计算脉冲在非线性耦合器中演化的Matlab 程序 yHS=8! @ I{v % This Matlab script file solves the coupled nonlinear Schrodinger equations of
i|zs
Li/ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
|TCHPKN % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
*`
}Rt % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
.<Y7,9;YEF {Vy2uow0 %fid=fopen('e21.dat','w');
Gt9(@USK N = 128; % Number of Fourier modes (Time domain sampling points)
YKF5|;} M1 =3000; % Total number of space steps
!? t#QD o J =100; % Steps between output of space
bDh, r!I T =10; % length of time windows:T*T0
B J,U,! T0=0.1; % input pulse width
wvH=4TT=w" MN1=0; % initial value for the space output location
e !_+TyI dt = T/N; % time step
B&J;yla6`d n = [-N/2:1:N/2-1]'; % Index
G$b*N4yR t = n.*dt;
@f<q&K%FJ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
^HpUbZpat) u20=u10.*0.0; % input to waveguide 2
{9(#X]' u1=u10; u2=u20;
pwq a/Yi U1 = u1;
@=@7Uu- U2 = u2; % Compute initial condition; save it in U
<5oG[1j ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
"AH1)skB: w=2*pi*n./T;
+6cOL48 " g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
>f Cz,.L L=4; % length of evoluation to compare with S. Trillo's paper
tbbZGyg5b dz=L/M1; % space step, make sure nonlinear<0.05
\*5`@ >_ for m1 = 1:1:M1 % Start space evolution
tPDd~f Ok u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
bUR; d78 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
sxac( L ca1 = fftshift(fft(u1)); % Take Fourier transform
:Iy 4 B+ ca2 = fftshift(fft(u2));
*AEN c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
&p/ ^A[ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
NkWU5E!
u2 = ifft(fftshift(c2)); % Return to physical space
rnB-e?> u1 = ifft(fftshift(c1));
:el]IH if rem(m1,J) == 0 % Save output every J steps.
%bs6Uy5g)a U1 = [U1 u1]; % put solutions in U array
aZ K% ?c U2=[U2 u2];
GR@jn]50 MN1=[MN1 m1];
/5@4}m>Z@ z1=dz*MN1'; % output location
``l7|b j J end
P2lDi!q| end
IhIPy~Hgt hg=abs(U1').*abs(U1'); % for data write to excel
u 3&9R)J1 ha=[z1 hg]; % for data write to excel
KHK|Zu#k ' t1=[0 t'];
Mp8BilH-T hh=[t1' ha']; % for data write to excel file
K x7'm1 %dlmwrite('aa',hh,'\t'); % save data in the excel format
tvh)N{j figure(1)
?V3kIb waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
}E?{M~"< figure(2)
Kwc~\k waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
8KQD
w: }jF67c-> 非线性超快脉冲耦合的数值方法的Matlab程序 lRIS&9vA3 u$A*Vsmr 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。
FQc8j:' 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
B?;!j)FUtt s@Q,
wa( )ad-p.Hus Ebmd[A&& % This Matlab script file solves the nonlinear Schrodinger equations
C7|z DJ_ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
UOi[#L@N % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
3+[R ! % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Rh%c<</`0s z%$,F9/ C=1;
@"B"*z-d M1=120, % integer for amplitude
3bMQ[G M3=5000; % integer for length of coupler
l]pHj4`uv N = 512; % Number of Fourier modes (Time domain sampling points)
)0RznFJ+X dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
-F&4<\=+ T =40; % length of time:T*T0.
Q /JX8<7K dt = T/N; % time step
@j|B1:O n = [-N/2:1:N/2-1]'; % Index
+7HM 7cw t = n.*dt;
>^<%9{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
hB]\vA7 w=2*pi*n./T;
O@$wU9 D< g1=-i*ww./2;
1:L _qL g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
"JHd F& g3=-i*ww./2;
w_O 3]; P1=0;
' a}<|Et. P2=0;
U{^~X_? P3=1;
x)+ 3SdH P=0;
Wmm 'j&hI for m1=1:M1
3k5C;5 p=0.032*m1; %input amplitude
`V(z z s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
? b}d"QsmU s1=s10;
WyO7,Qr\ s20=0.*s10; %input in waveguide 2
s>A!Egmo s30=0.*s10; %input in waveguide 3
)Ha`> s2=s20;
h3}gg@Fm s3=s30;
`i'72\( p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
L?W F[nF R %energy in waveguide 1
-F7GUB6B p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
H%}ro.u %energy in waveguide 2
\( S69@ f p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
mBp3_E.t %energy in waveguide 3
|U~m8e&: for m3 = 1:1:M3 % Start space evolution
!uoQLiH+ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
n!nXM s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
J\WUBt-M s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
A,P_| sca1 = fftshift(fft(s1)); % Take Fourier transform
6}Iu~| 5 sca2 = fftshift(fft(s2));
I U Mt^z sca3 = fftshift(fft(s3));
(JgW")M`cY sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
4| 6<nk_ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
zc}qAy'< sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
t[L_n m5- s3 = ifft(fftshift(sc3));
%syFHUBw s2 = ifft(fftshift(sc2)); % Return to physical space
PT`];C(he s1 = ifft(fftshift(sc1));
uQ} 0 hs end
3 &aB U [ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
K GVAP p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
ucVWvXCr p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
/b44;U`v5- P1=[P1 p1/p10];
x K8n~.T(' P2=[P2 p2/p10];
PYOU=R%o`8 P3=[P3 p3/p10];
\0{g~cU4 P=[P p*p];
U c6]]Bbc end
? iX1;c9 figure(1)
NXJyRAJ*% plot(P,P1, P,P2, P,P3);
"0,d)L0," a\UhOPFF 转自：
http://blog.163.com/opto_wang/
