计算脉冲在非线性耦合器中演化的Matlab 程序 p
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k/QZ T % This Matlab script file solves the coupled nonlinear Schrodinger equations of
_v~c3y). % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Q-A:0F&{t % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
xJCMxt2Y % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
W 7xh R _# x %fid=fopen('e21.dat','w');
.3xpDVW^e N = 128; % Number of Fourier modes (Time domain sampling points)
x`7Ch3`4} M1 =3000; % Total number of space steps
3y&N }'R(F J =100; % Steps between output of space
X`- 7: !+ T =10; % length of time windows:T*T0
R]dN-'U T0=0.1; % input pulse width
Ck`-<)u N MN1=0; % initial value for the space output location
w'Y(doY , dt = T/N; % time step
K1`Z}k_p. n = [-N/2:1:N/2-1]'; % Index
\X3Q,\H
@ t = n.*dt;
U;SReWqU u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
P
X9GiJN " u20=u10.*0.0; % input to waveguide 2
pe}mA}9U u1=u10; u2=u20;
UA>3,|gV1 U1 = u1;
ibzcO,c U2 = u2; % Compute initial condition; save it in U
b/#SkxW#S ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_*&I[%I5 w=2*pi*n./T;
p\;\hHai g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
#}M\ J0Q G L=4; % length of evoluation to compare with S. Trillo's paper
}%8 :8_Ke dz=L/M1; % space step, make sure nonlinear<0.05
u{|
Q[hf[ for m1 = 1:1:M1 % Start space evolution
F~bDA~ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
pm2-F] u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
HgGwV;W ca1 = fftshift(fft(u1)); % Take Fourier transform
? <F=*eS ca2 = fftshift(fft(u2));
I{bDa'rX c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
$,Eb(j c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
^$F Nu~ |K u2 = ifft(fftshift(c2)); % Return to physical space
0H$6_YX4 A u1 = ifft(fftshift(c1));
7Sha u%2C if rem(m1,J) == 0 % Save output every J steps.
PpXzWWU": U1 = [U1 u1]; % put solutions in U array
%fbV\@jDCX U2=[U2 u2];
`!Z0 ; qk MN1=[MN1 m1];
P}`|8b1W z1=dz*MN1'; % output location
`i!BXOOV{ end
/D d.C<F end
#}PQ !gZ hg=abs(U1').*abs(U1'); % for data write to excel
A&?8 r c ha=[z1 hg]; % for data write to excel
5taR[ukM t1=[0 t'];
R"wBDWs hh=[t1' ha']; % for data write to excel file
0sMNp %dlmwrite('aa',hh,'\t'); % save data in the excel format
bA_/ 6r)u figure(1)
kC ,=E9)O waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
J# >)+ figure(2)
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u1- waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
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w}t jo-2D[Q{ 非线性超快脉冲耦合的数值方法的Matlab程序 !Y8+ Z&^2 T }}T`Ce 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。
V jdu9Ez 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
._E 6? | 2Vhj<6 3 as~yF0 m&P B5s\= % This Matlab script file solves the nonlinear Schrodinger equations
' iM#iA 8 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
%nS( >X<B % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
JpRn)e'Z % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
m/e*P*\ = {g C?kp C=1;
ybC0Ee@ M1=120, % integer for amplitude
~| lEi1| M3=5000; % integer for length of coupler
<~ Dq8If N = 512; % Number of Fourier modes (Time domain sampling points)
A _!N,< - dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
&lCOhP# T =40; % length of time:T*T0.
>]L\B w dt = T/N; % time step
I[6ft_* n = [-N/2:1:N/2-1]'; % Index
A'tv[T d8, t = n.*dt;
} =p e;l ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
UVd
^tg w=2*pi*n./T;
-k?K|w*X g1=-i*ww./2;
SHc?C&^S g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
4 <j 7F4 g3=-i*ww./2;
D03QisH= P1=0;
B:>>D/O P2=0;
s||c#+j"8 P3=1;
mz2 v2ma P=0;
O:]e4r,' for m1=1:M1
yMz dM&a!* p=0.032*m1; %input amplitude
[t6Y,yo&h4 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
oO3X>y{gN s1=s10;
Ueu~803~ s20=0.*s10; %input in waveguide 2
qOTo p- s30=0.*s10; %input in waveguide 3
!gm@QO cF s2=s20;
i*]$_\yl" s3=s30;
DO
0 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
/u&7!>, %energy in waveguide 1
hz+O .k],? p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
vn+~P9SHQ %energy in waveguide 2
[ KDNKK p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
}*P?KV ( %energy in waveguide 3
wpI"kk_@@ for m3 = 1:1:M3 % Start space evolution
YfstE3BV s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
m;JB=MZ=m s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
UL.YDU) s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
JA$RY sca1 = fftshift(fft(s1)); % Take Fourier transform
qoP /` Y6 sca2 = fftshift(fft(s2));
5^97#;Q;J" sca3 = fftshift(fft(s3));
kxLWk%V sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
|\U 5m6 q sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
!{?<(6;t sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
l[6lXR&| s3 = ifft(fftshift(sc3));
Sc?q}tt^C s2 = ifft(fftshift(sc2)); % Return to physical space
&u4;A[- R s1 = ifft(fftshift(sc1));
>r YkVl v end
;LC?3. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
U;=1v:~d p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
_7;D0 l p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Eq=j+ch7 P1=[P1 p1/p10];
Ie[DTy P2=[P2 p2/p10];
z+K1[1SM P3=[P3 p3/p10];
/?1^&a P=[P p*p];
_/J`v`}G end
Ltk-1zhI figure(1)
6@ ;sOiN+ plot(P,P1, P,P2, P,P3);
vO)]~AiB ! mZWd' 转自：
http://blog.163.com/opto_wang/
