计算脉冲在非线性耦合器中演化的Matlab 程序 c3|/8 0 r ilg % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Ku;8Mx{ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
<'92\ O % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
c7/fQc)h4d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
j WerX -$ xXNL UP %fid=fopen('e21.dat','w');
T`r\y l} N = 128; % Number of Fourier modes (Time domain sampling points)
#brV{dHV, M1 =3000; % Total number of space steps
zXT[}J VV J =100; % Steps between output of space
.6y(ox|LL T =10; % length of time windows:T*T0
nISfRX U; T0=0.1; % input pulse width
d;LBV<Z? MN1=0; % initial value for the space output location
o>ZlA3tv dt = T/N; % time step
O ojQG
n = [-N/2:1:N/2-1]'; % Index
o3xfif t = n.*dt;
QTuj v<| u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
F(+dX4$ u20=u10.*0.0; % input to waveguide 2
Tp
fC u1=u10; u2=u20;
MDh^ic5 U1 = u1;
XjV,wsZ= U2 = u2; % Compute initial condition; save it in U
w @ \quy: ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
JnBg;D|)@ w=2*pi*n./T;
O^I%Xk g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
* 57y.](w L=4; % length of evoluation to compare with S. Trillo's paper
x2 m
A dz=L/M1; % space step, make sure nonlinear<0.05
8CN 0Q&| for m1 = 1:1:M1 % Start space evolution
7d'gG[Z^^ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
1
Ll<^P u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
a>/j W-? ca1 = fftshift(fft(u1)); % Take Fourier transform
parc\]M ca2 = fftshift(fft(u2));
K)8N 8Js( c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
F` gQ[ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
oB] u2 = ifft(fftshift(c2)); % Return to physical space
_9Y7. 5 u1 = ifft(fftshift(c1));
a Bx8wl*Vm if rem(m1,J) == 0 % Save output every J steps.
kpt 0spp U1 = [U1 u1]; % put solutions in U array
~pj/_@S@x U2=[U2 u2];
,T3_*:0hk! MN1=[MN1 m1];
K h;jiK ! z1=dz*MN1'; % output location
6=xbi{m$ end
}Qo:;&"3 end
iv]*HE hg=abs(U1').*abs(U1'); % for data write to excel
En]+mIEo ha=[z1 hg]; % for data write to excel
YQk<1./}I t1=[0 t'];
0(~,U!g[= hh=[t1' ha']; % for data write to excel file
2V 9vS %dlmwrite('aa',hh,'\t'); % save data in the excel format
t lz)V1L figure(1)
tZn=[X~Vw@ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
%knPeo& figure(2)
K,\Bj/V( waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
><Z`) }f G~;h D-D~. 非线性超快脉冲耦合的数值方法的Matlab程序 Sxw%6Va]p 4,pS C 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。
yxU??#v|g 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
"m m|0PUJ 'aoHNZfxw ( e$/@3* G[=8Ko0U+n % This Matlab script file solves the nonlinear Schrodinger equations
d5ivtK? % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
umD[4aP~; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
,/ P)c*at5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
|2eF~tJqc ssy+x;<x, C=1;
C3
m#v[+ M1=120, % integer for amplitude
.`ppp!:a4 M3=5000; % integer for length of coupler
5%E.UjC N = 512; % Number of Fourier modes (Time domain sampling points)
`*n K@: dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
p&%M=SzN T =40; % length of time:T*T0.
w/(hEF ' dt = T/N; % time step
Py)'%e n = [-N/2:1:N/2-1]'; % Index
+ ^9;<>P t = n.*dt;
=_/,C ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
4&c7^ 4w~ w=2*pi*n./T;
FOU^Wcop% g1=-i*ww./2;
=5-| H;da g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
FGP~^Dr/ g3=-i*ww./2;
V\V:uo(C P1=0;
!hJ%
:^ xL P2=0;
3)J0f+M>dv P3=1;
;|e6Qc9 P=0;
2-3| 0<` for m1=1:M1
L8FLHT+R- p=0.032*m1; %input amplitude
*qLOr6 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
p<@ 0b s1=s10;
?OU+)kgzh s20=0.*s10; %input in waveguide 2
<A,G:&d~ s30=0.*s10; %input in waveguide 3
W~1MeAI s2=s20;
AF
qut s3=s30;
Ti@X< C p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
}Dig'vpMx %energy in waveguide 1
G([!(8&2Y p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
*WQ}ucE^# %energy in waveguide 2
*1L;%u| [ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
om"q[Tudc %energy in waveguide 3
I<I?ks for m3 = 1:1:M3 % Start space evolution
q?=eD^] s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
b (,X3x* s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
o .}?K>5 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
AID}NQ Qj_ sca1 = fftshift(fft(s1)); % Take Fourier transform
?`hk0q X3 sca2 = fftshift(fft(s2));
qR~s& SC# sca3 = fftshift(fft(s3));
K%: : sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
" Iy @PR?> sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
$h Is ab_ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
}@pe `AF^ s3 = ifft(fftshift(sc3));
G B+U>nf s2 = ifft(fftshift(sc2)); % Return to physical space
XB &-k<C s1 = ifft(fftshift(sc1));
"-N)TIzLX end
lrSo@JQ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
S ? }@2[ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Uv6#d":f; p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
")U`W gx P1=[P1 p1/p10];
`j59MSuK P2=[P2 p2/p10];
\jdp L1 P3=[P3 p3/p10];
wR;_x x P=[P p*p];
Kt%` ]Wp end
IkSzjXE{ figure(1)
;X u&['
plot(P,P1, P,P2, P,P3);
"R$ee^ B
0%kq7>g 转自：
http://blog.163.com/opto_wang/
