计算脉冲在非线性耦合器中演化的Matlab 程序 9`"o,wGX3 oD$8( % This Matlab script file solves the coupled nonlinear Schrodinger equations of
IL:d`Kbqf % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
thoAEG 80 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
[-Zp[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
>&@hm4 +GgJFBl %fid=fopen('e21.dat','w');
)'<B\P/ N = 128; % Number of Fourier modes (Time domain sampling points)
wq[\ Fb ` M1 =3000; % Total number of space steps
)KZ1Z$< J =100; % Steps between output of space
` y &d T =10; % length of time windows:T*T0
R^ }}-Dv r T0=0.1; % input pulse width
\2?p MN1=0; % initial value for the space output location
M18H1e@Al dt = T/N; % time step
H-?wEMi)*u n = [-N/2:1:N/2-1]'; % Index
D;f[7Cac t = n.*dt;
=h?Q.vad u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+N161vo7 u20=u10.*0.0; % input to waveguide 2
c0J=gZiP u1=u10; u2=u20;
$jt UQ1 U1 = u1;
a,o>E4#c U2 = u2; % Compute initial condition; save it in U
0jS"PH?[ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
3Y\7+975m w=2*pi*n./T;
q|E0Y g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
8+m[ %5lu L=4; % length of evoluation to compare with S. Trillo's paper
'~dE0ohWb dz=L/M1; % space step, make sure nonlinear<0.05
~c
e?xr| for m1 = 1:1:M1 % Start space evolution
R&z) u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
/UJ@ e u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
< OKzb3e ca1 = fftshift(fft(u1)); % Take Fourier transform
PGT*4r21 ca2 = fftshift(fft(u2));
G1; .\ i c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
b&LfL$
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
@ljvTgZ(X u2 = ifft(fftshift(c2)); % Return to physical space
R 3MbTg u1 = ifft(fftshift(c1));
-Cb<T"7 if rem(m1,J) == 0 % Save output every J steps.
!J34yro+s U1 = [U1 u1]; % put solutions in U array
*. H1m{V U2=[U2 u2];
^*;{Uj+O~Y MN1=[MN1 m1];
5K1WfdBX7) z1=dz*MN1'; % output location
4dDDi,)U end
]!>ThBMa end
ZE#f{qF( hg=abs(U1').*abs(U1'); % for data write to excel
S.;>:Dd[K ha=[z1 hg]; % for data write to excel
x\=2D<@az t1=[0 t'];
Sz\"*W;> hh=[t1' ha']; % for data write to excel file
T [w]w
%dlmwrite('aa',hh,'\t'); % save data in the excel format
+k!Y]_&(:f figure(1)
j8@ Eqh waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
uV]4C^k;`[ figure(2)
{VWUK`3 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
PZ/ g D ,&S ^R yc 非线性超快脉冲耦合的数值方法的Matlab程序 Tc t[0B !/4f/g4Ze 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。
#1M Emt 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
^*7 ~ Wxk5 1vcI`8%S+u M Cam c X-oHQu5 % This Matlab script file solves the nonlinear Schrodinger equations
{(}Mu R % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
1a# oJ U % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
{~*aXu 3 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[\o+I:,}wi 1'5I]D
ec C=1;
{}?;|&_ M1=120, % integer for amplitude
^}XKhn.S' M3=5000; % integer for length of coupler
8ALvP}H N = 512; % Number of Fourier modes (Time domain sampling points)
!B==cNq dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
E p % 5wR T =40; % length of time:T*T0.
gf]biE"k dt = T/N; % time step
(>qX> n = [-N/2:1:N/2-1]'; % Index
I*e8 5wef t = n.*dt;
@l9 qH1
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
k^q}F%UV w=2*pi*n./T;
Jji~MiMn g1=-i*ww./2;
_(J 7^rN g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
; 6W lu3I g3=-i*ww./2;
0_Hdj K P1=0;
i2{xW`AcUh P2=0;
wj>mk P3=1;
$|v_ pjUu] P=0;
R9SJ ;Ts E for m1=1:M1
Ti/t\'6 p=0.032*m1; %input amplitude
9Vx2VjK2' s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
b _fI1 f| s1=s10;
73/kyu-0% s20=0.*s10; %input in waveguide 2
D_GIj$%N[ s30=0.*s10; %input in waveguide 3
qvz2u]IOw s2=s20;
7%Zl^c>q s3=s30;
q!#e2Dx p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
kBY 54pl %energy in waveguide 1
ScrE tN p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
bWv4'Y!p %energy in waveguide 2
iw<#V&([ J p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
sDnHd9v<?t %energy in waveguide 3
mj0{Nd for m3 = 1:1:M3 % Start space evolution
v* %#Fp,g8 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
%dTkw+J s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
J GP LVw s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Gx ?p,Fj sca1 = fftshift(fft(s1)); % Take Fourier transform
D%v4B`4ua' sca2 = fftshift(fft(s2));
]=p@1 sca3 = fftshift(fft(s3));
R}F0_. sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
` bd sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
$ WA Fr sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
.$+]N[-=
s3 = ifft(fftshift(sc3));
OKfJ s2 = ifft(fftshift(sc2)); % Return to physical space
Ec| Gom? s1 = ifft(fftshift(sc1));
u-Pa:wm0- end
orn9;|8q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
<,d .`0:y p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
ud K)F$7 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
2wE?O^J P1=[P1 p1/p10];
((A]FOIbO P2=[P2 p2/p10];
SU; PmG4 P3=[P3 p3/p10];
]Q=D'1 MM P=[P p*p];
(OT /o&cQ end
$X_JUzb figure(1)
<=8R EA? plot(P,P1, P,P2, P,P3);
Zrp`91&I zyTP|SXk 转自：
http://blog.163.com/opto_wang/
