计算脉冲在非线性耦合器中演化的Matlab 程序 @)o^uU T YIw1 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
`]Q:-h % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
hxQ qa 0B % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
fh L,aCS= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
/1Ue?)g DL$@?.?I %fid=fopen('e21.dat','w');
}=c85f~i N = 128; % Number of Fourier modes (Time domain sampling points)
rj(T~d4 M1 =3000; % Total number of space steps
~e6 Brq J =100; % Steps between output of space
(L^]Lk
x) T =10; % length of time windows:T*T0
pe^u$YE T0=0.1; % input pulse width
94B\5I} MN1=0; % initial value for the space output location
0 a80 LAK dt = T/N; % time step
89r DyRJ; n = [-N/2:1:N/2-1]'; % Index
/p8dZ+X t = n.*dt;
%CK^Si%+ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
|*}4 m'c u20=u10.*0.0; % input to waveguide 2
bv&; R u1=u10; u2=u20;
'Lu__NfN U1 = u1;
tH-C 8Qxy U2 = u2; % Compute initial condition; save it in U
X5 j1`t, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
y UpgoX( 6 w=2*pi*n./T;
Q ]} Hd- g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
@Y1s$,=xB L=4; % length of evoluation to compare with S. Trillo's paper
C=eF.FB;' dz=L/M1; % space step, make sure nonlinear<0.05
r-:Uz\gM for m1 = 1:1:M1 % Start space evolution
vM5k _D u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
zux{S; :? u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
{{QELfH2 ca1 = fftshift(fft(u1)); % Take Fourier transform
Ytl4kaYS ca2 = fftshift(fft(u2));
ZMel{w`n c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
+0OLc2
)w c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
)ubiB^g'm u2 = ifft(fftshift(c2)); % Return to physical space
J:Qa5MTWp u1 = ifft(fftshift(c1));
K*~0"F>"0 if rem(m1,J) == 0 % Save output every J steps.
r,h%[JKM U1 = [U1 u1]; % put solutions in U array
/Njd[= B U2=[U2 u2];
[PDNwh0g5 MN1=[MN1 m1];
))"6er n z1=dz*MN1'; % output location
abyo4i5T end
#`)(e JF end
iKT [=c hg=abs(U1').*abs(U1'); % for data write to excel
PpAu!2lt9 ha=[z1 hg]; % for data write to excel
MRdduPrM%$ t1=[0 t'];
2.l:O2< hh=[t1' ha']; % for data write to excel file
@0/+_2MH- %dlmwrite('aa',hh,'\t'); % save data in the excel format
z*a:L} $ figure(1)
|&zz,+ E waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
MB ]<Dyj , figure(2)
* -8&[D0 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
g\&g N fTK3,s1= 非线性超快脉冲耦合的数值方法的Matlab程序 UWd=!h^dt f=WDR m ] 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。
wY[+Z T 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
PamO8^!G x8V('` }j w|K'M?N14 8a p%? % This Matlab script file solves the nonlinear Schrodinger equations
|R/%D%_g % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
" i[@P) % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
nH[yJGZYSA % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Al} B34.uh ;z $(nhJ C=1;
/7Cc#P6 M1=120, % integer for amplitude
m c? Vq M3=5000; % integer for length of coupler
?i Wi N = 512; % Number of Fourier modes (Time domain sampling points)
,)Znb= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
7`DBS^O]dG T =40; % length of time:T*T0.
|}Nn!Sj>#; dt = T/N; % time step
5>D>% iaHv n = [-N/2:1:N/2-1]'; % Index
$Avjn m t = n.*dt;
Dv5D~on{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
{#?N w=2*pi*n./T;
%N> %!m g1=-i*ww./2;
Lh!J > g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
S.-TOE g3=-i*ww./2;
C26>BU< P1=0;
- "' j7t: P2=0;
w"-Lc4t+ P3=1;
b*c*r dTx P=0;
>4TaP*_ for m1=1:M1
i@"@9n~ p=0.032*m1; %input amplitude
1 mOh{:1u s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
7QiIiWqIWC s1=s10;
vqDu (6!2 s20=0.*s10; %input in waveguide 2
o ,AA C s30=0.*s10; %input in waveguide 3
!>..Q)z s2=s20;
|
*2w5iR s3=s30;
$P^q!H4D p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
v3~? ;f ,l %energy in waveguide 1
SB H(y ) p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
P}n_IV*@ %energy in waveguide 2
v&DI`x n~ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
' YmIKIw %energy in waveguide 3
p6>Svcc for m3 = 1:1:M3 % Start space evolution
`T@i. 'X s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
/Kql>$I s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
m
Bu s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
tk eoNuAM sca1 = fftshift(fft(s1)); % Take Fourier transform
%[Wh [zZy sca2 = fftshift(fft(s2));
C kOz sca3 = fftshift(fft(s3));
M ?Y;a5{ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
'3 /4?wi sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
@\0ez<.p} sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
4&<oFW\r s3 = ifft(fftshift(sc3));
N{9v1`B s2 = ifft(fftshift(sc2)); % Return to physical space
&Cr: 6W@ A s1 = ifft(fftshift(sc1));
iVhJ t#_b end
o=1Uh,S3R p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
|W,&
Hl7 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
e ^6)Zz1\ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
P{kur} T P1=[P1 p1/p10];
bh,[ 3X% P2=[P2 p2/p10];
EN<F# Y3E P3=[P3 p3/p10];
-$,TMqM P=[P p*p];
DE}K~}sbd end
Xix L R figure(1)
Gw/Pk4R plot(P,P1, P,P2, P,P3);
36}?dRw#p 4Tb
#fH% 转自：
http://blog.163.com/opto_wang/
