计算脉冲在非线性耦合器中演化的Matlab 程序 v<c@bDZ> FqpUw<]6s % This Matlab script file solves the coupled nonlinear Schrodinger equations of
1hnw+T<<W % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
uy^vQ/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
u# uT|a. % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<qp D Az4k Zn]njf1x %fid=fopen('e21.dat','w');
-p\uW 0XA N = 128; % Number of Fourier modes (Time domain sampling points)
38B h9>c3 M1 =3000; % Total number of space steps
{D9m>B3"{ J =100; % Steps between output of space
4 W$ t28) T =10; % length of time windows:T*T0
="*:H) T0=0.1; % input pulse width
f R?Xq@c MN1=0; % initial value for the space output location
7(oX 1hN dt = T/N; % time step
mqFo`Ee n = [-N/2:1:N/2-1]'; % Index
l[D5JnWxt t = n.*dt;
C_~hX G u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+^\TG>le u20=u10.*0.0; % input to waveguide 2
1<ic
5kB u1=u10; u2=u20;
R<GnPN:c U1 = u1;
Fw!TTH6l0 U2 = u2; % Compute initial condition; save it in U
9X- w5$< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
$xl>YYEBMH w=2*pi*n./T;
cB ,l= /? g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
[)E.T,fjMQ L=4; % length of evoluation to compare with S. Trillo's paper
9< $n'g dz=L/M1; % space step, make sure nonlinear<0.05
l,n
V*Z for m1 = 1:1:M1 % Start space evolution
2l#c?]TA u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
#-*#? - u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
/\0 rRT ca1 = fftshift(fft(u1)); % Take Fourier transform
X/l{E4Ex ca2 = fftshift(fft(u2));
2iJ)K rw c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Gec ? c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
<@puWm[p u2 = ifft(fftshift(c2)); % Return to physical space
)* \N[zm u1 = ifft(fftshift(c1));
jLZ^EM- if rem(m1,J) == 0 % Save output every J steps.
L~u@n 24 U1 = [U1 u1]; % put solutions in U array
#rkz:ir4 U2=[U2 u2];
X5hamkM*m MN1=[MN1 m1];
bI_T\Eft z1=dz*MN1'; % output location
I \DH end
E1& 9( L5 end
k,mgiGrQ hg=abs(U1').*abs(U1'); % for data write to excel
e M$NVpS3 ha=[z1 hg]; % for data write to excel
C =6.~&( t1=[0 t'];
x&kM /z?/ hh=[t1' ha']; % for data write to excel file
;`f14Fb %dlmwrite('aa',hh,'\t'); % save data in the excel format
8w Xnc% figure(1)
V oTnm waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
*/ 7+pk( figure(2)
V4.&"0\n # waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Z Vin+ z d}Y\; '2, 非线性超快脉冲耦合的数值方法的Matlab程序 _,?<r&>v6 jrl'?`O 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。
H`:2J8 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
,@#)) 2<RK Yi5^# G fUg<+|v* pp2,d`01[L % This Matlab script file solves the nonlinear Schrodinger equations
nb MxQOD k % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
l
7XeZ} S % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
2.> WR~ \ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~mR@L `" l l[AQyR1+/ C=1;
oE
H""Bd M1=120, % integer for amplitude
s6k@W T?"^ M3=5000; % integer for length of coupler
5C |Y-G N = 512; % Number of Fourier modes (Time domain sampling points)
I+VL~'VlS dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
5!b+^UR;z T =40; % length of time:T*T0.
~fV\
X* dt = T/N; % time step
>OLKaghV.5 n = [-N/2:1:N/2-1]'; % Index
P"%QFt, t = n.*dt;
UK7pQt}9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
hT0[ O w=2*pi*n./T;
J dK' ~-L g1=-i*ww./2;
$ \w<.)"# g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
EDA%qNd]j g3=-i*ww./2;
b5@ sG^ P1=0;
R_7[7 /a P2=0;
3b d(.he2u P3=1;
RnaxRnXVR P=0;
F+m%PVW: for m1=1:M1
j TyR+#Wn p=0.032*m1; %input amplitude
ev'` K=n8 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
:]rb} 1nLB s1=s10;
+I$,Y~&`> s20=0.*s10; %input in waveguide 2
vh/&KTe?: s30=0.*s10; %input in waveguide 3
e2><Y< s2=s20;
;J>upI s3=s30;
ms]r1x" p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
) /y7Fh %energy in waveguide 1
'xP&u<(F p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
lA/.4"nN %energy in waveguide 2
F{*h~7D-| p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
(2J\o %energy in waveguide 3
=.48^ $LWx for m3 = 1:1:M3 % Start space evolution
x_+-TC4IXn s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
v H?rln s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
$SOFq+- T s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ixY[ HDPq sca1 = fftshift(fft(s1)); % Take Fourier transform
]J(BaX4 sca2 = fftshift(fft(s2));
lZr}F.7 sca3 = fftshift(fft(s3));
3-PqUJT$ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
0z
=?}xr sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
!0Mx Bem sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
+L,V_z s3 = ifft(fftshift(sc3));
GyZpdp! s2 = ifft(fftshift(sc2)); % Return to physical space
yp!7^ s1 = ifft(fftshift(sc1));
GiK4LJ~cH) end
Q;xJ/4 Z" p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
}`~n$OVx p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Ht"?ajW{ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
x>bG xDtu* P1=[P1 p1/p10];
*8I"7'xh P2=[P2 p2/p10];
*yZ `aKfH P3=[P3 p3/p10];
Xmm) z P=[P p*p];
Pr KH{nyJk end
67g"8R#.V figure(1)
0g `$Dap plot(P,P1, P,P2, P,P3);
FPE%h =sw w$DHMpW' 转自：
http://blog.163.com/opto_wang/
