计算脉冲在非线性耦合器中演化的Matlab 程序 es6]c%o:t^ "9^OT % This Matlab script file solves the coupled nonlinear Schrodinger equations of
L2Vj2o"x? % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
P9W!xvV`w % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
K!<3|d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_ ;!$1lM[ kgv29j?k ; %fid=fopen('e21.dat','w');
Q2)CbHSz N = 128; % Number of Fourier modes (Time domain sampling points)
6)h~9iK M1 =3000; % Total number of space steps
qlNB\~HCe J =100; % Steps between output of space
>7$h T =10; % length of time windows:T*T0
"n, %Hh T0=0.1; % input pulse width
* YR>u @ MN1=0; % initial value for the space output location
3nbTK3, dt = T/N; % time step
!r#36kO n = [-N/2:1:N/2-1]'; % Index
,Qh9}I7;C t = n.*dt;
hU~up a<dD u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
?^by 3\,VZ u20=u10.*0.0; % input to waveguide 2
d(_;@%p1X u1=u10; u2=u20;
N|3a(mtiZ' U1 = u1;
PiVp(; rtQ U2 = u2; % Compute initial condition; save it in U
= e"RE/q2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
x,fX mgE w=2*pi*n./T;
ev[!:*6P g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ml1My1 L=4; % length of evoluation to compare with S. Trillo's paper
B;A< pNT dz=L/M1; % space step, make sure nonlinear<0.05
UfNcI[xr for m1 = 1:1:M1 % Start space evolution
"<$JU@P u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
+Y_ ]< u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
uE ^uP@d ca1 = fftshift(fft(u1)); % Take Fourier transform
*v:o`{vM[ ca2 = fftshift(fft(u2));
S] R.:T_% c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
[!S%nYs&8L c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
1Xkl.FcFw u2 = ifft(fftshift(c2)); % Return to physical space
nkO4~p u1 = ifft(fftshift(c1));
6sQY)F7p if rem(m1,J) == 0 % Save output every J steps.
L$3{L"/ U1 = [U1 u1]; % put solutions in U array
jV.9d@EC U2=[U2 u2];
]^6r7nfR6| MN1=[MN1 m1];
ai]KH7 z1=dz*MN1'; % output location
iI$;%uY3g end
_x]q`[Dih end
[2.;gZj hg=abs(U1').*abs(U1'); % for data write to excel
[+wLy3_ ha=[z1 hg]; % for data write to excel
,KaO8^PB t1=[0 t'];
7Ml OBPh hh=[t1' ha']; % for data write to excel file
}Ryrd!3bY %dlmwrite('aa',hh,'\t'); % save data in the excel format
G<F B:?| figure(1)
X?z
CB waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
L Jw y,- figure(2)
;XI=Y"h{% waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ZRP[N)Ld$ A(1WQUu j 非线性超快脉冲耦合的数值方法的Matlab程序 `s\E"QeZN ^5Ob( FvU 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。
[N_)V kpr 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
*EF`s~ h%ba! l}XnCOIT, eEX* \1Gg % This Matlab script file solves the nonlinear Schrodinger equations
IQyw>_ ~] % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
;0nL1R]w( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
o(@^V!}V % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+<^c2diX ?#|in} C=1;
gCZm7dgo M1=120, % integer for amplitude
t]XF*fZH M3=5000; % integer for length of coupler
|6w {%xC?" N = 512; % Number of Fourier modes (Time domain sampling points)
'^ `% dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
yhxZ^ (I T =40; % length of time:T*T0.
_53N uEM1 dt = T/N; % time step
y:VY8a 4 n = [-N/2:1:N/2-1]'; % Index
)vD|VLV t = n.*dt;
L[. )!c8k ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
w^)_Fk3 w=2*pi*n./T;
ADT8A."R[ g1=-i*ww./2;
K{`3,U2Wx g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
# OsUF,NU g3=-i*ww./2;
}3 S6TJ+ P1=0;
<(x!P=NM- P2=0;
#F:\_!2c P3=1;
znNv;-q P=0;
N3&n"w _d for m1=1:M1
Z#flu Q%V p=0.032*m1; %input amplitude
8RJa;JsH s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
_MzdbUb5, s1=s10;
wQrD(Dv(yA s20=0.*s10; %input in waveguide 2
f=Kt [|%'e s30=0.*s10; %input in waveguide 3
43/!pW s2=s20;
DX<xkS[P s3=s30;
vve[.Lud' p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
1zIrU6H2;_ %energy in waveguide 1
s AlOX` t p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
vf
h*`G$ %energy in waveguide 2
Z]k+dJ[- p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
D lx-mm_ %energy in waveguide 3
r95$( N for m3 = 1:1:M3 % Start space evolution
3NlG,e'T2 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
G~19Vv*; s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
y9-}LET3j
s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
~.<}/GP] _ sca1 = fftshift(fft(s1)); % Take Fourier transform
b)+;@wa~ sca2 = fftshift(fft(s2));
l1D"*J 2` sca3 = fftshift(fft(s3));
m.>y(TI sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
ez^b{s` sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
ziG]BZ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
RRJN@|" s3 = ifft(fftshift(sc3));
=d1i<iw?- s2 = ifft(fftshift(sc2)); % Return to physical space
LO;Z3Q>#0 s1 = ifft(fftshift(sc1));
Kv#TJ n end
KL+, [M@ F p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
<UBB&}R0 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
%^<A` Q_ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
_|KeB(W P1=[P1 p1/p10];
k+As#7V P2=[P2 p2/p10];
)ja NFJ
3 P3=[P3 p3/p10];
\t+q1S1 P=[P p*p];
9|&%"~6' end
TDj jaO figure(1)
`I)ftj % plot(P,P1, P,P2, P,P3);
qh~S)^zFJ tC'@yX 转自：
http://blog.163.com/opto_wang/
