计算脉冲在非线性耦合器中演化的Matlab 程序 /5pVzv+rm BRyrdt*_e % This Matlab script file solves the coupled nonlinear Schrodinger equations of
6C7|e0 0v % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
`B-jwVrN( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
rUmaKh?v|X % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
\ W4|.[ f@rR2xZoQ
%fid=fopen('e21.dat','w');
~x4] ^XS N = 128; % Number of Fourier modes (Time domain sampling points)
C/_Z9LL?F M1 =3000; % Total number of space steps
!5 9u z4 J =100; % Steps between output of space
b9X "p*'p T =10; % length of time windows:T*T0
b"k1N9 T0=0.1; % input pulse width
P-U9FKrt MN1=0; % initial value for the space output location
{el[W,CT# dt = T/N; % time step
O4t0 VL$ n = [-N/2:1:N/2-1]'; % Index
V q4g#PcG t = n.*dt;
G
LU7?2`t u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
wN Mf- ~ u20=u10.*0.0; % input to waveguide 2
*sz:c3{_ u1=u10; u2=u20;
1L 3 +KD~ U1 = u1;
P OB6#x U2 = u2; % Compute initial condition; save it in U
~T">)Y~+xI ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
3e,"B
S)+ w=2*pi*n./T;
Q!.JV. ( g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
r^zra|] L=4; % length of evoluation to compare with S. Trillo's paper
C)hS^ D: dz=L/M1; % space step, make sure nonlinear<0.05
1K\z amBg for m1 = 1:1:M1 % Start space evolution
a!guZUg6 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
1# }}: u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
DsX+/)d ca1 = fftshift(fft(u1)); % Take Fourier transform
s`#g<_ {X ca2 = fftshift(fft(u2));
"d"6.ND c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
ZB+~ 0 [C c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
oDW)2*8yF u2 = ifft(fftshift(c2)); % Return to physical space
q!f'?yFYK u1 = ifft(fftshift(c1));
[$]qJ~kz if rem(m1,J) == 0 % Save output every J steps.
B5v5D[ o5 U1 = [U1 u1]; % put solutions in U array
tw
k U2=[U2 u2];
\&BT#8ELG MN1=[MN1 m1];
<*_DC)&7 9 z1=dz*MN1'; % output location
5LaF'>1yY end
[jnA? Ge: end
NWue;u^ hg=abs(U1').*abs(U1'); % for data write to excel
&a8%j+j ha=[z1 hg]; % for data write to excel
03Uj 0.Z|7 t1=[0 t'];
<]Btx;} hh=[t1' ha']; % for data write to excel file
!(A< %dlmwrite('aa',hh,'\t'); % save data in the excel format
d C>[[_ figure(1)
/`s{!t#Y waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
=[do([ A figure(2)
#u"$\[ G waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Yg V" *~ 1$_|h@ 非线性超快脉冲耦合的数值方法的Matlab程序 yU|=)p5 T3bYj|rh= 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。
rczwxWK 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
a! g j _ yRy^'E~ W
%<,G V ^Ycn&`s % This Matlab script file solves the nonlinear Schrodinger equations
?G>E[!8ev % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
\ lW*.< % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
gY {/)" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
BN 1,R] *; W4#E&8g% C=1;
]?sw<D{ M1=120, % integer for amplitude
pnpf/T{xpM M3=5000; % integer for length of coupler
n,#o6ali> N = 512; % Number of Fourier modes (Time domain sampling points)
xey?.2K1A dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
h9Tst)iRi T =40; % length of time:T*T0.
woUt* G@ dt = T/N; % time step
T_ j0*A $ n = [-N/2:1:N/2-1]'; % Index
{W' {A t = n.*dt;
"G!,gtA~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
RPw1i* w=2*pi*n./T;
I I]-mb g1=-i*ww./2;
Bo4iX,zu g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
wBCBZs$H g3=-i*ww./2;
a(_3271 P1=0;
D\Fu4Eg P2=0;
9 Xe|*bT P3=1;
_};T:GOT P=0;
g oZw![4l for m1=1:M1
'tDVSj p=0.032*m1; %input amplitude
8Xa{. y" s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
a;f A0_ s1=s10;
uCjbb s20=0.*s10; %input in waveguide 2
^f ] 9^U{ s30=0.*s10; %input in waveguide 3
\iH\N/ s2=s20;
PmA_cP7~ s3=s30;
u}-)ywX p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
5Z_aN|Xn %energy in waveguide 1
7I0K=
'D7 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
" y-/ 9C %energy in waveguide 2
_#yd0 E p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
P\3H<?@4 %energy in waveguide 3
mr+8[0 for m3 = 1:1:M3 % Start space evolution
)U+&XjK s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
7Ga'FT .F s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
}LwKi-G? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Lpk`qJ sca1 = fftshift(fft(s1)); % Take Fourier transform
T^@P.zX sca2 = fftshift(fft(s2));
-+n ? Q; sca3 = fftshift(fft(s3));
6C- !^8[f sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
*#Iqz9X.Y3 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
o(YF`;OhvS sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
P G*FIRDb s3 = ifft(fftshift(sc3));
m88[(l s2 = ifft(fftshift(sc2)); % Return to physical space
x8Nij: K# s1 = ifft(fftshift(sc1));
#{~3bgY end
oF.H?lG7` p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
U=N]XwjVK< p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
W;T (q~XK p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
4EFP*7X P1=[P1 p1/p10];
i&Me7=~ P2=[P2 p2/p10];
XBos ^Q P3=[P3 p3/p10];
oN[# C>#( P=[P p*p];
~2}^
-, end
&Ui&2 EW figure(1)
yHxi^D] plot(P,P1, P,P2, P,P3);
QD^"cPC)mM +||[H)qym 转自：
http://blog.163.com/opto_wang/
