计算脉冲在非线性耦合器中演化的Matlab 程序 lL*"N|Y Qb@i_SX(fs % This Matlab script file solves the coupled nonlinear Schrodinger equations of
*z__$!LR % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
_f@nUv*
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Z L'krV % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
AdWP Xj$'i/=-+c %fid=fopen('e21.dat','w');
h"dn:5G:= N = 128; % Number of Fourier modes (Time domain sampling points)
j#
n M1 =3000; % Total number of space steps
Hx NoV.q J =100; % Steps between output of space
0A F}wz> T =10; % length of time windows:T*T0
c"pu"t@/Z T0=0.1; % input pulse width
ddw^oU MN1=0; % initial value for the space output location
g5t` YcL dt = T/N; % time step
#NWS)^&1b n = [-N/2:1:N/2-1]'; % Index
|b+CXEzo t = n.*dt;
Y``]66\Fp u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
g1&q6wCg| u20=u10.*0.0; % input to waveguide 2
4E@_Fn_# u1=u10; u2=u20;
!"dAwG ?S U1 = u1;
{GG;/Ns{f- U2 = u2; % Compute initial condition; save it in U
newURb,-! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
WU~L#Ih.V w=2*pi*n./T;
Nq#B4Zx g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
c. }#.-b8 L=4; % length of evoluation to compare with S. Trillo's paper
j>Cp4 dz=L/M1; % space step, make sure nonlinear<0.05
j5G=ZI86y for m1 = 1:1:M1 % Start space evolution
7,FhKTV1/ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
`(
_N9 .>B u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
ilwI qj ca1 = fftshift(fft(u1)); % Take Fourier transform
_ c,{}sn ca2 = fftshift(fft(u2));
)^m"fQ+ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
PBgU/zVn c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
I[bWd{i: u2 = ifft(fftshift(c2)); % Return to physical space
0+Q; a u1 = ifft(fftshift(c1));
"8/BVW^bv if rem(m1,J) == 0 % Save output every J steps.
,&s%^I+CC U1 = [U1 u1]; % put solutions in U array
Vj6 w7hz U2=[U2 u2];
m=V69
a# MN1=[MN1 m1];
L4v26*P z1=dz*MN1'; % output location
JwdvY] end
ap Wv+A end
f*Yr*yC hg=abs(U1').*abs(U1'); % for data write to excel
a$$aM2 .2 ha=[z1 hg]; % for data write to excel
O8/r-?4. t1=[0 t'];
h}= hh=[t1' ha']; % for data write to excel file
t_ id/ %dlmwrite('aa',hh,'\t'); % save data in the excel format
FA1h!Vit figure(1)
C&;m56 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
K?*p|&Fi?8 figure(2)
d?)Ic1][ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
9}' 9 2 c6tH'oV 非线性超快脉冲耦合的数值方法的Matlab程序 [H {2<! SDko# 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。
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.SY 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
r)oR `\7 WM nxN34 CRu {Ie5B {}"a_L&[; % This Matlab script file solves the nonlinear Schrodinger equations
DtkOb,wY % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
;Hn>Ew % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
CQH^VTQ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+<fT\Oq# c=33O,_ C=1;
t""d^a#Dp M1=120, % integer for amplitude
Gp2C wyv M3=5000; % integer for length of coupler
Q$ A;Fk}- N = 512; % Number of Fourier modes (Time domain sampling points)
qE M,~:lTn dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
B]:?4O v T =40; % length of time:T*T0.
=1 zRm >m dt = T/N; % time step
?gG%FzfQ/ n = [-N/2:1:N/2-1]'; % Index
q>[}JtXK t = n.*dt;
9b)'vr*Hy7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
(/A
6kp? w=2*pi*n./T;
_^`TG ]F g1=-i*ww./2;
rAS2 qt g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Gk!CU"`sP g3=-i*ww./2;
g:Fo7*i P1=0;
spma\,o P2=0;
3 ]w a8| P3=1;
kg^5D3!2{Q P=0;
<"nF`'olV for m1=1:M1
@*iT%p_L p=0.032*m1; %input amplitude
3]67U}` s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
+ De-U. s1=s10;
Wt!8.d} = s20=0.*s10; %input in waveguide 2
:.S wO<j s30=0.*s10; %input in waveguide 3
vW jHHw s2=s20;
@^n E^; s3=s30;
n\u3$nGL1` p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
B*n_
VBd %energy in waveguide 1
U[6
~ad
a p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
oWBjPsQ %energy in waveguide 2
t LM/STb6 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
)npvy>C'( %energy in waveguide 3
| v:fP;zc for m3 = 1:1:M3 % Start space evolution
)zu m.6p T s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
51`*VR]`K s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
bM"d$tl$?' s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
U[NQ" sca1 = fftshift(fft(s1)); % Take Fourier transform
pPJE.[)V/ sca2 = fftshift(fft(s2));
wPaMYxO/ sca3 = fftshift(fft(s3));
V@\A<q%jTs sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
SeBl*V sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
s(y=u > sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Q'0:k{G
s3 = ifft(fftshift(sc3));
G1ED=N_# s2 = ifft(fftshift(sc2)); % Return to physical space
z
9~|Su s1 = ifft(fftshift(sc1));
r_pZK(G % end
M)CQ|P p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
lLN5***47J p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
wQ '_ , d p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Z=^~]Mfa P1=[P1 p1/p10];
$mn+ P2=[P2 p2/p10];
9HZR%s[J P3=[P3 p3/p10];
6d;RtCENo P=[P p*p];
'y|p)r" end
, b74 m figure(1)
B4w/cIj_ plot(P,P1, P,P2, P,P3);
-8z@FLUK- PF0AU T 转自：
http://blog.163.com/opto_wang/
