计算脉冲在非线性耦合器中演化的Matlab 程序 -%Rw2@vU d"yJ0F % This Matlab script file solves the coupled nonlinear Schrodinger equations of
D<hX%VJ%M % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
/lC,5y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
?)ct@,Ek$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
2n+ud ?|l 6j8\3H~ %fid=fopen('e21.dat','w');
@SH[<c N = 128; % Number of Fourier modes (Time domain sampling points)
R$ !] z( M1 =3000; % Total number of space steps
u/<ZGW(&s( J =100; % Steps between output of space
x<`^4|< T =10; % length of time windows:T*T0
?0'e_s T0=0.1; % input pulse width
l{*m-u 5&; MN1=0; % initial value for the space output location
a ~YrQI- @ dt = T/N; % time step
-X_\3J n = [-N/2:1:N/2-1]'; % Index
k')H5h+Q= t = n.*dt;
LF `] =.Q u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
<ne?;P1L u20=u10.*0.0; % input to waveguide 2
,SPgop' u1=u10; u2=u20;
*s#6e} U1 = u1;
3ZC@q
#R
A U2 = u2; % Compute initial condition; save it in U
-Bq]E,Xf) ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<"K2t
Tg. w=2*pi*n./T;
]c v/dY# g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
fW C(L s L=4; % length of evoluation to compare with S. Trillo's paper
OLtXk dz=L/M1; % space step, make sure nonlinear<0.05
dWi< U4 for m1 = 1:1:M1 % Start space evolution
C =CZtjUt u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
(-Q~@Q1 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
2
FoLJ ca1 = fftshift(fft(u1)); % Take Fourier transform
xbxzB<yL ca2 = fftshift(fft(u2));
Y4w]jIv c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
}Ml BmD c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
H
"Io!{aKU u2 = ifft(fftshift(c2)); % Return to physical space
KWeE!f 7G u1 = ifft(fftshift(c1));
AFM+`{Cq if rem(m1,J) == 0 % Save output every J steps.
IhBQ1,&J U1 = [U1 u1]; % put solutions in U array
j D*<M/4 U2=[U2 u2];
mZXtHFMu MN1=[MN1 m1];
iITM BS`} z1=dz*MN1'; % output location
s FJ:09L| end
t*; KxQ+'? end
?hAO-* ); hg=abs(U1').*abs(U1'); % for data write to excel
\D k >dE&I ha=[z1 hg]; % for data write to excel
.N>*+U>>P t1=[0 t'];
FaWDAL=Vhk hh=[t1' ha']; % for data write to excel file
,}khu %dlmwrite('aa',hh,'\t'); % save data in the excel format
Pwj|]0Y@ figure(1)
* ] waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
3M(*q4A$" figure(2)
.#Nf0 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
e`U
6JzC "+4Jmf9 非线性超快脉冲耦合的数值方法的Matlab程序 WO{7/h</ 0 'THL%lK 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。
WUjRnzVM 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
pEz^z9 [E%g3>/mt VwR ZgL r~JGs?GH % This Matlab script file solves the nonlinear Schrodinger equations
CS(XN>N % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
9BpxbU+L; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
mA$86 X_ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
l53Q"ajG 94et ]u%7 C=1;
\2=I//YF M1=120, % integer for amplitude
DA iS|x M3=5000; % integer for length of coupler
sV-P R] N = 512; % Number of Fourier modes (Time domain sampling points)
? % 8%1d dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
M9o/ 6 T =40; % length of time:T*T0.
]cv|d c= dt = T/N; % time step
F-b]>3r n = [-N/2:1:N/2-1]'; % Index
nS h~ mP t = n.*dt;
9_d# F'#F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
f8SO:ihXL w=2*pi*n./T;
]" e'z g1=-i*ww./2;
cr<j<#(Z} g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
^&C/,,U g3=-i*ww./2;
^n<YO=|u P1=0;
i$p2am8f P2=0;
RM,aG}6M)M P3=1;
;-JF b$m P=0;
S[q:b
. for m1=1:M1
aNY-F)XWa p=0.032*m1; %input amplitude
ybsw{[X> M s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Dq<DW2It> s1=s10;
1fsNQ!vQP s20=0.*s10; %input in waveguide 2
aem gGw< s30=0.*s10; %input in waveguide 3
P
qC#[0Qy s2=s20;
?;htK_E\* s3=s30;
N?-ZvE\C p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
*k_<|{>j( %energy in waveguide 1
4i{Xs5zk p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
3M+rFB}tS %energy in waveguide 2
)`{m |\b p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
i!8"T# %energy in waveguide 3
A D<>)( for m3 = 1:1:M3 % Start space evolution
0>BI [x@ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
P(Rl/e yRM s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
LQr!0p.i" s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
"_LqIW1 sca1 = fftshift(fft(s1)); % Take Fourier transform
L7aVj&xM sca2 = fftshift(fft(s2));
Li|~% E1 sca3 = fftshift(fft(s3));
9 Xl#$d5 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
4H, c;g=! sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
:L+ xEL sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
#9r}Kr =P s3 = ifft(fftshift(sc3));
Yb`b / BMR s2 = ifft(fftshift(sc2)); % Return to physical space
z9OpMA s1 = ifft(fftshift(sc1));
jQ 'g'c! end
$z* "@ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
d>mZY66P p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
- E GZ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
J
;z`bk^ P1=[P1 p1/p10];
#BcUE?K*N P2=[P2 p2/p10];
,D*bLXWh P3=[P3 p3/p10];
@i V-pJ- P=[P p*p];
GRYw_}Aa end
zI,Qc60B figure(1)
et~D9='E plot(P,P1, P,P2, P,P3);
60{DR >S <`=Kt[_BQ 转自：
http://blog.163.com/opto_wang/
