计算脉冲在非线性耦合器中演化的Matlab 程序 WE")xhV6 !6Q `>s] % This Matlab script file solves the coupled nonlinear Schrodinger equations of
|=\91fP68` % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Xem 05%, % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
On4w/L9L5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
a'uU,Eb}#w kBbl+1{H %fid=fopen('e21.dat','w');
.!i0_Rv5x N = 128; % Number of Fourier modes (Time domain sampling points)
en>9E .?N M1 =3000; % Total number of space steps
27>a#vCT J =100; % Steps between output of space
J/t!- ! T =10; % length of time windows:T*T0
Ivsb<qzG T0=0.1; % input pulse width
"IG+V:{ou MN1=0; % initial value for the space output location
f/ajejYo?, dt = T/N; % time step
3% ^z ?_ n = [-N/2:1:N/2-1]'; % Index
>\Z R*CS t = n.*dt;
E T)>#zp+s u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
pW{8R^vKm u20=u10.*0.0; % input to waveguide 2
%w7m\nw@ u1=u10; u2=u20;
i&A%"lOI9 U1 = u1;
Tw//!rp G U2 = u2; % Compute initial condition; save it in U
rs:Q%V
^ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_R7 w?!t8 w=2*pi*n./T;
v)):$s?WB g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
|) Pi6Y L=4; % length of evoluation to compare with S. Trillo's paper
W/r^ugDV dz=L/M1; % space step, make sure nonlinear<0.05
G
AQ
'Ti1! for m1 = 1:1:M1 % Start space evolution
t+Z`n(> u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
6^;^r Ulm u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
dv7 <AJ ca1 = fftshift(fft(u1)); % Take Fourier transform
Pdw#o^Iq^ ca2 = fftshift(fft(u2));
,- '4L9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
C0fmmI0z~ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
8Bpip u2 = ifft(fftshift(c2)); % Return to physical space
C c*( { u1 = ifft(fftshift(c1));
~F w<eY if rem(m1,J) == 0 % Save output every J steps.
pUCK-rL U1 = [U1 u1]; % put solutions in U array
&aPl`"j U2=[U2 u2];
MdC<4^| MN1=[MN1 m1];
xhw-2dl*H z1=dz*MN1'; % output location
cS|VJWgTZ end
,+._;[k end
b U` =* hg=abs(U1').*abs(U1'); % for data write to excel
2yKz-"E ha=[z1 hg]; % for data write to excel
5j{N p,K t1=[0 t'];
j$x )pB3 ] hh=[t1' ha']; % for data write to excel file
S &JJIFftO %dlmwrite('aa',hh,'\t'); % save data in the excel format
n|i" S` figure(1)
\DA$6w\\ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
wqD5d
figure(2)
~O;y?]U waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
`.=sTp2rbc _8><| 3d 非线性超快脉冲耦合的数值方法的Matlab程序 n#*`!# t`G)b&3_O 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
\M(* =5 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+l?; ) *7" L]6 *Oo &}oAj e *]r % This Matlab script file solves the nonlinear Schrodinger equations
{J]-<:XD % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
[f!O6moR6 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
{8@\Ij % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
G>
\T bx )%Ru #}1X6 C=1;
x*}bo))hb M1=120, % integer for amplitude
?a.+j8pbGg M3=5000; % integer for length of coupler
|}[nH> N = 512; % Number of Fourier modes (Time domain sampling points)
EO)%UrWnC dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
"Xn%at4 T =40; % length of time:T*T0.
%f& < wC dt = T/N; % time step
](K0Fwo`;" n = [-N/2:1:N/2-1]'; % Index
VC- ;S7k t = n.*dt;
5j ^NV&/_ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
2~c~{ jl\ w=2*pi*n./T;
O~ @fXMthh g1=-i*ww./2;
z`$J_Cj Y g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
;(6P6@+o g3=-i*ww./2;
'C?NJ~MN P1=0;
XU-m"_t P2=0;
ml u 3K P3=1;
N.j
"S'(i P=0;
bAF )Bli for m1=1:M1
.px:e)iW p=0.032*m1; %input amplitude
~]uZy=P? 5 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
x5Zrz<Y$w s1=s10;
^_>!B) s20=0.*s10; %input in waveguide 2
0ys~2Y!eH s30=0.*s10; %input in waveguide 3
nr\q7 s2=s20;
+F@_Es<6 s3=s30;
w'ybbv{c p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
@"|i"Hk^ %energy in waveguide 1
Lz4eh WntO p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
M{N(~ql %energy in waveguide 2
K7`YJp`i p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
. (`3JQ2s %energy in waveguide 3
Mm= Mz for m3 = 1:1:M3 % Start space evolution
tRfm+hqRZ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
y' x F0 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
{'bip`U. s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
\pY^^ l* sca1 = fftshift(fft(s1)); % Take Fourier transform
X
K>&$<5{ sca2 = fftshift(fft(s2));
$v27]"] sca3 = fftshift(fft(s3));
3/goCg sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
k#)Ad*t sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
&%F@O<: sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
rPiNv
30L s3 = ifft(fftshift(sc3));
q<{NO/Mm s2 = ifft(fftshift(sc2)); % Return to physical space
8+'C_t/0i s1 = ifft(fftshift(sc1));
z, f=}t[.Y end
cT' w= p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
P-Su5F p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
E{Vo'!LY p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
SUdm 0y P1=[P1 p1/p10];
RKkGITDk P2=[P2 p2/p10];
K|^wc$ P3=[P3 p3/p10];
Ruaur] P=[P p*p];
sbsu(Sz+ end
.BZ VX=x figure(1)
qfL-r,XS`F plot(P,P1, P,P2, P,P3);
t#~?{i@m #hx yO q, 转自：
http://blog.163.com/opto_wang/
