计算脉冲在非线性耦合器中演化的Matlab 程序 MAYb.>X#> b@CjnAZ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
d'96$e o~ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
[QxP9EC % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'etA1]<N @.7/lRr@bp %fid=fopen('e21.dat','w');
) >1}I_1j) N = 128; % Number of Fourier modes (Time domain sampling points)
)IcSdS0@M M1 =3000; % Total number of space steps
QwX81*n x J =100; % Steps between output of space
D`@a*YIq T =10; % length of time windows:T*T0
d'W2I*Zc< T0=0.1; % input pulse width
_5rK uL MN1=0; % initial value for the space output location
!-`L1D_hy dt = T/N; % time step
&j:e<{@ n = [-N/2:1:N/2-1]'; % Index
MZ}0.KmaZ t = n.*dt;
//c 6vG u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
ntH`\ )xi u20=u10.*0.0; % input to waveguide 2
l PZ># u1=u10; u2=u20;
;\w3IAa|V U1 = u1;
CaZc{ U2 = u2; % Compute initial condition; save it in U
dI\_ I] ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
kqKT>xo4EZ w=2*pi*n./T;
2vpQ"e- A g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
/V*SI!C<f L=4; % length of evoluation to compare with S. Trillo's paper
>fYcr #i0[ dz=L/M1; % space step, make sure nonlinear<0.05
m+X HFU for m1 = 1:1:M1 % Start space evolution
?w(hPUd!2 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
\C$e+qb~{ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
M ]047W ca1 = fftshift(fft(u1)); % Take Fourier transform
lPR^~&/ ca2 = fftshift(fft(u2));
Xb:*
KeZq c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
[RKk-8I c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
pG "wQ u2 = ifft(fftshift(c2)); % Return to physical space
.hH_1Mo8 u1 = ifft(fftshift(c1));
MDytA0M if rem(m1,J) == 0 % Save output every J steps.
XB!qPh . U1 = [U1 u1]; % put solutions in U array
c/+6M U2=[U2 u2];
DU6j0lz MN1=[MN1 m1];
bJ n&Y z1=dz*MN1'; % output location
9@CRL= end
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end
f~W+Rt7o hg=abs(U1').*abs(U1'); % for data write to excel
SWw!s &lP& ha=[z1 hg]; % for data write to excel
5 <k)tF% t1=[0 t'];
=-Hhm($n hh=[t1' ha']; % for data write to excel file
C5^WJx[ %dlmwrite('aa',hh,'\t'); % save data in the excel format
L|Wrd T D; figure(1)
2z {B waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
?u#s ?$ Y? figure(2)
\bT0\
(Js\ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
2 &*# k -6J <{1V 非线性超快脉冲耦合的数值方法的Matlab程序 jywS<9c@ w#)u+^ - 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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uiC %T 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
E+i(p+=4 3ux7^ au l F64g &iWTf K7 % This Matlab script file solves the nonlinear Schrodinger equations
`^/8dIya % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
.'o=J`| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
!4Zy$6 9R % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-
c>Vw&1 +pgHCzwJE C=1;
h._eP.W ` M1=120, % integer for amplitude
2p9^ = M3=5000; % integer for length of coupler
'AK '(cZ N = 512; % Number of Fourier modes (Time domain sampling points)
Gjeb)Y6N dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
9IXy96 ]]6 T =40; % length of time:T*T0.
~ zfF*A dt = T/N; % time step
A-L1vu; n = [-N/2:1:N/2-1]'; % Index
0p[k7W u t = n.*dt;
{HY3E}YJL ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
]h1.1@ >xc w=2*pi*n./T;
t0fgG/f' g1=-i*ww./2;
Q\s+w){f% g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
c`x4."m g3=-i*ww./2;
? ch?q~e) P1=0;
dH5*% P2=0;
vTFG*\Cq P3=1;
?@PSD\
P=0;
cvy
5|;- u for m1=1:M1
Y [)mHs2 p=0.032*m1; %input amplitude
rAtCG1Vr s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
yCR8 c,'8 s1=s10;
{,uSDI Oj$ s20=0.*s10; %input in waveguide 2
Y$XzZ> VW s30=0.*s10; %input in waveguide 3
9=$ p V== s2=s20;
5cf?u3r!qJ s3=s30;
[xY-=-T*4 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
|WS@q' %energy in waveguide 1
Q?T+^J p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
[Y!HQ9^LEp %energy in waveguide 2
l"JM%LV p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
e.L&A | %energy in waveguide 3
b]?5r)GK for m3 = 1:1:M3 % Start space evolution
{hN\=_6*EW s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
/"="y'Wx s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
N`7OJ)l s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
zQ:nL*X'Z" sca1 = fftshift(fft(s1)); % Take Fourier transform
+}at#%1@ sca2 = fftshift(fft(s2));
lIEZ=CEmY sca3 = fftshift(fft(s3));
jFg19C{=X sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
z[ ;n2o|s sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
}~&0<8m sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
o =94H7@ s3 = ifft(fftshift(sc3));
Has}oe[ s2 = ifft(fftshift(sc2)); % Return to physical space
~]no7 O4 s1 = ifft(fftshift(sc1));
837:;<T end
N:Q.6_%^ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
2 {WZ?H93a p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
!XjZt p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
NG3:= P1=[P1 p1/p10];
m Qx1co P2=[P2 p2/p10];
yqK_|7I+ P3=[P3 p3/p10];
&S *{a P=[P p*p];
cM9> V2:P end
U) xeta+ figure(1)
< ~CY?
plot(P,P1, P,P2, P,P3);
Yur}<>`( ^F?B_' 转自：
http://blog.163.com/opto_wang/
