计算脉冲在非线性耦合器中演化的Matlab 程序 i" pOYZW1 o8v,17 8 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
~ qI r'?D % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
=LGSywWM9 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
gXM+N (M- % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$15H_X*! 9!kp3x/` %fid=fopen('e21.dat','w');
?~(#~3x N = 128; % Number of Fourier modes (Time domain sampling points)
Xo&\~b#- M1 =3000; % Total number of space steps
/7fd"U$Lh J =100; % Steps between output of space
f re 5{=@ T =10; % length of time windows:T*T0
F ^aD# T0=0.1; % input pulse width
7(a1@ V H MN1=0; % initial value for the space output location
"z;R"sv\ dt = T/N; % time step
gVI`&W__, n = [-N/2:1:N/2-1]'; % Index
t\ TxK 7i t = n.*dt;
_N)&<'lB< u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Px9 K u20=u10.*0.0; % input to waveguide 2
#TC}paIpj u1=u10; u2=u20;
ST0TWE' U1 = u1;
O0s!3hKu U2 = u2; % Compute initial condition; save it in U
i]L=M
5^C ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
]!~?j3-k Q w=2*pi*n./T;
os &FrtDg g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
lI+^}-< L=4; % length of evoluation to compare with S. Trillo's paper
+!!G0Zj/ dz=L/M1; % space step, make sure nonlinear<0.05
.N@+M s3 for m1 = 1:1:M1 % Start space evolution
TbN{ex* u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
SynRi/BRmw u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
/wl] kGF ca1 = fftshift(fft(u1)); % Take Fourier transform
~8"oH5 ca2 = fftshift(fft(u2));
|lg jI!iK c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
z
Tz_"N I c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
"v( pluN| u2 = ifft(fftshift(c2)); % Return to physical space
o4J@M{xb_ u1 = ifft(fftshift(c1));
-sZb+2tDa if rem(m1,J) == 0 % Save output every J steps.
aM(# J7; U1 = [U1 u1]; % put solutions in U array
k_ywwkG9lU U2=[U2 u2];
E*wG5] at MN1=[MN1 m1];
I,`;#Q)nx z1=dz*MN1'; % output location
8 DY:a['-d end
MGxkqy ? end
he:z9EG} hg=abs(U1').*abs(U1'); % for data write to excel
jD} h`(bE ha=[z1 hg]; % for data write to excel
B]: |;d t1=[0 t'];
/BD'{tZ]Sl hh=[t1' ha']; % for data write to excel file
]!@=2kG4 %dlmwrite('aa',hh,'\t'); % save data in the excel format
-mn/Yv figure(1)
*|<~IQg waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
u[Si=)`VPk figure(2)
D~U RY_[A waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
C "B'Dj p<#aXs jy 非线性超快脉冲耦合的数值方法的Matlab程序 kh:_,g 0I<L<^s3^U 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。
_cj=}!I 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
_ DT,iF*6 DR:DXJc G5 K?Q+n
&qWB\m % This Matlab script file solves the nonlinear Schrodinger equations
D, [Nn_N % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
II| ;_j % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@ =~k[o % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*w O~RnP UZrEFpi C=1;
*Egg*2P;"Q M1=120, % integer for amplitude
s }OL)rW=} M3=5000; % integer for length of coupler
a$Y{ut0t( N = 512; % Number of Fourier modes (Time domain sampling points)
wet[f {c dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
g,!.`[e'ex T =40; % length of time:T*T0.
iLN UydiS dt = T/N; % time step
1[u{y{9 q n = [-N/2:1:N/2-1]'; % Index
doHE]gC2Uz t = n.*dt;
PnInsf%; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
=~Qg(=U0U w=2*pi*n./T;
2[uFAgf@ g1=-i*ww./2;
]@<VLP? g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
3S]Q IZ1 g3=-i*ww./2;
1iLo $ P1=0;
=b>TF B=*N P2=0;
/|P{t{^WM P3=1;
3nc\6v% P=0;
KV | D]} for m1=1:M1
"aCB} p=0.032*m1; %input amplitude
!rAH@y.l s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
V| kN 1
A s1=s10;
zIu/!a w s20=0.*s10; %input in waveguide 2
6QbDU[ s30=0.*s10; %input in waveguide 3
@KU;' th s2=s20;
>yXhP6 s3=s30;
zhd1)lgY p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
CJ%'VijhD %energy in waveguide 1
0F%8d@Y2 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
rTR"\u7&H %energy in waveguide 2
8h@ L_*Kr p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
} F!Uu
KR %energy in waveguide 3
^uN[rHZ*u for m3 = 1:1:M3 % Start space evolution
kk6
!krZ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
`y^\c#k s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
}Oc+EV-Z s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
OUF%DMl4 sca1 = fftshift(fft(s1)); % Take Fourier transform
: i?6#_2IC sca2 = fftshift(fft(s2));
<nD@4J-A0 sca3 = fftshift(fft(s3));
SJa>!]U'xI sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
%aMC[ i sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
=FV(m
S sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
EFh^C.S8 s3 = ifft(fftshift(sc3));
1.3dy]vG s2 = ifft(fftshift(sc2)); % Return to physical space
Kc2y s1 = ifft(fftshift(sc1));
gjN'D!'E1D end
lG Wz p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
+~iiy;i( p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
)1M2}11uS p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
g `S ;xs P1=[P1 p1/p10];
QY&c=bWAX" P2=[P2 p2/p10];
*->*p35 P3=[P3 p3/p10];
rC_1f3A P=[P p*p];
Kmaz"6A end
E~fb#6 figure(1)
E] /2 u3p plot(P,P1, P,P2, P,P3);
{G x=QNd 6Yodx$ 转自：
http://blog.163.com/opto_wang/
