计算脉冲在非线性耦合器中演化的Matlab 程序 8 n56rOW!
,{%[/#~6 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
,Vogo5~X % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
"/q6E % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
\"Np '$4eu % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
OSBE5 ?VJ Fp^Ra %fid=fopen('e21.dat','w');
Tb}b* d 3 N = 128; % Number of Fourier modes (Time domain sampling points)
V{8mx70 M1 =3000; % Total number of space steps
v K$W)(Z J =100; % Steps between output of space
d"V^^I)yx& T =10; % length of time windows:T*T0
u`ZnxD> T0=0.1; % input pulse width
WA<~M) rb MN1=0; % initial value for the space output location
%T&kK2d; dt = T/N; % time step
H;v*/~zl n = [-N/2:1:N/2-1]'; % Index
% $J^dF_0 t = n.*dt;
Dx8^V%b u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
4"GY0)
Q u20=u10.*0.0; % input to waveguide 2
x[_+U 4-/ u1=u10; u2=u20;
:5dq<>~ U1 = u1;
F:n7y ey U2 = u2; % Compute initial condition; save it in U
0_ ;-QAd ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
dfNNCPu]+ w=2*pi*n./T;
CzwnmSv{. g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
$+Xohtt L=4; % length of evoluation to compare with S. Trillo's paper
?&[`=ZVn dz=L/M1; % space step, make sure nonlinear<0.05
Ts.6 1Rx for m1 = 1:1:M1 % Start space evolution
H#f
FU u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
n|8fdiK#} u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
5y.kOe4vH ca1 = fftshift(fft(u1)); % Take Fourier transform
ZN.
#g_ ca2 = fftshift(fft(u2));
oR5 'g7? c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
O)&V}h U* c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
w E'~Qj u2 = ifft(fftshift(c2)); % Return to physical space
V-VR+ Ndz u1 = ifft(fftshift(c1));
<FP&1Eg!| if rem(m1,J) == 0 % Save output every J steps.
Y gg+*z
U1 = [U1 u1]; % put solutions in U array
vzfWPjpKW U2=[U2 u2];
O5E \#*<K MN1=[MN1 m1];
tY V mB:l z1=dz*MN1'; % output location
1B 2>8 N end
m'Ran3rp end
O
Qd,.m hg=abs(U1').*abs(U1'); % for data write to excel
6L8wsz CW ha=[z1 hg]; % for data write to excel
$~_TE\F1 t1=[0 t'];
Mu Tl N hh=[t1' ha']; % for data write to excel file
"I
u3&mc %dlmwrite('aa',hh,'\t'); % save data in the excel format
1X]?-+',. figure(1)
WxFVbt w waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
[V
=O $X_ figure(2)
|'.\}xt7 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
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$cO} } DoNp[` 非线性超快脉冲耦合的数值方法的Matlab程序 "1Vuf<?C a8NL 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。
)A,M T i 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
I_\j05 d7A vx 86oa>#opU Rkgpa/te" % This Matlab script file solves the nonlinear Schrodinger equations
L2+~I<|> % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
|%Pd*y ZA % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
',~,h J0 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`i;f
ji5 c0WH C=1;
z`XX[9 $qm M1=120, % integer for amplitude
Rjt]^gb!* M3=5000; % integer for length of coupler
`5:b=^'D / N = 512; % Number of Fourier modes (Time domain sampling points)
ibha` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
yHe%e1 T =40; % length of time:T*T0.
n2cb,b/7 dt = T/N; % time step
(}
?")$. n = [-N/2:1:N/2-1]'; % Index
7 41Sd8 t = n.*dt;
%d3qMnYu ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
'b~,/lZd w=2*pi*n./T;
)CKPzNf g1=-i*ww./2;
e-Mei7{% g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
.]24V!J(1w g3=-i*ww./2;
0.!_k )tu P1=0;
z&C z!HrS P2=0;
P 9 c! P3=1;
/?Vwo SgV^ P=0;
BS!VAHO"V for m1=1:M1
NH~\kV p=0.032*m1; %input amplitude
muc6gwBp s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
QY|Rz(;m s1=s10;
ir !/{IQx s20=0.*s10; %input in waveguide 2
b@`h]]~: s30=0.*s10; %input in waveguide 3
[7 _1GSS1 s2=s20;
'*lVVeSiFw s3=s30;
^ZuwUuuf p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
C%H {" %energy in waveguide 1
ZOw%Fw4B p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
m9M#)< @* %energy in waveguide 2
Q #IlUo p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
#g=7fu{n: %energy in waveguide 3
O/ybqU\7 for m3 = 1:1:M3 % Start space evolution
y rH@:D/ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
"Rc Ny~ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
%^Zu^uu s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
2+s#5K&i sca1 = fftshift(fft(s1)); % Take Fourier transform
/0 CS2mLC sca2 = fftshift(fft(s2));
A*^aBWFR sca3 = fftshift(fft(s3));
@S9^~W3G3 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
OGcq]ue sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
ur\<NApT; sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
8n??/VDRl s3 = ifft(fftshift(sc3));
> zA*W<g s2 = ifft(fftshift(sc2)); % Return to physical space
+adwEYRrr s1 = ifft(fftshift(sc1));
N(s5YX7<hd end
Q-<h)WTA p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
lV".-:u_ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
=hY 9lxW p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
#K&XY6cTj P1=[P1 p1/p10];
' 9u(9S P2=[P2 p2/p10];
0#Ae< P3=[P3 p3/p10];
` {/"? s| P=[P p*p];
)5Wt(p:T6_ end
hg7^#f95u figure(1)
T_)G 5a plot(P,P1, P,P2, P,P3);
ghGpi U$ ?xW,2S 转自：
http://blog.163.com/opto_wang/
