计算脉冲在非线性耦合器中演化的Matlab 程序 F%.UpV, s< Fp17 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
/x4L,UJ= P % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
.gM6m8l9wp % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
b cT'!: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@}Q!K* -w f>N: %fid=fopen('e21.dat','w');
m4yWhUi(o N = 128; % Number of Fourier modes (Time domain sampling points)
9 Q *:II M1 =3000; % Total number of space steps
i52JY&N J =100; % Steps between output of space
>UV}^OO T =10; % length of time windows:T*T0
4?bvJJuf) T0=0.1; % input pulse width
>
6=3y4tP MN1=0; % initial value for the space output location
Ik G;j+= dt = T/N; % time step
Az-!X!O*f n = [-N/2:1:N/2-1]'; % Index
;/kmV~KG t = n.*dt;
i g
. u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+1@'2w{ u20=u10.*0.0; % input to waveguide 2
oX'@,(6) u1=u10; u2=u20;
+zXcTT[V U1 = u1;
;}M&fXFp"| U2 = u2; % Compute initial condition; save it in U
LOr( HgyC ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
B79~-,Yh w=2*pi*n./T;
<_]W 1V:0 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
~N7;.
3 7 L=4; % length of evoluation to compare with S. Trillo's paper
t*dq*( 3"c dz=L/M1; % space step, make sure nonlinear<0.05
zbGZ\ pz for m1 = 1:1:M1 % Start space evolution
o wI:Qs_/4 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
V-E 77u6{0 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
-F 9 xPw ca1 = fftshift(fft(u1)); % Take Fourier transform
E25w ^x2 ca2 = fftshift(fft(u2));
'Sesh'2
/ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
C\OZs%]At c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
{+[ Ex2b$ u2 = ifft(fftshift(c2)); % Return to physical space
yk(r R u1 = ifft(fftshift(c1));
V DZOJM)( if rem(m1,J) == 0 % Save output every J steps.
fL("MDt U1 = [U1 u1]; % put solutions in U array
|n^rI\ p% U2=[U2 u2];
3g5r}Ug MN1=[MN1 m1];
ruyQ}b:zS z1=dz*MN1'; % output location
n, LM"N:
end
`M(st%@n end
N FC/4 hg=abs(U1').*abs(U1'); % for data write to excel
1 o_ 6WU ha=[z1 hg]; % for data write to excel
u^#e 7u t1=[0 t'];
q~Al[`K hh=[t1' ha']; % for data write to excel file
Le{.B@2-" %dlmwrite('aa',hh,'\t'); % save data in the excel format
p L^3*B.Nr figure(1)
N2 Ysi$ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
q*C-DiV figure(2)
3N|6?'m waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
*-uzsq.W y~wr4Q= 非线性超快脉冲耦合的数值方法的Matlab程序 |`s:&<W+kp shP }T[< 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。
7+IRI|d 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
-WR<tkK 2-W y@\ ^ zS ;/% 6j+X@|2^ % This Matlab script file solves the nonlinear Schrodinger equations
zSu,S4m_; % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
? STO#<a % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
lV$#>2Hh5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
{ E7STLQ_% F%af05L[ C=1;
x8~*+ j M1=120, % integer for amplitude
q_mxZM
-> M3=5000; % integer for length of coupler
0&b;!N!vJ N = 512; % Number of Fourier modes (Time domain sampling points)
KmM:V2@A$ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
TIR Is1 T =40; % length of time:T*T0.
G;/l[mv h, dt = T/N; % time step
'5~l{3Lw
n = [-N/2:1:N/2-1]'; % Index
w`3.wALb t = n.*dt;
N93R (x)% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
UI%4d3 w=2*pi*n./T;
4\g[ & g1=-i*ww./2;
]mUt[Yy:z g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
e$JCak= g3=-i*ww./2;
C5$?Y8B3 P1=0;
6Z2|j~ P2=0;
5zkj ;?s P3=1;
xU}J6 Tv P=0;
(/!@
-]1 for m1=1:M1
qDz[=6BF p=0.032*m1; %input amplitude
Dl AwB1Ak s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
o^//|]H3Y s1=s10;
j]]5&u/l s20=0.*s10; %input in waveguide 2
o)x&| 0_ s30=0.*s10; %input in waveguide 3
>l/pwb@ s2=s20;
J #t8x L s3=s30;
$J,$_O6 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
n%i L+I %energy in waveguide 1
"r3h+(5 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
~l {Qz0& %energy in waveguide 2
i~R+ g3oi p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
&^ uaoB0 %energy in waveguide 3
<F"G~.^ *s for m3 = 1:1:M3 % Start space evolution
HDKY7Yr s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
LP'q$iB! s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Wm5[+z|2?9 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
MpvG F7H sca1 = fftshift(fft(s1)); % Take Fourier transform
`P-d. M6Oa sca2 = fftshift(fft(s2));
|$ZS26aYw} sca3 = fftshift(fft(s3));
i[{*(Y$L sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
UQ7La 7" sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
pGy k61 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
VGu(HB8n# s3 = ifft(fftshift(sc3));
]KXyi;n2 s2 = ifft(fftshift(sc2)); % Return to physical space
DIWyv- s1 = ifft(fftshift(sc1));
pF8:?p['z end
}J9 2 TV p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
4mEJu p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
4;gw&sFF p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
es\
qnq P1=[P1 p1/p10];
bu rSb:JF P2=[P2 p2/p10];
PxvxZJf$@ P3=[P3 p3/p10];
8m
`Y P=[P p*p];
pS7 y3(_ end
Gl45HyY_ figure(1)
0Q8iX) plot(P,P1, P,P2, P,P3);
LTH, a?lD XFl&(I4tB 转自：
http://blog.163.com/opto_wang/
