计算脉冲在非线性耦合器中演化的Matlab 程序 4w5);x. g{^~g % This Matlab script file solves the coupled nonlinear Schrodinger equations of
I%:\"g "c % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
t>! Ok % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
74r$)\q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$f?GD<}?7r &u2H^ j %fid=fopen('e21.dat','w');
Z`<5SHQd N = 128; % Number of Fourier modes (Time domain sampling points)
X;]I jha<* M1 =3000; % Total number of space steps
B~B, L*kC2 J =100; % Steps between output of space
ezb*tN! T =10; % length of time windows:T*T0
3Fw7q" T0=0.1; % input pulse width
N*+ L'bO MN1=0; % initial value for the space output location
yV*jc`1
dt = T/N; % time step
Rt>mAU$} n = [-N/2:1:N/2-1]'; % Index
k+BY 3a t = n.*dt;
@jCMQYR u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
4sq](! A u20=u10.*0.0; % input to waveguide 2
o3$dl`' u1=u10; u2=u20;
{T -=&%|| U1 = u1;
,N1pw w? U2 = u2; % Compute initial condition; save it in U
!dq$qUl/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
$0R5 ]]db) w=2*pi*n./T;
{)(Mkm +d g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
q P0UcG L=4; % length of evoluation to compare with S. Trillo's paper
@ZRg9M:N dz=L/M1; % space step, make sure nonlinear<0.05
Gz52^O : for m1 = 1:1:M1 % Start space evolution
f0879(,i u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
1 -$+@Xl u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Eh^gR`I ca1 = fftshift(fft(u1)); % Take Fourier transform
: {
iK 5 ca2 = fftshift(fft(u2));
5"y)<VLJX c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
g:Q:cSg< c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
+%H=+fJ2} u2 = ifft(fftshift(c2)); % Return to physical space
#jJ0Mxg u1 = ifft(fftshift(c1));
MOPHu
O{^ if rem(m1,J) == 0 % Save output every J steps.
%l,CJd5 U1 = [U1 u1]; % put solutions in U array
$_3 )m U2=[U2 u2];
h$mGaw vZ~ MN1=[MN1 m1];
*R}p9;dpO z1=dz*MN1'; % output location
m>|7&l_ end
jvxCCYXR end
0{
_6le] hg=abs(U1').*abs(U1'); % for data write to excel
|ZC' a! ha=[z1 hg]; % for data write to excel
P%ThW9^vnj t1=[0 t'];
Y9I|s{~ hh=[t1' ha']; % for data write to excel file
KrR`A(=WL %dlmwrite('aa',hh,'\t'); % save data in the excel format
@Ko#n DEq figure(1)
=KAN|5yn waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
F"cZ$TL] figure(2)
qHgzgS7a waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
R13V }yL ~^'WHuz Py 非线性超快脉冲耦合的数值方法的Matlab程序 X#Ob^E%J l[ i1,4 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
D<:zw/IRE Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1/,~0N9 1;PI%++ *2fJ dY E62_k
0q % This Matlab script file solves the nonlinear Schrodinger equations
M2;6Cz>,P % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
q6b&b^r+H % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
4 L
5$=V % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_Fn`G .r< Z?d] [zGw C=1;
sgnc$ x" M1=120, % integer for amplitude
` 4?|yp.|L M3=5000; % integer for length of coupler
mN> (n+ly N = 512; % Number of Fourier modes (Time domain sampling points)
NB5lxaL dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
F@HJ3O9 T =40; % length of time:T*T0.
:Gzp
(@<@e dt = T/N; % time step
GvvKM=1 n = [-N/2:1:N/2-1]'; % Index
6oFA=CjU{ t = n.*dt;
}#2(WHf =< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
F(ZczwvR w=2*pi*n./T;
3bJ|L3G g1=-i*ww./2;
'vYt_T g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
q: X^V$` g3=-i*ww./2;
u%6b |M@P P1=0;
hd,O/-m# P2=0;
-r]L MQ P3=1;
7G7"Zule*j P=0;
bR1Q77<G\ for m1=1:M1
}: u -l3e p=0.032*m1; %input amplitude
Bj"fUI!dK s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
<:&{ c-f/ s1=s10;
lauq(aD_C s20=0.*s10; %input in waveguide 2
ZD7qw*3+ s30=0.*s10; %input in waveguide 3
,b5vnW\ s2=s20;
N7KG_o% s3=s30;
^. p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
P RNq8nmxC %energy in waveguide 1
sl(go^ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
K r<UPr %energy in waveguide 2
yqtaQ0F~ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
];5Auh 0o %energy in waveguide 3
r:Q=6j, for m3 = 1:1:M3 % Start space evolution
B9Wd
' s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
G'';VoW= s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
I~Qi):&x s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
| 7 Ab _ sca1 = fftshift(fft(s1)); % Take Fourier transform
)D) 4=LJ sca2 = fftshift(fft(s2));
fU\;\ sca3 = fftshift(fft(s3));
6#.9T;& sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
~=t9-AF- sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
a#x@ e?GvI sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
:h/v"2uDN s3 = ifft(fftshift(sc3));
1)qD)E5&cf s2 = ifft(fftshift(sc2)); % Return to physical space
g[ uf
e< s1 = ifft(fftshift(sc1));
&}|`h8JA]K end
(_+ux1h6^ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
QAMcI:5 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
e
'F:LMX p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
V ]"pM]>3X P1=[P1 p1/p10];
GXNkl?# P2=[P2 p2/p10];
d2)]6)z6 P3=[P3 p3/p10];
U.b|3E/^ P=[P p*p];
*UXa.kT@ end
%o0 H#7' figure(1)
${}9/(x/^ plot(P,P1, P,P2, P,P3);
1'iQlnMO@ (
z F_< 转自：
http://blog.163.com/opto_wang/
