计算脉冲在非线性耦合器中演化的Matlab 程序 */:uV
B,b2 aJ Z"D8C % This Matlab script file solves the coupled nonlinear Schrodinger equations of
V!v:]E % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
':{>a28= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
/!h;c$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
N IdZ WOzf]3Xcj %fid=fopen('e21.dat','w');
6AG`&'" N = 128; % Number of Fourier modes (Time domain sampling points)
wX >*H M1 =3000; % Total number of space steps
Hso|e?Z J =100; % Steps between output of space
jTO),
v: w T =10; % length of time windows:T*T0
Od f[* T0=0.1; % input pulse width
(T`E!A0I\? MN1=0; % initial value for the space output location
MZ+^-@ X dt = T/N; % time step
Xtt ? ] n = [-N/2:1:N/2-1]'; % Index
Bn@(zHG+5& t = n.*dt;
}\J2?Et{ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
fU=B4V4@ u20=u10.*0.0; % input to waveguide 2
8J$|NYv_b u1=u10; u2=u20;
x
}Ad_#q U1 = u1;
PB;eHy U2 = u2; % Compute initial condition; save it in U
1-lu\"H` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%_ !bRo w=2*pi*n./T;
VD_$$Gn*q g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
2hzsKkrA
{ L=4; % length of evoluation to compare with S. Trillo's paper
_ODbY;M dz=L/M1; % space step, make sure nonlinear<0.05
_S>JKz for m1 = 1:1:M1 % Start space evolution
(L^]Lk
x) u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
lpz2 m\ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
'Ut7{rZ5 ca1 = fftshift(fft(u1)); % Take Fourier transform
0lhVqy}:}o ca2 = fftshift(fft(u2));
! 1e6Ss c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
/p8dZ+X c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
%CK^Si%+ u2 = ifft(fftshift(c2)); % Return to physical space
|*}4 m'c u1 = ifft(fftshift(c1));
bv&; R if rem(m1,J) == 0 % Save output every J steps.
}Y;K~J U1 = [U1 u1]; % put solutions in U array
/!c${W!sY U2=[U2 u2];
d_IAs MN1=[MN1 m1];
|JQQU! x z1=dz*MN1'; % output location
Ii G6<|d8H end
"'D=,* end
)c `7( nY hg=abs(U1').*abs(U1'); % for data write to excel
@`gk|W3 ha=[z1 hg]; % for data write to excel
V4_ =<W t1=[0 t'];
dq] 0 X?[6 hh=[t1' ha']; % for data write to excel file
N; \' N
ne %dlmwrite('aa',hh,'\t'); % save data in the excel format
nDHTV !]< figure(1)
Z]B~{!W1 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
!QvZ<5( figure(2)
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waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
3\XU_Xs(] Y'8?.a]' 非线性超快脉冲耦合的数值方法的Matlab程序
5~>z h DAXX; 4 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。
Ft&]7dT{W 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
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fw ]=h) 1,% R;7J=g Y\No4w ^|d % This Matlab script file solves the nonlinear Schrodinger equations
b45-:mi!&# % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
~^1 {B\I % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
,%M$0poKM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4rLL[?? PK `D8)=u C=1;
2+e}*&iQpp M1=120, % integer for amplitude
ee^{hQi M3=5000; % integer for length of coupler
` Tv[DIVW N = 512; % Number of Fourier modes (Time domain sampling points)
njputEG X dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
eS~LF.^Jw T =40; % length of time:T*T0.
?`PvL!' dt = T/N; % time step
ui/a|Q n = [-N/2:1:N/2-1]'; % Index
%-1O.Q|f t = n.*dt;
' F9 jq ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Pu" P9 w=2*pi*n./T;
zd >t-?g g1=-i*ww./2;
&7K?w~ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
KV0]m ^@x g3=-i*ww./2;
%`1q-,>v P1=0;
ZzJ?L4J5v P2=0;
U_I5fK = P3=1;
|xd sl , P=0;
6\q]rfQ for m1=1:M1
K3#@SY j p=0.032*m1; %input amplitude
dtRwTUMe? s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
b?tB(if!I s1=s10;
%D\[* s20=0.*s10; %input in waveguide 2
x"~8*V'0 s30=0.*s10; %input in waveguide 3
#."-#"0 s2=s20;
Q7jb'y$ozO s3=s30;
z`f($t[ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
#_^Lb]jk M %energy in waveguide 1
Ac2n p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
2y;Skp %energy in waveguide 2
VJ] JjB
j p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
'!!CeDy %energy in waveguide 3
.$+#1- for m3 = 1:1:M3 % Start space evolution
F%@aB<Nu s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
/<|%yE&KhJ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
*zb Nd: i9 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Whm ,F^ sca1 = fftshift(fft(s1)); % Take Fourier transform
. 6+Z^,3 sca2 = fftshift(fft(s2));
dMv=gdY sca3 = fftshift(fft(s3));
$5aV:Z3P sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
4.[^\N sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
l5!|I:/*; sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
N frw0b s3 = ifft(fftshift(sc3));
^/I
7|u] s2 = ifft(fftshift(sc2)); % Return to physical space
OEA&~4&{7 s1 = ifft(fftshift(sc1));
SB H(y ) end
P}n_IV*@ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
{?}E^5Z*g p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
R3gdLa. p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
r*2+xDoEi P1=[P1 p1/p10];
L*xhGoC= P2=[P2 p2/p10];
5Ha9lM2gh P3=[P3 p3/p10];
RzE_K' M P=[P p*p];
ls\WXCH end
S&Zm0Ku figure(1)
. qO @Q = plot(P,P1, P,P2, P,P3);
C~,a!qY 5F)C jQ 转自：
http://blog.163.com/opto_wang/
