计算脉冲在非线性耦合器中演化的Matlab 程序 873 bg|^hs B~}BDnu 6 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
\2+ngq) % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
rPy,PQG2w % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Ju#j%! % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
wg[
+NWJ r&xIVFPI[ %fid=fopen('e21.dat','w');
GmNC w5F N = 128; % Number of Fourier modes (Time domain sampling points)
O9N!SQs80 M1 =3000; % Total number of space steps
'eBD/w5U J =100; % Steps between output of space
\y271}' T =10; % length of time windows:T*T0
.s4vJKK0 T0=0.1; % input pulse width
L44|/~ MN1=0; % initial value for the space output location
}. D18bE( dt = T/N; % time step
3c#^@Bj(-e n = [-N/2:1:N/2-1]'; % Index
[@/p 8I t = n.*dt;
$yU}56(z~ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
;g8v7 >p u20=u10.*0.0; % input to waveguide 2
*\#<2 QAe u1=u10; u2=u20;
[L-wAk:Fb U1 = u1;
^7>~y( U2 = u2; % Compute initial condition; save it in U
Pi1LOCq ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
bn|HvLQ"1 w=2*pi*n./T;
M*n94L=Sg& g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
OU` !c[O L=4; % length of evoluation to compare with S. Trillo's paper
(D[~Z! dz=L/M1; % space step, make sure nonlinear<0.05
,#BD/dF for m1 = 1:1:M1 % Start space evolution
]6^S: K_" u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
2?LPr u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
E3p$^['vx ca1 = fftshift(fft(u1)); % Take Fourier transform
1O,5bi>t7 ca2 = fftshift(fft(u2));
bHm/Z Zx c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
l #C<b Dw c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
9ec? L u2 = ifft(fftshift(c2)); % Return to physical space
>q?{'#i
/ u1 = ifft(fftshift(c1));
h3E}Sa(MQ: if rem(m1,J) == 0 % Save output every J steps.
;~r- P$kCY U1 = [U1 u1]; % put solutions in U array
}s?w-u+(c6 U2=[U2 u2];
VDv.N@ ) 7 MN1=[MN1 m1];
\c{sG\ > z1=dz*MN1'; % output location
O0r vr$. end
_~tF2`,Y_p end
kz}Bc
F hg=abs(U1').*abs(U1'); % for data write to excel
X! 6dg.n5 ha=[z1 hg]; % for data write to excel
}LS.bQKqi, t1=[0 t'];
-]}#Z:& hh=[t1' ha']; % for data write to excel file
P//nYPyzg %dlmwrite('aa',hh,'\t'); % save data in the excel format
%OHWGac"i figure(1)
#X``^
waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
L;g2ZoqIr0 figure(2)
2N |iOog waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
4Vv E(f z^*g 2J, 非线性超快脉冲耦合的数值方法的Matlab程序 R-W.$-rF A>Qu`%g* 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
9MJ:]F5+ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*1-0s*T ^o>WCU = mHW%^R= F5H*z\/={ % This Matlab script file solves the nonlinear Schrodinger equations
T>*G1 -J# % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
5cM%PYU4:v % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
GNwFB)?j % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
f6SXXkO+ K5bR7f: C=1;
^wSGrV' M1=120, % integer for amplitude
^; U }HAY M3=5000; % integer for length of coupler
!] 7b31$M_ N = 512; % Number of Fourier modes (Time domain sampling points)
s! D?% dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
z*b|N45O T =40; % length of time:T*T0.
-;8 a* F dt = T/N; % time step
8kd):gZKZ n = [-N/2:1:N/2-1]'; % Index
c*axw%Us t = n.*dt;
VR_/Vh ]@ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`tT7&*Os w=2*pi*n./T;
>(YH@Z&; g1=-i*ww./2;
0S+$l g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
mW[w4J+7P g3=-i*ww./2;
T^ +K`U P1=0;
gyy}-^`F P2=0;
%< ;u
JP K P3=1;
bs%
RWwn P=0;
WFFd3 TN%< for m1=1:M1
.MDSP/s p=0.032*m1; %input amplitude
fpZHE=} r s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
\% }]wf} s1=s10;
=D?HL? s20=0.*s10; %input in waveguide 2
WHjJ R s30=0.*s10; %input in waveguide 3
e50xcf1u s2=s20;
`z/ p,. u s3=s30;
zcOm"- E- p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
T8*;?j*@ %energy in waveguide 1
(?7}\B\ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
JAMV@ %energy in waveguide 2
wUg=j nY p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Z 6WNMQ1: %energy in waveguide 3
HpeU'0u0VK for m3 = 1:1:M3 % Start space evolution
ox.kL s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
-!T24/l s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
H8@z/ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
>x~Qa@s; sca1 = fftshift(fft(s1)); % Take Fourier transform
/-^{$$eu sca2 = fftshift(fft(s2));
f/.f08 sca3 = fftshift(fft(s3));
DtS7)/<T
sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
4}0YLwgJ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
cuf]-C1_ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
-
?
i s3 = ifft(fftshift(sc3));
S ;#7B?j s2 = ifft(fftshift(sc2)); % Return to physical space
U T 7'- s1 = ifft(fftshift(sc1));
e !w{ap8u end
vkYiO]y p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
l8 %BRG p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Lcy6G%A p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
4`V&Yqwl P1=[P1 p1/p10];
J*%IvRg
P2=[P2 p2/p10];
Gp?pSI,b.t P3=[P3 p3/p10];
h y\iot P=[P p*p];
M3d%$q)<rW end
u
Vv %k5 figure(1)
NUh%\{ plot(P,P1, P,P2, P,P3);
w:1U wgcPC u?z,Vs" 转自：
http://blog.163.com/opto_wang/
