计算脉冲在非线性耦合器中演化的Matlab 程序 O)&V}h U* &Y\`FY\ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
IF<jq\M % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
H=*;3 gM,' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
O5E \#*<K % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
,}J(& \h :$q E7 %fid=fopen('e21.dat','w');
o_ {-X 1w N = 128; % Number of Fourier modes (Time domain sampling points)
JVN0];IL} M1 =3000; % Total number of space steps
l@':mX3xd J =100; % Steps between output of space
"zv?qS T =10; % length of time windows:T*T0
T$SGf.- T0=0.1; % input pulse width
&)1 +WrU MN1=0; % initial value for the space output location
W<\KRF$S; dt = T/N; % time step
F6yMk% n = [-N/2:1:N/2-1]'; % Index
t X)^$3A t = n.*dt;
* !vwW
T u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
6m?}oMz u20=u10.*0.0; % input to waveguide 2
o H$4 K8j u1=u10; u2=u20;
@2V#bK U1 = u1;
{"-u aH>, U2 = u2; % Compute initial condition; save it in U
u1rT:\G1 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
L )kwMk w=2*pi*n./T;
H|5\c= g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
d7A vx L=4; % length of evoluation to compare with S. Trillo's paper
2>p>AvcK dz=L/M1; % space step, make sure nonlinear<0.05
ZPRkk?M}. for m1 = 1:1:M1 % Start space evolution
%R." u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
sZ_+6+ : u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
[ 8[g_ ca1 = fftshift(fft(u1)); % Take Fourier transform
;~F&b:CyG ca2 = fftshift(fft(u2));
!2=< MO c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
bDK72cQ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
eqV;4dhm u2 = ifft(fftshift(c2)); % Return to physical space
lx(kbSxF u1 = ifft(fftshift(c1));
T:dV[3 if rem(m1,J) == 0 % Save output every J steps.
@w?hX K= U1 = [U1 u1]; % put solutions in U array
^Yul|0*J U2=[U2 u2];
@!`x^Tzz MN1=[MN1 m1];
| bDUekjR z1=dz*MN1'; % output location
T@Mrbravc end
)CKPzNf end
e-Mei7{% hg=abs(U1').*abs(U1'); % for data write to excel
.]24V!J(1w ha=[z1 hg]; % for data write to excel
;L r]w8 d t1=[0 t'];
zb.dVK`7N- hh=[t1' ha']; % for data write to excel file
vL}e1V: %dlmwrite('aa',hh,'\t'); % save data in the excel format
' >4 H#tu figure(1)
o !bV;] waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
d0YDNP%,_ figure(2)
sN"<baZ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
U4M}E h8 HHzA mHt 非线性超快脉冲耦合的数值方法的Matlab程序 `)?N7g[ \u it77x3Mm
F 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
W"$sN8K>) 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
\SKobO?qI /-s-W<S[ ZMEU4?F n< 3qr}ZG^ % This Matlab script file solves the nonlinear Schrodinger equations
d;@"Naw % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
fR h}n ^X % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
B63pu X{u# % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
xl>8B/Zmf# j]P'xrWl]8 C=1;
eCFMWFh C M1=120, % integer for amplitude
, Ox$W M3=5000; % integer for length of coupler
}JI@f14 N = 512; % Number of Fourier modes (Time domain sampling points)
H< 51dJn~ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
2fN2!OT T =40; % length of time:T*T0.
\:y oS>G dt = T/N; % time step
%>Q[j`9y n = [-N/2:1:N/2-1]'; % Index
\w#)uYK{i_ t = n.*dt;
XC vL` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
v9*31Jx w=2*pi*n./T;
?*LVn~y g1=-i*ww./2;
[8jIu&tJf g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
4Dy|YH$>S g3=-i*ww./2;
x/N jdK P1=0;
i/|}#yw8A P2=0;
sD#*W< P3=1;
/Ixv{H)H P=0;
hU'h78bt( for m1=1:M1
{f"oqry_g p=0.032*m1; %input amplitude
YC[c QX s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Q%r KKOX8 s1=s10;
Lo,u H`qU s20=0.*s10; %input in waveguide 2
\Vb|bw'e( s30=0.*s10; %input in waveguide 3
QZ&
4W s2=s20;
gx9=L&=d s3=s30;
&ea6YQ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Y[!s:3\f %energy in waveguide 1
{ k>T*/ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
[]:&WA 9N %energy in waveguide 2
7?ICXhu9 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
"*< )pnJ %energy in waveguide 3
7y4jk for m3 = 1:1:M3 % Start space evolution
hh!4 DHv s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
"O~7s} s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
nD.K*# u s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
i" #pk"@` sca1 = fftshift(fft(s1)); % Take Fourier transform
^ 6b27_= sca2 = fftshift(fft(s2));
y* *YFQ*sc sca3 = fftshift(fft(s3));
$+|.
@ss sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
:Z%-&) F sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
@.)WS\Cv#E sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
]w0_!Z& s3 = ifft(fftshift(sc3));
?U+nR/H:6 s2 = ifft(fftshift(sc2)); % Return to physical space
(<2!^v0.M s1 = ifft(fftshift(sc1));
&6e A. end
yXQ 28A p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
`*WzHDv5p p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
]TVc 'G; p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
#+&"m7
s P1=[P1 p1/p10];
oP~%7J t P2=[P2 p2/p10];
~6=aoF5"3? P3=[P3 p3/p10];
;Wgkf_3 P=[P p*p];
=%SH2kb end
+#L'g c figure(1)
U1Y0G[i) plot(P,P1, P,P2, P,P3);
_Un*x5u2O GXi)3I% 转自：
http://blog.163.com/opto_wang/
