计算脉冲在非线性耦合器中演化的Matlab 程序 J3V=
46Yc ,L2ZinU: % This Matlab script file solves the coupled nonlinear Schrodinger equations of
%6 zB Sje % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
6Gl J>r+n % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Qp5VP@t % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-m zIT4 XX TL.. %fid=fopen('e21.dat','w');
,Fl)^Gl8? N = 128; % Number of Fourier modes (Time domain sampling points)
?>:g?. + M1 =3000; % Total number of space steps
0 ] ,r0 J =100; % Steps between output of space
4\N ;2N T =10; % length of time windows:T*T0
P bn*_/H T0=0.1; % input pulse width
/{ J4:N'B> MN1=0; % initial value for the space output location
L<cx:Vz dt = T/N; % time step
H7Rx>h_ n = [-N/2:1:N/2-1]'; % Index
C3f' {} t = n.*dt;
.NC!7+1m u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
9<?M 8_ u20=u10.*0.0; % input to waveguide 2
M]
%?>G u1=u10; u2=u20;
[85spub&} U1 = u1;
8NJqV+jn)t U2 = u2; % Compute initial condition; save it in U
yxQ1`'[CR ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
n38p !oS w=2*pi*n./T;
@i_FTN g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
jRlYU`? L=4; % length of evoluation to compare with S. Trillo's paper
BwEN ~2u6 dz=L/M1; % space step, make sure nonlinear<0.05
fplo w for m1 = 1:1:M1 % Start space evolution
y14;%aQN u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
|^I0dR/w: u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
;8&3 dm] ca1 = fftshift(fft(u1)); % Take Fourier transform
~Ffo-Nd- ca2 = fftshift(fft(u2));
?! :ha;n c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
NA`SyKtg_ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
`?rSlR@+[I u2 = ifft(fftshift(c2)); % Return to physical space
B]wk+8SMY. u1 = ifft(fftshift(c1));
H RC T } if rem(m1,J) == 0 % Save output every J steps.
)EuvRLo{S7 U1 = [U1 u1]; % put solutions in U array
1=c\Rr9] U2=[U2 u2];
9L?. m& MN1=[MN1 m1];
Fyx|z'4b z1=dz*MN1'; % output location
M)+H{5bt end
`AtBtjs RV end
X7 MM2V hg=abs(U1').*abs(U1'); % for data write to excel
U$.@]F4& ha=[z1 hg]; % for data write to excel
T*Exs|N2P- t1=[0 t'];
n nEgx;Nl0 hh=[t1' ha']; % for data write to excel file
P ) "m0Lu< %dlmwrite('aa',hh,'\t'); % save data in the excel format
nNV'O(x} figure(1)
ZF8 yw(z waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
N)| yu1S figure(2)
~
'cmSiz- waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
}'V5/>m[ 6vo;! V6 非线性超快脉冲耦合的数值方法的Matlab程序 `2WFk8) F t#})Awy^R 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。
] @c+]{ 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
#U4F0BdA 33x {CY15 jXx<`I+] 4r#= * % This Matlab script file solves the nonlinear Schrodinger equations
wE>\7a*P% % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
{X+3;& @ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
iRb T/cc{ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-UEZ#Q )p0^zv{ C=1;
!u[9a;Sa# M1=120, % integer for amplitude
$y &E(J M3=5000; % integer for length of coupler
+F` S>U N = 512; % Number of Fourier modes (Time domain sampling points)
;-lXU0}& dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Wx}8T[A} T =40; % length of time:T*T0.
z"L/G dt = T/N; % time step
Lc,Pom n = [-N/2:1:N/2-1]'; % Index
m+R [#GE8# t = n.*dt;
jl$ece5v ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
rig,mv w=2*pi*n./T;
t;Sb/ 3 g1=-i*ww./2;
`/XY>T}- g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
M61 xPq8y5 g3=-i*ww./2;
Su7?;Oh/yI P1=0;
_$Yk M, P2=0;
y/{fX(aV P3=1;
nZyX|SPk P=0;
YMcD|Kb p for m1=1:M1
H3 ^},. p=0.032*m1; %input amplitude
a=9:[ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
ay
;S4c/_ s1=s10;
gMmaK0uhS s20=0.*s10; %input in waveguide 2
!4R WYMV " s30=0.*s10; %input in waveguide 3
SI-q C s2=s20;
5h-SCB>P s3=s30;
rC% *$g $ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
C. yQ=\U2 %energy in waveguide 1
z uad~%D<I p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
9G#n 0&wRJ %energy in waveguide 2
ColV8oVnU p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
4y?n
[/M/ %energy in waveguide 3
2j88<Yh]H for m3 = 1:1:M3 % Start space evolution
1>_8d"<Gd s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Smn;(K s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
,+DG2u s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
O7m(o:t x3 sca1 = fftshift(fft(s1)); % Take Fourier transform
^R7lom. sca2 = fftshift(fft(s2));
QL&Z jSN sca3 = fftshift(fft(s3));
-` kW&I0 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
X ::JV7hu sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
ThajH K|U sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
t7Iv?5]N s3 = ifft(fftshift(sc3));
IqaT?+O\?r s2 = ifft(fftshift(sc2)); % Return to physical space
N=5a54!/ s1 = ifft(fftshift(sc1));
!Vn\u end
Bi 3<7 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
s4y73-J^.v p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
N 1}sHyVq7 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
KE5kOU; P1=[P1 p1/p10];
*=/ { HvJ P2=[P2 p2/p10];
-hGk?_Nqa/ P3=[P3 p3/p10];
3tIVXtUCUk P=[P p*p];
x;P_1J%Q end
/tx]5`#@7] figure(1)
kX7C3qdmt plot(P,P1, P,P2, P,P3);
x:NY \._ r1`x=r
转自：
http://blog.163.com/opto_wang/
