计算脉冲在非线性耦合器中演化的Matlab 程序 Hv>C#U c;,jb % This Matlab script file solves the coupled nonlinear Schrodinger equations of
%eoO3"// % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
opz.kP[e, % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
urT!?*g, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
MKd{ y~' (h0i2>K %fid=fopen('e21.dat','w');
xUYUO yV N = 128; % Number of Fourier modes (Time domain sampling points)
f-5vE9G3y7 M1 =3000; % Total number of space steps
*Z7W'- J =100; % Steps between output of space
H<dOh5MFh T =10; % length of time windows:T*T0
cdL$T6y T0=0.1; % input pulse width
u1y c MN1=0; % initial value for the space output location
+
M2|-C dt = T/N; % time step
XUU l*5 ^ n = [-N/2:1:N/2-1]'; % Index
I71kFtvcy* t = n.*dt;
MVV9[f u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
#vhxW=L`= u20=u10.*0.0; % input to waveguide 2
mA5x ke_) u1=u10; u2=u20;
qyMR0ai- U1 = u1;
umXa U2 = u2; % Compute initial condition; save it in U
_20nOg `o ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
|F3 6 ^ w=2*pi*n./T;
z BWn*A[4 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
D_ ,}lsrb L=4; % length of evoluation to compare with S. Trillo's paper
gIS<"smOo dz=L/M1; % space step, make sure nonlinear<0.05
7O {c>@\
for m1 = 1:1:M1 % Start space evolution
n!mtMPH$ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
>Pv#)qtm u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
bet?5Dk ca1 = fftshift(fft(u1)); % Take Fourier transform
4oLrCQZ\ ca2 = fftshift(fft(u2));
C=}YKsi|R| c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
3O<:eS~ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
k<uC [)_ u2 = ifft(fftshift(c2)); % Return to physical space
x$9UHEb kM u1 = ifft(fftshift(c1));
xW*L^97 ; if rem(m1,J) == 0 % Save output every J steps.
'+B cPB?E U1 = [U1 u1]; % put solutions in U array
W:{1R&$l U2=[U2 u2];
XW6Ewrm=vT MN1=[MN1 m1];
^B2>lx \n z1=dz*MN1'; % output location
.63:G< end
nG&= $7x^ end
,Z*?"d hg=abs(U1').*abs(U1'); % for data write to excel
h^ ex? ha=[z1 hg]; % for data write to excel
^- T!(P: t1=[0 t'];
M xUj7ae hh=[t1' ha']; % for data write to excel file
Ji SJi? %dlmwrite('aa',hh,'\t'); % save data in the excel format
,qJ/Jt$A figure(1)
O3#4B!J$E waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
I,D24W4l figure(2)
w> `3{MTQ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
A?8 f 6 >6 [{\uPK 非线性超快脉冲耦合的数值方法的Matlab程序 ]ERPWW;^ O-6848iCX 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
P6* IR| Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]V J$;v'{[ 17 [7)M88 9mkt.>$ H2 7_T]\ % This Matlab script file solves the nonlinear Schrodinger equations
xuQ$67F`;z % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
:.6kXX'~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
6s BS;+C % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
h 9c54Ux xN 0n0 C=1;
a6"Pe07t M1=120, % integer for amplitude
k'Fc:T8:~5 M3=5000; % integer for length of coupler
hZ-No N = 512; % Number of Fourier modes (Time domain sampling points)
|XOD~Plo^ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
:
'M$:ZJ T =40; % length of time:T*T0.
0V
,R|Ln dt = T/N; % time step
E[HX bj" n = [-N/2:1:N/2-1]'; % Index
0XFJ/ t = n.*dt;
Epsc2TuH7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
fb[f > 1| w=2*pi*n./T;
Z8+{ - g1=-i*ww./2;
D %kY g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
W 4Nbl g3=-i*ww./2;
61>@-55k9 P1=0;
IQxY]0\uf6 P2=0;
ECqcK~h#E P3=1;
-qz; P=0;
+CtsD9PA for m1=1:M1
" jly[M}C p=0.032*m1; %input amplitude
L31B:t^ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
\ Fj$^I>C s1=s10;
vs;T} ' O s20=0.*s10; %input in waveguide 2
K?:rrd=7q s30=0.*s10; %input in waveguide 3
~|kre:j9 s2=s20;
!q;EC`i# s3=s30;
4Mi~eL%D
( p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
2,?4'0Z @R %energy in waveguide 1
v+A$CGH96 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
i]!C H2\ %energy in waveguide 2
2[: *0 DV# p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
(( F[]<? %energy in waveguide 3
IT]D ; for m3 = 1:1:M3 % Start space evolution
)?RR1 P-ID s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
1\t}pGSOeh s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
9{\e E]0 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
2i`N 26On sca1 = fftshift(fft(s1)); % Take Fourier transform
4^(u6tX5|+ sca2 = fftshift(fft(s2));
pJ-/"Q|:i sca3 = fftshift(fft(s3));
K*jV=lG sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
O?|opD sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
>7.
$=y8b sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
J(F]?H s3 = ifft(fftshift(sc3));
Y}%=:Yt s2 = ifft(fftshift(sc2)); % Return to physical space
cN_e0;*Ua s1 = ifft(fftshift(sc1));
k]W ~_ end
91|=D
\8aE p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
#!0le :_ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
2
>G"A p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
|uVhfD=NG P1=[P1 p1/p10];
n.P$7%G`2 P2=[P2 p2/p10];
I_N(e|s\U P3=[P3 p3/p10];
[4B.;MS( P=[P p*p];
Wo&10S w end
N)G.^9 figure(1)
}
<; y, 4f plot(P,P1, P,P2, P,P3);
v[WbQ5AND Ex^| [iV 转自：
http://blog.163.com/opto_wang/
