- 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。
T^q^JOC4 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
QZJnb%] =t
%;mi,M tAkv'. mV+9*or % This Matlab script file solves the nonlinear Schrodinger equations
o .V
JnrJ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
e ^Z Y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Hc-up.?v'v % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4I#@xm8) |Xt 6`~iC C=1;
;]k \F M1=120, % integer for amplitude
_ jH./ @G M3=5000; % integer for length of coupler
<o/l K\> N = 512; % Number of Fourier modes (Time domain sampling points)
-/Zy{2 <u dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
X^rFR k T =40; % length of time:T*T0.
\jb62Jp dt = T/N; % time step
g_rk_4] n = [-N/2:1:N/2-1]'; % Index
G8' t = n.*dt;
/x<u v_" ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
'uF-}_
| w=2*pi*n./T;
*S?'[PS]1 g1=-i*ww./2;
\-sW>LIA g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
yCuL o` g3=-i*ww./2;
G cB <i P1=0;
DXQ]b)y+N P2=0;
y9k'jEZ"oh P3=1;
Wi w~oXo P=0;
lMcO2006L for m1=1:M1
4q.yp0E p=0.032*m1; %input amplitude
+VL:O]`DJ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
y`z4S, s1=s10;
FL4BdJ\ s20=0.*s10; %input in waveguide 2
Ai )>ot s30=0.*s10; %input in waveguide 3
wd3OuDrU s2=s20;
,3!TyQ \m' s3=s30;
nw#AK td@x p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
PPh<9$1\g %energy in waveguide 1
j&
ykce p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
XA;f.u %energy in waveguide 2
Y!+H9R p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
gYbcBb%z %energy in waveguide 3
ouO9%)zv
for m3 = 1:1:M3 % Start space evolution
Pz\ByD s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
+3sbpl2} s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
RJKi98xwJ
s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
/qMiv7m~Q sca1 = fftshift(fft(s1)); % Take Fourier transform
PHJHW#sv sca2 = fftshift(fft(s2));
P1)87P sca3 = fftshift(fft(s3));
O*Y ? :
t sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
\< dg sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
j<`3xd' sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
9E Y`j,{4 s3 = ifft(fftshift(sc3));
]{|lGtK % s2 = ifft(fftshift(sc2)); % Return to physical space
lBm`W]3T s1 = ifft(fftshift(sc1));
sb hzER end
h wA&SS p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
G/#m. =t p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
An ^)K p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
W*Ow%$%2 P1=[P1 p1/p10];
<4< y P2=[P2 p2/p10];
pvb&vtp P3=[P3 p3/p10];
Y[_|sIy* P=[P p*p];
B/o8r4[80 end
,k*%=TF7N figure(1)
E " >` plot(P,P1, P,P2, P,P3);
G B"Orm . \)6b LB!
转自：
http://blog.163.com/opto_wang/
