计算脉冲在非线性耦合器中演化的Matlab 程序 5/eS1NJ@ yP=isi#dDY % This Matlab script file solves the coupled nonlinear Schrodinger equations of
,Elga}7u % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
-QNMB4 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5['B-
Iw % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
) 9sr,3w \gW\Sa ^ %fid=fopen('e21.dat','w');
Q`wA"mw6k N = 128; % Number of Fourier modes (Time domain sampling points)
&Bdt+ OQ ; M1 =3000; % Total number of space steps
'[d dE!ta J =100; % Steps between output of space
SO jDtZ T =10; % length of time windows:T*T0
A#07Ly8kXn T0=0.1; % input pulse width
(NW N & MN1=0; % initial value for the space output location
xo"4mbTV dt = T/N; % time step
z E7ocul n = [-N/2:1:N/2-1]'; % Index
XU })3]/ t = n.*dt;
NS/L! "g u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
QvQf@o u20=u10.*0.0; % input to waveguide 2
QbKYB u1=u10; u2=u20;
X52jqXjg U1 = u1;
,Vn]Ft?n U2 = u2; % Compute initial condition; save it in U
m$ UT4,Ol ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
v'~nABYH w=2*pi*n./T;
8`*9jr g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
0tL/:zID L=4; % length of evoluation to compare with S. Trillo's paper
Vv"wf;# dz=L/M1; % space step, make sure nonlinear<0.05
QNI|h;D for m1 = 1:1:M1 % Start space evolution
7JwWM2N?V u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
vi.AzO u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
pvdZ>D-IU ca1 = fftshift(fft(u1)); % Take Fourier transform
i3WmD@ ca2 = fftshift(fft(u2));
6V?&hq&t c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
!'t2 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
|+=:x]#vV u2 = ifft(fftshift(c2)); % Return to physical space
e /#&5ISk u1 = ifft(fftshift(c1));
.A[.?7g if rem(m1,J) == 0 % Save output every J steps.
K# +] U1 = [U1 u1]; % put solutions in U array
Tb6x@MorP U2=[U2 u2];
Q7aDl8L xn MN1=[MN1 m1];
z4`n% ~w1b z1=dz*MN1'; % output location
`; %aQR end
!P ^$g
R end
uU !i`8 hg=abs(U1').*abs(U1'); % for data write to excel
2o5< nGn ha=[z1 hg]; % for data write to excel
-&$%m)wN t1=[0 t'];
>!p K94 hh=[t1' ha']; % for data write to excel file
BRLU&@G`1 %dlmwrite('aa',hh,'\t'); % save data in the excel format
!3v"7l{LF figure(1)
OQ*. ho waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
10 a*7 L figure(2)
2 EcYO$R! waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
'\YhRU pXlBKJmW 非线性超快脉冲耦合的数值方法的Matlab程序 r.5Js*VX! Q+ M3Pqy 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
_qo1 GM& Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
? bg pUv <RsKV$Je
I /;$ew ~} s1apHwJ - % This Matlab script file solves the nonlinear Schrodinger equations
uM<+2 S % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
3VB V_/i; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
b!P;xLcb % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
&t:M Wb; 7B2Og{P C=1;
F5q1VEe M1=120, % integer for amplitude
:L zj'Ij M3=5000; % integer for length of coupler
p6\9H G N = 512; % Number of Fourier modes (Time domain sampling points)
u"| nu!p` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
M_)T=s * T =40; % length of time:T*T0.
1T ?%i dt = T/N; % time step
CfnCi_=[ ` n = [-N/2:1:N/2-1]'; % Index
#7"5Y_0- t = n.*dt;
FMr$cKvE]W ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
2 g==98>cg w=2*pi*n./T;
RIc< g1=-i*ww./2;
yiA\$mtO g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
78#ud15Ml g3=-i*ww./2;
nu -wQr P1=0;
Tj+WO6#V P2=0;
]g!<5 w P3=1;
/ qze P=0;
@V u[Tg}J for m1=1:M1
4f-C]N= p=0.032*m1; %input amplitude
>R-$JrU.= s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
e]fC!>w (\ s1=s10;
5Ozj&Zq s20=0.*s10; %input in waveguide 2
^i 7a2<
z s30=0.*s10; %input in waveguide 3
Q{kuB+s s2=s20;
%.Y`X(g6/ s3=s30;
j*
?MFvwE p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
xGPv3TLH^ %energy in waveguide 1
x B[#
a* p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
#2=3 0 %energy in waveguide 2
h {b tT p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
K)Ka"H %energy in waveguide 3
~vS.D r for m3 = 1:1:M3 % Start space evolution
%hQ`b$07t s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
t|_g O!w8 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
!4fL|0 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
c+VUk*c3 sca1 = fftshift(fft(s1)); % Take Fourier transform
|.yRo_ sca2 = fftshift(fft(s2));
h2K sca3 = fftshift(fft(s3));
c6.|; 4 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
VgL<ux q sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
n$iz sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
a r%Rr" s3 = ifft(fftshift(sc3));
wEyh;ID3# s2 = ifft(fftshift(sc2)); % Return to physical space
.kV/ 0!q? s1 = ifft(fftshift(sc1));
J)f?x T* end
p !
1zhD p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
SM?<woY=* p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
sj2+|> p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
>ZWm0nTr P1=[P1 p1/p10];
YTsn;3d]} P2=[P2 p2/p10];
(>'d`^kjk P3=[P3 p3/p10];
#4?3OU# P=[P p*p];
EY(4 <;) end
B{< 6 & bQ figure(1)
$TiAJ}: plot(P,P1, P,P2, P,P3);
&40d J~SQ gUl Z cb 转自：
http://blog.163.com/opto_wang/
