计算脉冲在非线性耦合器中演化的Matlab 程序 y>)MAzz~\ moaodmt]x % This Matlab script file solves the coupled nonlinear Schrodinger equations of
~+=E"9Oo % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
; HP#bx % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
K\~v& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
q P'[&h5Y
] ;&"1A %fid=fopen('e21.dat','w');
/e .D /;] N = 128; % Number of Fourier modes (Time domain sampling points)
V\"1wV~E M1 =3000; % Total number of space steps
RvR:e| J =100; % Steps between output of space
22|"K**3J| T =10; % length of time windows:T*T0
-IbbP uRq T0=0.1; % input pulse width
*<UGgnmLE MN1=0; % initial value for the space output location
Y| :YrZSC dt = T/N; % time step
UTvs
|[ n = [-N/2:1:N/2-1]'; % Index
VE*j*U
j t = n.*dt;
uS&LG#a u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
&lq^dFP&Su u20=u10.*0.0; % input to waveguide 2
Hxn<(gd
G u1=u10; u2=u20;
A*R n <{U U1 = u1;
] {Z8 U2 = u2; % Compute initial condition; save it in U
\@8*T S ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
D,E$_0 w=2*pi*n./T;
K I`11lJW~ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
SD^E7W$? L=4; % length of evoluation to compare with S. Trillo's paper
F(;jM( dz=L/M1; % space step, make sure nonlinear<0.05
^j [Ku for m1 = 1:1:M1 % Start space evolution
o(zTNk5d u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
/z#F,NB u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
ld95[cTP ca1 = fftshift(fft(u1)); % Take Fourier transform
m bGcDG[HQ ca2 = fftshift(fft(u2));
>K5~:mx#3 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
S*xhX1yUi c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
McP~}"!^ u2 = ifft(fftshift(c2)); % Return to physical space
Li]k7w?H u1 = ifft(fftshift(c1));
0U%Xm[: if rem(m1,J) == 0 % Save output every J steps.
Co[n--@C U1 = [U1 u1]; % put solutions in U array
-p] >Be+^x U2=[U2 u2];
%<AS?Ry MN1=[MN1 m1];
hF.6}28U1 z1=dz*MN1'; % output location
r ^ Y~mq end
$o"g73`3 end
JtFiFa CxY hg=abs(U1').*abs(U1'); % for data write to excel
4#7Umj ha=[z1 hg]; % for data write to excel
.yX>.>"T| t1=[0 t'];
26 ?23J
; hh=[t1' ha']; % for data write to excel file
nEyI t&> 9 %dlmwrite('aa',hh,'\t'); % save data in the excel format
?&xlT+JM figure(1)
rd"
&QB{ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
/BT1oWi1y figure(2)
R:f7LRF/\ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
"$ DldHC gB >pd?d 非线性超快脉冲耦合的数值方法的Matlab程序 wFb@1ae\ fnWsm4 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。
*i@T!O(1)M 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
drIK(u\_ +sRP<as r :NH6tAL vd(dNu&,< % This Matlab script file solves the nonlinear Schrodinger equations
kW +G1| % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
,VWGq@o% % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
tt{`\1q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
nj A="f j C=1;
H-2_j M1=120, % integer for amplitude
&[~[~m| M3=5000; % integer for length of coupler
N+J>7_k N = 512; % Number of Fourier modes (Time domain sampling points)
fhr-Y'
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
;ct U&` T =40; % length of time:T*T0.
(Q_2ODKo dt = T/N; % time step
)2V@ p~k? n = [-N/2:1:N/2-1]'; % Index
:".w{0l@ t = n.*dt;
"{ FoA3g| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
${>DhfF w=2*pi*n./T;
a:b^!H># g1=-i*ww./2;
a q kix"J g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
CV3DMA g3=-i*ww./2;
="3,}q R P1=0;
^yJ:+m;6K P2=0;
-TS?
fne) P3=1;
R04J3D| P=0;
/WYh[XKe for m1=1:M1
Q;wB{vr$ p=0.032*m1; %input amplitude
Q6x% s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
$H;+}VQ s1=s10;
>)3Vb O s20=0.*s10; %input in waveguide 2
]
D6|o5 s30=0.*s10; %input in waveguide 3
2yxi= XWZ s2=s20;
*Ru2:}?MpS s3=s30;
c{4R*|^ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
"lrA%~3%[P %energy in waveguide 1
PU Cx]5 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
tl^ m=(ZQ %energy in waveguide 2
>{t+4 p4k. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
IT&i,`cJ~F %energy in waveguide 3
*/_@a? for m3 = 1:1:M3 % Start space evolution
x5F@ad 9 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
jyQ VSQ s s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
m8AAp1= s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
4U{m7[ sca1 = fftshift(fft(s1)); % Take Fourier transform
^Plc}W7h sca2 = fftshift(fft(s2));
EY$?^iS sca3 = fftshift(fft(s3));
61|B]ei/ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
C0(sAF@ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
>3P9 i ;W sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
k{-`]qiK s3 = ifft(fftshift(sc3));
|^ iA6)Q s2 = ifft(fftshift(sc2)); % Return to physical space
_l T0H u s1 = ifft(fftshift(sc1));
O^N P0E end
)E-E0Hl>7 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
;($1Z7j+ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
]]/lC p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
}p{;^B P1=[P1 p1/p10];
c ,$mWTC P2=[P2 p2/p10];
Dql K. P3=[P3 p3/p10];
<\ETPL ,< P=[P p*p];
S_5?U2%D end
'=#5(O%pp figure(1)
=YHt9fb$c plot(P,P1, P,P2, P,P3);
Spo +@G xYwkFB$$* 转自：
http://blog.163.com/opto_wang/
