计算脉冲在非线性耦合器中演化的Matlab 程序 Jg| XH
L) ?.;c $' % This Matlab script file solves the coupled nonlinear Schrodinger equations of
)P |),S,;Z % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
oM`0y@QCf % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Zz T9j~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
p= } Nn( @ J`"[% U %fid=fopen('e21.dat','w');
,nDaqQ-C!! N = 128; % Number of Fourier modes (Time domain sampling points)
#4 pB@_ M1 =3000; % Total number of space steps
TbW38\>.R J =100; % Steps between output of space
>I&5j/&}+ T =10; % length of time windows:T*T0
AkQ ~k0i}b T0=0.1; % input pulse width
J nM["Q=` MN1=0; % initial value for the space output location
V33T+P~j dt = T/N; % time step
j# q-^h3H n = [-N/2:1:N/2-1]'; % Index
0Z{ZO*rK t = n.*dt;
f=K]XTw~ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
ut7 zVp<" u20=u10.*0.0; % input to waveguide 2
^3L0w}# u1=u10; u2=u20;
v,>Dbx n U1 = u1;
4@#
`t5H U2 = u2; % Compute initial condition; save it in U
j+
0I-p ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
o:Sa,
!DK w=2*pi*n./T;
#'9HU2 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
-C?ZB}` L=4; % length of evoluation to compare with S. Trillo's paper
?+}_1x` dz=L/M1; % space step, make sure nonlinear<0.05
Y glmX"fLf for m1 = 1:1:M1 % Start space evolution
Qjv}$`M u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
I(BQ34 q u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
]|P iF+ ca1 = fftshift(fft(u1)); % Take Fourier transform
l)l^[2 ca2 = fftshift(fft(u2));
ExL0?FemWV c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Cd}<a?m, c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
'kO!^6=4M u2 = ifft(fftshift(c2)); % Return to physical space
&Ys<@M7E: u1 = ifft(fftshift(c1));
IKil r' if rem(m1,J) == 0 % Save output every J steps.
*mvlb
(' & U1 = [U1 u1]; % put solutions in U array
x)O!["'" U2=[U2 u2];
V{3x!+q MN1=[MN1 m1];
|imM# wF z1=dz*MN1'; % output location
z/ @slT end
6fEqqUeV end
1ztG;\ hg=abs(U1').*abs(U1'); % for data write to excel
>V8-i` ha=[z1 hg]; % for data write to excel
K} X&AJ5A t1=[0 t'];
\\B(r hh=[t1' ha']; % for data write to excel file
)W
_v:?A9 %dlmwrite('aa',hh,'\t'); % save data in the excel format
Iom'Y@x figure(1)
+E(L \ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
<&g,Nc'5C figure(2)
EaY?aAuS: waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
>$/>#e~ Xr GglBIV 非线性超快脉冲耦合的数值方法的Matlab程序 8 \A#CQ5b `Cynj+PCe 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
@>2i+)=E5 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
!Pfr , a L2i_X@/ 4yr'W8X_ w ;:*P % This Matlab script file solves the nonlinear Schrodinger equations
,A e6/D$h/ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
u[=r,^YQ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
YWO)HsjP % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
">, |V-H A&Usddcp C=1;
jZkcBIK2 M1=120, % integer for amplitude
b& N'C9/8 M3=5000; % integer for length of coupler
>rmqBDKaQ N = 512; % Number of Fourier modes (Time domain sampling points)
>7T'OC dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
w4{<n /" T =40; % length of time:T*T0.
x}I+Iggi dt = T/N; % time step
~1AgD-:Jz n = [-N/2:1:N/2-1]'; % Index
\aUC(K~o\; t = n.*dt;
By",rD- r ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
W UXx;9 > w=2*pi*n./T;
:g=qz~2Xk g1=-i*ww./2;
.|>3k'< l g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
goOCu g3=-i*ww./2;
Y0dEH^I P1=0;
cj|80$cSA P2=0;
Ma']?Rb` P3=1;
g63(E,;;J P=0;
s.QwSbw-g for m1=1:M1
@&3EJ1 p=0.032*m1; %input amplitude
i0kak`x0 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
`*cxH.. s1=s10;
b;W3 j s20=0.*s10; %input in waveguide 2
CMG&7(MR s30=0.*s10; %input in waveguide 3
H0gbSd+ s2=s20;
t[;LD_ s3=s30;
JWhdMU p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
*/^q{PsN %energy in waveguide 1
;yLu R p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
p\tm:QWD; %energy in waveguide 2
*-=(Q` 3 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Y^;ovH~ ve %energy in waveguide 3
y@: h4u"3 for m3 = 1:1:M3 % Start space evolution
/ h H s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
F Q7T'G![ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
SpLzm A s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
8f)?{AX0 sca1 = fftshift(fft(s1)); % Take Fourier transform
z2_*%S@ sca2 = fftshift(fft(s2));
=_ ./~ sca3 = fftshift(fft(s3));
HU8900k+ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
~Z?TFg
sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
L:pYn_ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
r?lf($ D * s3 = ifft(fftshift(sc3));
2~1SQ.Q<RY s2 = ifft(fftshift(sc2)); % Return to physical space
JPc+rfF s1 = ifft(fftshift(sc1));
0y" $MC v end
FxtQ Xu-g p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
r6MMCJ|G p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
G%AbC" p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
9~5uaP$S P1=[P1 p1/p10];
RXpw! P2=[P2 p2/p10];
P g0x/X{t P3=[P3 p3/p10];
9N%We|L,c P=[P p*p];
D9 C aFu end
Vod\a 5c figure(1)
hOu3 bA plot(P,P1, P,P2, P,P3);
.9 on@S uk< 4+x,2) 转自：
http://blog.163.com/opto_wang/
