计算脉冲在非线性耦合器中演化的Matlab 程序 Q8i6kf! O!tD1^O!1} % This Matlab script file solves the coupled nonlinear Schrodinger equations of
37Y]sJrs$ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
=ndKG5 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
qC1@p?8$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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"#Fz :~Y$\Ww(~ %fid=fopen('e21.dat','w');
ow "Xv N = 128; % Number of Fourier modes (Time domain sampling points)
7/L7L5h< M1 =3000; % Total number of space steps
67?5Cv J =100; % Steps between output of space
_!zY(9% T =10; % length of time windows:T*T0
l H.2H T0=0.1; % input pulse width
$EF@x}h:A MN1=0; % initial value for the space output location
g=Di2j{A dt = T/N; % time step
|e\%pfZ n = [-N/2:1:N/2-1]'; % Index
_!7o t = n.*dt;
9j`-fs@: u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
8v K &d> u20=u10.*0.0; % input to waveguide 2
PQ>J oRs u1=u10; u2=u20;
-yeT $P&| U1 = u1;
tw66XxE U2 = u2; % Compute initial condition; save it in U
jL SZ#H ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_rd{cvdR w=2*pi*n./T;
iY-dM(_:] g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
,H*3_c&Q L=4; % length of evoluation to compare with S. Trillo's paper
s? Kn,6Y dz=L/M1; % space step, make sure nonlinear<0.05
P>|2~YxjU for m1 = 1:1:M1 % Start space evolution
9&cZIP u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
\BL9}5y u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
<=Qk^Y2k ca1 = fftshift(fft(u1)); % Take Fourier transform
jxvVp*-=<j ca2 = fftshift(fft(u2));
5oS\ uX| c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
eAMT7 2_ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
,"o \_{<z u2 = ifft(fftshift(c2)); % Return to physical space
"|if<hx+ u1 = ifft(fftshift(c1));
KXJHb{? if rem(m1,J) == 0 % Save output every J steps.
kN)ev?pQ[ U1 = [U1 u1]; % put solutions in U array
(&(f`c@I U2=[U2 u2];
JFZ p^{ MN1=[MN1 m1];
i weP3u## z1=dz*MN1'; % output location
W= !f end
#82B`y<<y/ end
rzu^br9X hg=abs(U1').*abs(U1'); % for data write to excel
T (qu~} ha=[z1 hg]; % for data write to excel
9!LA AE` t1=[0 t'];
'' 6 hh=[t1' ha']; % for data write to excel file
J5k% %dlmwrite('aa',hh,'\t'); % save data in the excel format
f@0`, figure(1)
&>o)7H]; waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
(]:G" W8f figure(2)
Qxwe,: waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
a;K:~R+@, XebCl{HHp 非线性超快脉冲耦合的数值方法的Matlab程序 y_6 HQ: S~T[*Z/m 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。
z2V !u\It 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
nFqMS|EN -LyI u# u tr_fFu Z(L>~+% % This Matlab script file solves the nonlinear Schrodinger equations
{)mlXo(On % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
rhrlEf@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
<\5{R@A*6 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
3r\QLIr L8 g=)@ yZ3>v C=1;
5M*p1 ^ > M1=120, % integer for amplitude
[Mi ~4b M3=5000; % integer for length of coupler
:9<5GF( N = 512; % Number of Fourier modes (Time domain sampling points)
{'1,JwSmb dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Nx 99dr T =40; % length of time:T*T0.
1 !sYd@iD@ dt = T/N; % time step
M0 |z^2 n = [-N/2:1:N/2-1]'; % Index
"jSn` t = n.*dt;
y.zW >Mfl ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&b_duWs w=2*pi*n./T;
x RfX:3 g1=-i*ww./2;
rZLMY M g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
.MKxHM7 g3=-i*ww./2;
[(C lvGx P1=0;
F Ekx&9] P2=0;
4
QWHGh" P3=1;
q
bo`E!K P=0;
Px<;-H` for m1=1:M1
R&?p^!`% p=0.032*m1; %input amplitude
HkrNt/] s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
,q 4 Y
N-3 s1=s10;
W|:WAxJ*d s20=0.*s10; %input in waveguide 2
Q]8r72uSk s30=0.*s10; %input in waveguide 3
`!i>fo~ s2=s20;
~%]+5^Ka] s3=s30;
o\N),;LM p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
]]+"`t,- %energy in waveguide 1
2'D2> ^os p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
>">-4L17m %energy in waveguide 2
.L}ar7 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
C`fQ` RL\ %energy in waveguide 3
/wQDcz for m3 = 1:1:M3 % Start space evolution
q N>j2~ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
dwRJ0D]& s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
~!I
\{( s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
i 9d.Ls sca1 = fftshift(fft(s1)); % Take Fourier transform
=dPrG=A sca2 = fftshift(fft(s2));
&a V`u?'e sca3 = fftshift(fft(s3));
& W1cc#( sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
T a_#Rg*! sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
5( 3tPbm{ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
$(BW |Pc s3 = ifft(fftshift(sc3));
~MOIrF s2 = ifft(fftshift(sc2)); % Return to physical space
HM`;%0T0( s1 = ifft(fftshift(sc1));
'h$1vT end
4g|}]K1s p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
0y?bwxkc p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
YQ]W<0( p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
|1#*`2j\=9 P1=[P1 p1/p10];
Ls( &. P2=[P2 p2/p10];
J=
T! P3=[P3 p3/p10];
b^0=X!bg P=[P p*p];
d+8Sypv^4* end
8/k* "^3 figure(1)
m}rUc29cS, plot(P,P1, P,P2, P,P3);
|(]XZ !{ lwSA!W 转自：
http://blog.163.com/opto_wang/
