计算脉冲在非线性耦合器中演化的Matlab 程序 /U| > Hk GA$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
.I6:iB % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
lu]Z2xSv % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
)p,uZ`~v % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]e*Zx;6oi .Pp; % %fid=fopen('e21.dat','w');
\,U#^Vr N = 128; % Number of Fourier modes (Time domain sampling points)
SAuZWA4g[ M1 =3000; % Total number of space steps
d+
LEi^ J =100; % Steps between output of space
Xp(e/QB T =10; % length of time windows:T*T0
x2P}8Idg?A T0=0.1; % input pulse width
'Gn-8r+ MN1=0; % initial value for the space output location
Rn l
4 dt = T/N; % time step
pt"yJtM'P n = [-N/2:1:N/2-1]'; % Index
6]GE n=t t = n.*dt;
6SYQRK u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
A578g u20=u10.*0.0; % input to waveguide 2
&e#>%0aS u1=u10; u2=u20;
MhE'_sq U1 = u1;
^ X&`:f U2 = u2; % Compute initial condition; save it in U
] D(laqS;" ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
# g.J,L w=2*pi*n./T;
XIv{jzgF g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
@;T>*_Yhn L=4; % length of evoluation to compare with S. Trillo's paper
<tT*.nM\ dz=L/M1; % space step, make sure nonlinear<0.05
@<GVY))R8 for m1 = 1:1:M1 % Start space evolution
~2R3MF.C u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Gi<ik~ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
1QfOD-lv ca1 = fftshift(fft(u1)); % Take Fourier transform
? J ;* ca2 = fftshift(fft(u2));
(<u3<40[YN c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
n+5X*~D c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
9J"Y u2 = ifft(fftshift(c2)); % Return to physical space
_}_lrg}U u1 = ifft(fftshift(c1));
u )'l|Y if rem(m1,J) == 0 % Save output every J steps.
(h"Yw U1 = [U1 u1]; % put solutions in U array
c)N&}hFYC U2=[U2 u2];
j( *;W}*^ MN1=[MN1 m1];
8vN} v3HV& z1=dz*MN1'; % output location
Y0kDHG end
/ae]v+ end
aL wd#/! hg=abs(U1').*abs(U1'); % for data write to excel
Q77iMb] ha=[z1 hg]; % for data write to excel
mY+.( N7m t1=[0 t'];
nN|zEw] hh=[t1' ha']; % for data write to excel file
>s@6rNgf %dlmwrite('aa',hh,'\t'); % save data in the excel format
=~Ac=j!q figure(1)
GJ >vL waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
tDuQ+|~M figure(2)
.Yxx
waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
-0KQR{LI HJY_l 非线性超快脉冲耦合的数值方法的Matlab程序 @!92Ok jg
~ ;s 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。
F",S}cK*MH 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=.}484>J 1dhp/Qh SE0"25\_G R/H ?/ % This Matlab script file solves the nonlinear Schrodinger equations
+vxU~WIV& % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
RI#C r+/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
8T5s6EmIOW % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
b"Hg4i ) NN<kO#c+2 C=1;
bSW!2#~ M1=120, % integer for amplitude
Z`fm;7NiVG M3=5000; % integer for length of coupler
Ji7%=_@'-# N = 512; % Number of Fourier modes (Time domain sampling points)
%@<}z|.4 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
t I9$m[ T =40; % length of time:T*T0.
PVAs# ~ dt = T/N; % time step
(7nWv43 n = [-N/2:1:N/2-1]'; % Index
Dk#$PjcRE t = n.*dt;
v})0zz?,1 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1=DUFl. w=2*pi*n./T;
&`7tX.iMlh g1=-i*ww./2;
Sd]` I) g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
nq#k}Qx: g3=-i*ww./2;
-\;x>=#B P1=0;
YoD1\ a| P2=0;
D7%`hU P3=1;
C\7q AR\ P=0;
;9,<&fe for m1=1:M1
?YY'-\h? p=0.032*m1; %input amplitude
w'q}aQS s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
%YhZ#>WT s1=s10;
A_: Bz: s20=0.*s10; %input in waveguide 2
?i*k wEj= s30=0.*s10; %input in waveguide 3
*Yk3 y-
s2=s20;
d+KLtvB%M s3=s30;
S#{e@ C p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
|H&2[B"l %energy in waveguide 1
/nEh,<Y) p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
z JWh %energy in waveguide 2
c ?mCt0Cg p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
brN:Ypf-e %energy in waveguide 3
&?(r# T for m3 = 1:1:M3 % Start space evolution
A{G iz&p s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
/?l@7 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
be `\ O s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
]|[, N> sca1 = fftshift(fft(s1)); % Take Fourier transform
#RK?3?wcr sca2 = fftshift(fft(s2));
? 6B
n&qa sca3 = fftshift(fft(s3));
l]whL1N3 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
k<uC [)_ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
tk4~ 8 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
oB8u[ ! s3 = ifft(fftshift(sc3));
ZK))91;v s2 = ifft(fftshift(sc2)); % Return to physical space
U 7U-H\t7 s1 = ifft(fftshift(sc1));
B nH< -n_ end
Ch607 i= p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
b, YTw p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
xMDx<sk p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
t^. U<M P1=[P1 p1/p10];
6sb,*uSn% P2=[P2 p2/p10];
hVRpk0IJDK P3=[P3 p3/p10];
MWGW[V; P=[P p*p];
FbQ"ZTN\;Y end
P?*$Wf,~n figure(1)
ny17(Y = plot(P,P1, P,P2, P,P3);
%fMK^H 8{ K2<Q9 ,v t 转自：
http://blog.163.com/opto_wang/
