计算脉冲在非线性耦合器中演化的Matlab 程序 M+-*QyCFK LmRy1T,act % This Matlab script file solves the coupled nonlinear Schrodinger equations of
'Oxy$U
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
O6@j &*jS % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
.[YuRLGz % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)"qa k T n #mA/H;wV %fid=fopen('e21.dat','w');
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enE^e+9 N = 128; % Number of Fourier modes (Time domain sampling points)
}? lrU.@zg M1 =3000; % Total number of space steps
E!;SL|lj . J =100; % Steps between output of space
] ;KJ6 T =10; % length of time windows:T*T0
9/9j+5}+ T0=0.1; % input pulse width
"RedK '7g MN1=0; % initial value for the space output location
K:J3Z5 " dt = T/N; % time step
-7SAK1 c$ n = [-N/2:1:N/2-1]'; % Index
"WlZ)wyF% t = n.*dt;
P=qa::A u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
1v#%Ei$6`t u20=u10.*0.0; % input to waveguide 2
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06^U u1=u10; u2=u20;
]{!U@b U1 = u1;
.b_)%jd x U2 = u2; % Compute initial condition; save it in U
MlcR"gl* ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
?llXd 4 w=2*pi*n./T;
Id*Ce2B g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ht|z<XJ L=4; % length of evoluation to compare with S. Trillo's paper
}~2LW" 1' dz=L/M1; % space step, make sure nonlinear<0.05
88Ey12$ for m1 = 1:1:M1 % Start space evolution
M\vwI" u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
vx\r!] u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
AW%50V ca1 = fftshift(fft(u1)); % Take Fourier transform
Y$o< 6 [7 ca2 = fftshift(fft(u2));
zy?.u.4L c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
"33Fv9C#bK c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
eP.wOl u2 = ifft(fftshift(c2)); % Return to physical space
hZdoc< u1 = ifft(fftshift(c1));
90Pl$#cb2 if rem(m1,J) == 0 % Save output every J steps.
dA#Q}.*r U1 = [U1 u1]; % put solutions in U array
3^IpE];+:u U2=[U2 u2];
<5d ~P/, MN1=[MN1 m1];
&\#sI9 z1=dz*MN1'; % output location
9Q.rMs>qj end
09|K>UC)v end
i3dkY evs? hg=abs(U1').*abs(U1'); % for data write to excel
vN Vox0V ha=[z1 hg]; % for data write to excel
ZLc -RM t1=[0 t'];
: D euX hh=[t1' ha']; % for data write to excel file
e%@'5k\SK %dlmwrite('aa',hh,'\t'); % save data in the excel format
9"NF/)_ figure(1)
EH$1fvE waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Ut*`:]la figure(2)
ICpAt~3[M waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
.I$qCb|FP dFRsm0 T 非线性超快脉冲耦合的数值方法的Matlab程序 ?e` ^P FFl!\y*0z 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。
z[LNf.)} 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
>/g#lS 5 Jk&3%^P{m UXeN 8 f6EZ(
v % This Matlab script file solves the nonlinear Schrodinger equations
B%"
d~5Y % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
nx@ =>E+a % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
E08 klC0 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
G (Lzf( \O} E7 - C=1;
FI[A[*fi M1=120, % integer for amplitude
4 <9=5 q] M3=5000; % integer for length of coupler
b $'FvZbk N = 512; % Number of Fourier modes (Time domain sampling points)
+GG9^:<yr dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
jDKO}
bQ T =40; % length of time:T*T0.
y GI;ye'U dt = T/N; % time step
qJ;jfh! n = [-N/2:1:N/2-1]'; % Index
vY4\59]P t = n.*dt;
.Fs7z7?Y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1=t>HQ w=2*pi*n./T;
@"hb) 8ng g1=-i*ww./2;
qT ,Te g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
rk&IlAE g3=-i*ww./2;
}e !x5g P1=0;
zxMX Xm; P2=0;
'GB. UKlR P3=1;
#J@[Wd P=0;
RzxNbeki[W for m1=1:M1
yQU_>_!n p=0.032*m1; %input amplitude
~{d $!`|a s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
uH/J] zKR s1=s10;
i;]"n;>+/ s20=0.*s10; %input in waveguide 2
6tX q: s30=0.*s10; %input in waveguide 3
!i{aMxUP s2=s20;
mIurA?&7! s3=s30;
~s%
Md p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
0vFD3}~> %energy in waveguide 1
L\Aq6q@c p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Y ?S!8-z %energy in waveguide 2
jB`,u|FG p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
| 1E|hh@k %energy in waveguide 3
-- PtZ]Z for m3 = 1:1:M3 % Start space evolution
&]8P1{ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
y 6LWx: s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
l%[EXZ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Q7*SE%H sca1 = fftshift(fft(s1)); % Take Fourier transform
B{| 8#jqY sca2 = fftshift(fft(s2));
Yb +yw_5 sca3 = fftshift(fft(s3));
sA/pVU sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
$AfM>+GQ`n sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
< %($7VMev sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Ewu O&q
s3 = ifft(fftshift(sc3));
~kShq% s2 = ifft(fftshift(sc2)); % Return to physical space
kB3H="3 [[ s1 = ifft(fftshift(sc1));
$8;R[SU6Y end
'3_]Gu-D p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
U[SaY0 Z p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
p=;=w_^y p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
e^d 0zl{ P1=[P1 p1/p10];
s8wmCzB~ P2=[P2 p2/p10];
Q?e*4ba P3=[P3 p3/p10];
6`O.!|) P=[P p*p];
{kp"nl$< end
~R_zt D+C( figure(1)
8JM&(Q%# plot(P,P1, P,P2, P,P3);
+,2:g}5 V@R rn <l 转自：
http://blog.163.com/opto_wang/
