计算脉冲在非线性耦合器中演化的Matlab 程序 X1Qr _o-BR 4iwf\# % This Matlab script file solves the coupled nonlinear Schrodinger equations of
47 KNT7C % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
d [r-k 2 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
kL|\wci % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
yX`#s]M Wj&nUp{ %fid=fopen('e21.dat','w');
vTdUuj3N N = 128; % Number of Fourier modes (Time domain sampling points)
sMP:sCRC M1 =3000; % Total number of space steps
^CUSlnB\( J =100; % Steps between output of space
I`NUurQTX T =10; % length of time windows:T*T0
R }1W T0=0.1; % input pulse width
P7Xg{L&@. MN1=0; % initial value for the space output location
GLCAiSMz[ dt = T/N; % time step
m~;B:LN< n = [-N/2:1:N/2-1]'; % Index
"e@n:N! t = n.*dt;
+>!V ] S u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
>zQOK- u20=u10.*0.0; % input to waveguide 2
e gI&epN u1=u10; u2=u20;
m^Glc ?g< U1 = u1;
wqP2Gw7jh6 U2 = u2; % Compute initial condition; save it in U
$C u R}g ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
!.*iw
k` w=2*pi*n./T;
UU[H@ym# g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
<6/= y1QC) L=4; % length of evoluation to compare with S. Trillo's paper
~cIl$b dz=L/M1; % space step, make sure nonlinear<0.05
UA0 F): for m1 = 1:1:M1 % Start space evolution
$Zxt&a u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
/D'M 2 4 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
hCAZ{+`z ca1 = fftshift(fft(u1)); % Take Fourier transform
W&YU^&`Yr ca2 = fftshift(fft(u2));
FIS "Z( c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
DHv2&zH c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
b1xpz1 u2 = ifft(fftshift(c2)); % Return to physical space
q*bt4,D&Es u1 = ifft(fftshift(c1));
-%,"iaO if rem(m1,J) == 0 % Save output every J steps.
BZ+;n
|<r U1 = [U1 u1]; % put solutions in U array
>'b=YlUL U2=[U2 u2];
)S*1C@ MN1=[MN1 m1];
&?y 7I Pp z1=dz*MN1'; % output location
x#r<,uNn, end
*C7F2o end
&iBNO,v hg=abs(U1').*abs(U1'); % for data write to excel
H:Y&OZ ha=[z1 hg]; % for data write to excel
45<y{8 t1=[0 t'];
9 I{/zKq hh=[t1' ha']; % for data write to excel file
G>K@AW # %dlmwrite('aa',hh,'\t'); % save data in the excel format
s6n`?,vw figure(1)
pawl|Z'Ez waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
@PX\{6&
figure(2)
nxfoW y waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Bd#
TUy < *wM=aq 非线性超快脉冲耦合的数值方法的Matlab程序 s$ z2 c ]Lm 'RlV 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。
%j5ywr: 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
~KPv7WfG ) ,` 8eQC $(rc/h0/E T H:W#Ot % This Matlab script file solves the nonlinear Schrodinger equations
Z9[+'ZWt % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
.3X Y&6 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
]iVLHVqz % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'!Wvqs '3Q3lM'lh C=1;
8: dQ._#v M1=120, % integer for amplitude
#]Y*0Wzpfn M3=5000; % integer for length of coupler
snC/H G 7 N = 512; % Number of Fourier modes (Time domain sampling points)
Wekqn !h dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
"@yyXS
r T =40; % length of time:T*T0.
24B<[lSK dt = T/N; % time step
%u!b& 5]e n = [-N/2:1:N/2-1]'; % Index
`]<`$71w t = n.*dt;
B<,YPS8w ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
FFvCi@oT w=2*pi*n./T;
JvL{| KtyU g1=-i*ww./2;
Ch5+N6c^ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
e;( g3=-i*ww./2;
>cgpaj x* P1=0;
,H[SI0]; P2=0;
Bp_wnd P3=1;
Z
a(|(M H P=0;
ahGT 4d`)9 for m1=1:M1
OfZN|S+~W p=0.032*m1; %input amplitude
sn{tra s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
{HrZ4xQnpV s1=s10;
q>s`uFRg( s20=0.*s10; %input in waveguide 2
MKg,!TELe s30=0.*s10; %input in waveguide 3
S
v`qB'e2 s2=s20;
#/70!+J_UF s3=s30;
1@qgF p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
:L i/=>R^ %energy in waveguide 1
@R q}nq=k p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Mvcfk$pA %energy in waveguide 2
D/ Dt p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Adx`8}N8 %energy in waveguide 3
sWqM?2 g for m3 = 1:1:M3 % Start space evolution
\?lz&< s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
rx!=q8=0R s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Yj3I5RG s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
`JURQ:l)3^ sca1 = fftshift(fft(s1)); % Take Fourier transform
46No%cSiG sca2 = fftshift(fft(s2));
5?u}#zO sca3 = fftshift(fft(s3));
=RsXI&&vh sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
f.xA_ Y> sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
"![L#)"s sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
.*5 Z"Q['G s3 = ifft(fftshift(sc3));
B\CN<<N>dD s2 = ifft(fftshift(sc2)); % Return to physical space
lpm JLH.F s1 = ifft(fftshift(sc1));
\".^K5Pm end
))T>jh p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
#R&H &1 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
8P: spD0 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
wCKj 7y[ P1=[P1 p1/p10];
%X1x4t] P2=[P2 p2/p10];
@g-Tk P3=[P3 p3/p10];
MaY682}|y P=[P p*p];
B[o`k]] end
NXk!qGV2 figure(1)
)"<8K}%! plot(P,P1, P,P2, P,P3);
osP\D iQ sen=0SB/ 转自：
http://blog.163.com/opto_wang/
