计算脉冲在非线性耦合器中演化的Matlab 程序 T~]~'+<Pi l?m"o-Gp3 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
\}b2 oiY % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
) ;0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Nh!`"B2B % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
f+ r>ur}\) CPJ <A,V %fid=fopen('e21.dat','w');
R{@saa5I(> N = 128; % Number of Fourier modes (Time domain sampling points)
x $LCLP#$H M1 =3000; % Total number of space steps
[PIMG2"G J =100; % Steps between output of space
jW: 7PS T =10; % length of time windows:T*T0
Cv,WG]E7( T0=0.1; % input pulse width
iE'_x$i MN1=0; % initial value for the space output location
%p}vX9U') dt = T/N; % time step
zb0NqIN: n = [-N/2:1:N/2-1]'; % Index
e)e(f"t6Q t = n.*dt;
3WwS+ 6R u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
p.W7>o,[w u20=u10.*0.0; % input to waveguide 2
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F u1=u10; u2=u20;
!`{?qQ[= U1 = u1;
N?@^BZ U2 = u2; % Compute initial condition; save it in U
9~ UR(Ts}l ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
0!\gK <,z w=2*pi*n./T;
$wM..ee g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
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/;(#{U; L=4; % length of evoluation to compare with S. Trillo's paper
g}+|0F TV dz=L/M1; % space step, make sure nonlinear<0.05
XC3)#D#HGh for m1 = 1:1:M1 % Start space evolution
L0![SE> u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
d*6f,z2= u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
5Dkb/Ia gi ca1 = fftshift(fft(u1)); % Take Fourier transform
gT8(LDJ ca2 = fftshift(fft(u2));
Q6(~VvC- c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
2O kID
WcM c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
1| sem(t u2 = ifft(fftshift(c2)); % Return to physical space
)?72 +X u1 = ifft(fftshift(c1));
ci;2XLAM if rem(m1,J) == 0 % Save output every J steps.
NO*, }aeG U1 = [U1 u1]; % put solutions in U array
qJ;~ANwt U2=[U2 u2];
6m&GN4Ca MN1=[MN1 m1];
Vg$d|m${ z1=dz*MN1'; % output location
E3wpC#[Q1 end
>v,X:B?+FL end
m'2 F#{ hg=abs(U1').*abs(U1'); % for data write to excel
8O^x~[sQ ha=[z1 hg]; % for data write to excel
1sXCu|\q t1=[0 t'];
U.TZd" hh=[t1' ha']; % for data write to excel file
:cA P{rSe %dlmwrite('aa',hh,'\t'); % save data in the excel format
!> Nlp,r&~ figure(1)
.w4| $.H waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
@ 51!3jeu figure(2)
CAc]SxLh waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
9'( _*KSH rai'x/Ut}+ 非线性超快脉冲耦合的数值方法的Matlab程序 6Jgl"Jw8 ?,VpZ%Df2 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。
`*U @d%a 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
]{tWfv|Xg8 bm;iX*~ O+-+=W <);j5) / % This Matlab script file solves the nonlinear Schrodinger equations
0@_8JB ?E % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
N~|f^#L % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
*$7^.eHfdd % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
:awa TY]0aw2]|7 C=1;
\B' )2phE M1=120, % integer for amplitude
g(P7CX+y M3=5000; % integer for length of coupler
*l d)nH{ N = 512; % Number of Fourier modes (Time domain sampling points)
W<<G
'Km dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
|e8A)xM]wC T =40; % length of time:T*T0.
b$2=w^* dt = T/N; % time step
5JOfJ$(n n = [-N/2:1:N/2-1]'; % Index
UL ew ~j t = n.*dt;
.;? ha' ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
lsV> sW4]Z w=2*pi*n./T;
ydD:6 bBX g1=-i*ww./2;
YEV;GFI1 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
kYS#P(1 g3=-i*ww./2;
7 _Vd%<: P1=0;
8+!G /p P2=0;
mTH[*Y, P3=1;
~JZLWTEe P=0;
#N T~GhWFf for m1=1:M1
T72Li"00 p=0.032*m1; %input amplitude
y2%[/L: u~ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
>$}Mr%49 s1=s10;
<!dZ=9^^ 1 s20=0.*s10; %input in waveguide 2
5@.8O VPz s30=0.*s10; %input in waveguide 3
oItC;T s2=s20;
`mkOjsj & s3=s30;
v2|zIZ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
U-?r>K2
%energy in waveguide 1
=YYqgNz+\w p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
~ DLxIe %energy in waveguide 2
Y+S<?8pA p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
je\]j-0$u %energy in waveguide 3
s,J\nbj0h for m3 = 1:1:M3 % Start space evolution
lN.&46
e s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
f: q2JgX s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
!h&h;m/c s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
z@[n?t!7k sca1 = fftshift(fft(s1)); % Take Fourier transform
Gyu = } sca2 = fftshift(fft(s2));
M|{KQ3q:9 sca3 = fftshift(fft(s3));
L%7WHtU*# sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
[Qk j} sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
l7ES*==&@0 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
E#w2'( t s3 = ifft(fftshift(sc3));
0Q%I[f8 s2 = ifft(fftshift(sc2)); % Return to physical space
k="w EZ;Q s1 = ifft(fftshift(sc1));
}8.$)&O$^ end
">|L< p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
'&/Y}] p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
=w7k@[Bq p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
.Xta;Py|J P1=[P1 p1/p10];
@)ozgs@e P2=[P2 p2/p10];
"gpfD-BX P3=[P3 p3/p10];
p<a~L~xH6 P=[P p*p];
k:s86q end
1\ f8-:C figure(1)
Sr10ot&ox plot(P,P1, P,P2, P,P3);
t I +]x]m+ #z}IW(u< 转自：
http://blog.163.com/opto_wang/
