计算脉冲在非线性耦合器中演化的Matlab 程序 iEe#aO"D! Rw/Ciw2@? % This Matlab script file solves the coupled nonlinear Schrodinger equations of
,|A{!j` % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Jlz9E|*qV % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}H5/3be % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Gj)uy jct NfOp=X?Y %fid=fopen('e21.dat','w');
b##1hm~+9 N = 128; % Number of Fourier modes (Time domain sampling points)
$ND90my M1 =3000; % Total number of space steps
URLk9PI J =100; % Steps between output of space
.ByU T =10; % length of time windows:T*T0
+3)[> {~1Z T0=0.1; % input pulse width
X'jr|s^s MN1=0; % initial value for the space output location
Wy8,<K{ dt = T/N; % time step
9Eu #l V n = [-N/2:1:N/2-1]'; % Index
D@:"f?K> t = n.*dt;
MJ A~jjy4 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
w1c w1xX* u20=u10.*0.0; % input to waveguide 2
{!MVc<G. u1=u10; u2=u20;
loBtd%wY U1 = u1;
6W$rY] h! U2 = u2; % Compute initial condition; save it in U
BD4`eiu" ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
IKo;9|2U w=2*pi*n./T;
SYeE) mI
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Ox~ 9_d L=4; % length of evoluation to compare with S. Trillo's paper
W-ez[ raY dz=L/M1; % space step, make sure nonlinear<0.05
1TIlINlJ for m1 = 1:1:M1 % Start space evolution
>gnF]< u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Hv8H.^D> u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
b[yE~EQxr ca1 = fftshift(fft(u1)); % Take Fourier transform
>K5~:mx#3 ca2 = fftshift(fft(u2));
@UV{:]f ~e c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
gJK KR]4* c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
>J@egIKzP u2 = ifft(fftshift(c2)); % Return to physical space
F3Ap1-%z u1 = ifft(fftshift(c1));
^4 8\>-Q\ if rem(m1,J) == 0 % Save output every J steps.
F3Dt7q U1 = [U1 u1]; % put solutions in U array
+aj^Cs1$ U2=[U2 u2];
P.h.M A] MN1=[MN1 m1];
Je@ k iE z1=dz*MN1'; % output location
9ad6uTc end
[IMQIX end
{-h, ZdH^ hg=abs(U1').*abs(U1'); % for data write to excel
*i@T!O(1)M ha=[z1 hg]; % for data write to excel
v8~YR'T0`V t1=[0 t'];
.it2NS hh=[t1' ha']; % for data write to excel file
Zih ?Bm %dlmwrite('aa',hh,'\t'); % save data in the excel format
tt{`\1q figure(1)
E(;i> waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
p[-{]! figure(2)
. ,R4WA, waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
YZ **;"<G r )8z#W>s 非线性超快脉冲耦合的数值方法的Matlab程序 y l/a:Q 0;<OYbm3< 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。
fI]b zv; 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
.8(%4ejJ( *KJ7nRKx(w I7zn>^0} SX_ 4=^ % This Matlab script file solves the nonlinear Schrodinger equations
5r7h=[ N % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
>)3Vb O % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
lkwh'@s. % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
DEtf(lW_ `)tA
YH C=1;
tl^ m=(ZQ M1=120, % integer for amplitude
qd8pF!u|# M3=5000; % integer for length of coupler
TY6
rwU N = 512; % Number of Fourier modes (Time domain sampling points)
?bI?GvSh dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
'\t7jQ T =40; % length of time:T*T0.
0Cq!\nzz dt = T/N; % time step
P7r4ePtLk{ n = [-N/2:1:N/2-1]'; % Index
Noz&noq t = n.*dt;
-_|]N/v\ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
A {(T'/~" w=2*pi*n./T;
s.rT] g1=-i*ww./2;
}e2F{pQ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
1Is%] 6 g3=-i*ww./2;
G#lg|# -# P1=0;
RJPcn)@l P2=0;
@w oC8X P3=1;
9wMEvX70 P=0;
)eq}MaW+j for m1=1:M1
l &|)O6N p=0.032*m1; %input amplitude
2d~LNy s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
ohsH 2]C s1=s10;
g ;LVECk s20=0.*s10; %input in waveguide 2
_+n;A46 s30=0.*s10; %input in waveguide 3
Fr; lG s2=s20;
^#w{/C/n s3=s30;
x.\XUJ4x p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
QkE,T0,/?h %energy in waveguide 1
ZqP7@fO_% p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
k/bque %energy in waveguide 2
o8tS p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
/{R3@,D[] %energy in waveguide 3
GA ik;R for m3 = 1:1:M3 % Start space evolution
XN(tcdCG s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
1LyT7h s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
@>:i -5 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
6ZOAmH fs sca1 = fftshift(fft(s1)); % Take Fourier transform
AsAFUuI sca2 = fftshift(fft(s2));
"*bk{)dz} sca3 = fftshift(fft(s3));
Y-]YDXrPQ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
iD`k"\>9 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
h>|u:]I> sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
L~
2q1 s3 = ifft(fftshift(sc3));
;Z4o{(/zU s2 = ifft(fftshift(sc2)); % Return to physical space
~lk@6{`l|1 s1 = ifft(fftshift(sc1));
quRPg) end
B0"0_ n7- p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
[-]A^?yBM p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
hb<k]-'! p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
5v3RVaq Z P1=[P1 p1/p10];
2/ EK`S P2=[P2 p2/p10];
FW5}oD( H P3=[P3 p3/p10];
zv@bI~3~ P=[P p*p];
EIPnm%{1 end
6J"(xT figure(1)
KqK9X plot(P,P1, P,P2, P,P3);
NhC Av + hMWo\qM 转自：
http://blog.163.com/opto_wang/
