计算脉冲在非线性耦合器中演化的Matlab 程序 gZQ,br* ni$7)YcF % This Matlab script file solves the coupled nonlinear Schrodinger equations of
V_*T Y6 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
X!r9 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Tdvw7I- q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
c%,~ 1l e >W}3H5w0 %fid=fopen('e21.dat','w');
W#1t%hT$ N = 128; % Number of Fourier modes (Time domain sampling points)
C"w>U M1 =3000; % Total number of space steps
,<]X0;~oB J =100; % Steps between output of space
}{<@wE%s T =10; % length of time windows:T*T0
6X{RcX]/ T0=0.1; % input pulse width
m:@-]U@ 6 MN1=0; % initial value for the space output location
r9@4-U7v& dt = T/N; % time step
Y'6GY*d L n = [-N/2:1:N/2-1]'; % Index
8':^tMd t = n.*dt;
,1 +AfI u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
u'"VbW3u n u20=u10.*0.0; % input to waveguide 2
5N=QS1<$5 u1=u10; u2=u20;
L$*sv. U1 = u1;
)sg@HFhY' U2 = u2; % Compute initial condition; save it in U
Qx,jUL#2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Zr`pOUk!4 w=2*pi*n./T;
{L 7O{:J g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
:BFecS&i5 L=4; % length of evoluation to compare with S. Trillo's paper
lc%2fVG-e dz=L/M1; % space step, make sure nonlinear<0.05
i^LLKx7M& for m1 = 1:1:M1 % Start space evolution
0_7A
< u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
}r`m(z$ z u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
(9bFIvMc ca1 = fftshift(fft(u1)); % Take Fourier transform
cnfjO g'\{ ca2 = fftshift(fft(u2));
8:V:^`KaSs c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
5x";}Vp>P c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
-:w+`x?XaB u2 = ifft(fftshift(c2)); % Return to physical space
}lZfZ?oAz u1 = ifft(fftshift(c1));
d\Q~L 3x if rem(m1,J) == 0 % Save output every J steps.
vMOI&_[\z U1 = [U1 u1]; % put solutions in U array
#k D8U# U2=[U2 u2];
FF]xwptrx MN1=[MN1 m1];
A 8bDg:G1i z1=dz*MN1'; % output location
1^<R2x end
O=c^Ak end
7;H!F!K] hg=abs(U1').*abs(U1'); % for data write to excel
Nrp0z: ha=[z1 hg]; % for data write to excel
RtZK2 t1=[0 t'];
~4HS
2\ hh=[t1' ha']; % for data write to excel file
u;$g1 3 %dlmwrite('aa',hh,'\t'); % save data in the excel format
WVPnyVDc figure(1)
CT1)tRN waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
L[4Su;D figure(2)
8sm8L\- waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ZuV/!9qU FM\yf ]' 非线性超快脉冲耦合的数值方法的Matlab程序 {%WQQs
c=? =u 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
qi !Nv$e 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
7}+U;0,) &m@~R | +r0ItqkM 3\J-=U % This Matlab script file solves the nonlinear Schrodinger equations
kaBP& 6|Z
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
}%z {tn % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
F2QX ^* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
iQry X(z hq}kAv4B= C=1;
_=ani9E]uF M1=120, % integer for amplitude
+S!gS|8P M3=5000; % integer for length of coupler
ESdjDg$[u N = 512; % Number of Fourier modes (Time domain sampling points)
l (;~9u0sa dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
DQ'yFPE T =40; % length of time:T*T0.
2 , bo dt = T/N; % time step
*`]LbS n = [-N/2:1:N/2-1]'; % Index
R0>GM`{ t = n.*dt;
6$#p}nE ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:xdl I`S w=2*pi*n./T;
!)1r{u g1=-i*ww./2;
` d rds g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
eJWcr Vpn g3=-i*ww./2;
5#Z> }@/ P1=0;
fJ
\bm P2=0;
?f{{{0$S P3=1;
obYXDj2 P=0;
>f 7;45i for m1=1:M1
JO*} \Es p=0.032*m1; %input amplitude
v6r,2Va/ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-rC_8.u : s1=s10;
Q
a(>$. h s20=0.*s10; %input in waveguide 2
>z &|<H% s30=0.*s10; %input in waveguide 3
6I,^4U s2=s20;
fQZ,kl s3=s30;
y7)s0g>%H p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Qrr8i:Y^ %energy in waveguide 1
\[m{ &%^G p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
,{{e'S9cy %energy in waveguide 2
Yvky =RM p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Jzqv6A3G %energy in waveguide 3
RweK<Flo'S for m3 = 1:1:M3 % Start space evolution
%`r Z]^H s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
FT0HU<." 1 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
F(j vdq s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
e;QPn( sca1 = fftshift(fft(s1)); % Take Fourier transform
+k@$C,A sca2 = fftshift(fft(s2));
nP9zTa sca3 = fftshift(fft(s3));
8t{- sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
E038p]M! sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
``l7|b j J sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
P2lDi!q| s3 = ifft(fftshift(sc3));
IhIPy~Hgt s2 = ifft(fftshift(sc2)); % Return to physical space
u 3&9R)J1 s1 = ifft(fftshift(sc1));
zq(R !a6 end
$9_yD&& p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
XYeuYLut p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
nYf Z[Q>v p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
#0yU
K5J P1=[P1 p1/p10];
x3dP`<
P2=[P2 p2/p10];
{yPJYF_l P3=[P3 p3/p10];
nq9|cS% - P=[P p*p];
y]dA<d?u end
MiB"Cc U figure(1)
"qb1 jv#to plot(P,P1, P,P2, P,P3);
4dfR}C 0~.OMG:= 转自：
http://blog.163.com/opto_wang/
