计算脉冲在非线性耦合器中演化的Matlab 程序 dMI G2log dkQP.Tj$i % This Matlab script file solves the coupled nonlinear Schrodinger equations of
[LV> z % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
fOP3`G^\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Qr-,J_ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
F8\JL % }z2[w@M %fid=fopen('e21.dat','w');
Q4g69IE N = 128; % Number of Fourier modes (Time domain sampling points)
Q0g^% M1 =3000; % Total number of space steps
E[FE-{B# J =100; % Steps between output of space
1`~.!yd8( T =10; % length of time windows:T*T0
7IrH(~Fo T0=0.1; % input pulse width
:edy(vC< MN1=0; % initial value for the space output location
IUD@Kf]S dt = T/N; % time step
`1lGAKv n = [-N/2:1:N/2-1]'; % Index
s dN1BV2 t = n.*dt;
n-O QCz9Xl u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Q n;,OB k u20=u10.*0.0; % input to waveguide 2
eEY z A u1=u10; u2=u20;
VWk{?*Dp U1 = u1;
%kP=VUXj U2 = u2; % Compute initial condition; save it in U
CbOCL~ " ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_KZ TY`/* w=2*pi*n./T;
8KsPAK_ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
N%)q.'M L=4; % length of evoluation to compare with S. Trillo's paper
$M$-c{>s dz=L/M1; % space step, make sure nonlinear<0.05
z00,Vr^m for m1 = 1:1:M1 % Start space evolution
=}Yz[-I u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
HK VtO%& u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
} q,d JE ca1 = fftshift(fft(u1)); % Take Fourier transform
StiWa<"c ca2 = fftshift(fft(u2));
oFsV0 {x%) c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
~"8r=8| c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
:BB=E'293 u2 = ifft(fftshift(c2)); % Return to physical space
hUEA)c u1 = ifft(fftshift(c1));
dq0! .gBT2 if rem(m1,J) == 0 % Save output every J steps.
$KP&#;9 U1 = [U1 u1]; % put solutions in U array
)^
P Wr^ U2=[U2 u2];
HumL( S'm MN1=[MN1 m1];
iV!V!0- @ z1=dz*MN1'; % output location
YdN]Tqc end
dk 0} q6~ end
-&lD0p>*g hg=abs(U1').*abs(U1'); % for data write to excel
3^-\=taN<m ha=[z1 hg]; % for data write to excel
W>'(MB$3 t1=[0 t'];
"/ %o'Fq hh=[t1' ha']; % for data write to excel file
I__ a}|T% %dlmwrite('aa',hh,'\t'); % save data in the excel format
&q#.
> figure(1)
MSB /O. waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
m ^w{:\p figure(2)
,;f5OUl?[ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
,wn gS= AHHV \r 非线性超快脉冲耦合的数值方法的Matlab程序 ,hm &] 4[)tO-v:Y 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。
Vlge*4q 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
\ u;`Lf ?-tNRIPW@p LjIkZ 'HuF T1'\!6_5 % This Matlab script file solves the nonlinear Schrodinger equations
kdaq_O: s % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
qd<I;*WV % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
&y7xL-xP % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0E)M6
jJ A2 $05a$% C=1;
<~S]jtL.j: M1=120, % integer for amplitude
d N7.W
M3=5000; % integer for length of coupler
& xp]9$ N = 512; % Number of Fourier modes (Time domain sampling points)
?Cx=!k. dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
ae](= OQ T =40; % length of time:T*T0.
= |2F? dt = T/N; % time step
fK2r6D9 n = [-N/2:1:N/2-1]'; % Index
cIcu=U t = n.*dt;
^;tB,7:*V ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
|dDKO w=2*pi*n./T;
2'-84 g1=-i*ww./2;
%jHe_8=o g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
GRaU]Z]ck g3=-i*ww./2;
?Iq{6O>D. P1=0;
) TRU x P2=0;
5"X@<;H% P3=1;
+cKOIMu9 P=0;
7 p1B"% for m1=1:M1
1N<n)>X4
p=0.032*m1; %input amplitude
eN\+ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
@;N(3| n7 s1=s10;
;cZp$
xb3 s20=0.*s10; %input in waveguide 2
w'E?L`c s30=0.*s10; %input in waveguide 3
#=;vg s2=s20;
/)kx`G_ s3=s30;
E VC] B} p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
B< HN$/ %energy in waveguide 1
[rL 8L6,! p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
B^/k `h6J %energy in waveguide 2
*aFY+.;U` p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
=LGSywWM9 %energy in waveguide 3
gXM+N (M- for m3 = 1:1:M3 % Start space evolution
E+LQyvF[ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
uGm?e]7Hx< s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
?%Ww3cU+J s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
UEhFId sca1 = fftshift(fft(s1)); % Take Fourier transform
c{KJNH%7 sca2 = fftshift(fft(s2));
(E,Ibz2G:e sca3 = fftshift(fft(s3));
s`0IyQXVU sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
$R NHRA. sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
\ 9iiS(e sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
#9F>21UU s3 = ifft(fftshift(sc3));
=\oL'> q s2 = ifft(fftshift(sc2)); % Return to physical space
.wyuB;: s1 = ifft(fftshift(sc1));
~sPXkLqK
end
M&<qGV$A p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
e s~1@Jb
p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
p \9}}t7n p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
8R:Glif P1=[P1 p1/p10];
1N:~5S}s> P2=[P2 p2/p10];
s9OW. i]zX P3=[P3 p3/p10];
9qgs*]J P=[P p*p];
N u\<Xr8 end
%5DM ew figure(1)
ezCJq`b plot(P,P1, P,P2, P,P3);
' W>y v <;O^3 _' 转自：
http://blog.163.com/opto_wang/
