计算脉冲在非线性耦合器中演化的Matlab 程序 x @1px&^ jd ["e I % This Matlab script file solves the coupled nonlinear Schrodinger equations of
y#]}5gJ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
gB(9vhj $ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
R&6n?g6@/V % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
|7rR99 p>k]C:h %fid=fopen('e21.dat','w');
KqN!?anPr N = 128; % Number of Fourier modes (Time domain sampling points)
7*zB*"B'1t M1 =3000; % Total number of space steps
2 5x cD1* J =100; % Steps between output of space
ixO Ed Q T =10; % length of time windows:T*T0
Cn abD{uTf T0=0.1; % input pulse width
y._'K+nl MN1=0; % initial value for the space output location
Z:I*y7V- dt = T/N; % time step
%z(9lAe n = [-N/2:1:N/2-1]'; % Index
%
2I t = n.*dt;
9aT L22U? u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
|WB"=PE u20=u10.*0.0; % input to waveguide 2
C= >B_EO u1=u10; u2=u20;
.|T2\M U1 = u1;
j h;
9
[ U2 = u2; % Compute initial condition; save it in U
^fkC yE;= ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
f ucUwf\_ w=2*pi*n./T;
66oK3%[ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
M[A-1]' L=4; % length of evoluation to compare with S. Trillo's paper
0r1g$mKb dz=L/M1; % space step, make sure nonlinear<0.05
Oz :D.V
3~ for m1 = 1:1:M1 % Start space evolution
$v FrU v u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
SV& kWbS u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Q`N18I3 ca1 = fftshift(fft(u1)); % Take Fourier transform
d{W}p~UbH ca2 = fftshift(fft(u2));
[u[ U_g* c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
GOGt?iw*< c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
L*P_vCC u2 = ifft(fftshift(c2)); % Return to physical space
W3^.5I u1 = ifft(fftshift(c1));
Ru :n~77{ if rem(m1,J) == 0 % Save output every J steps.
qc3~cH.@ U1 = [U1 u1]; % put solutions in U array
|Z
d]= tue U2=[U2 u2];
~u! gUJ: MN1=[MN1 m1];
&(g|="T z1=dz*MN1'; % output location
5)mVy?Z end
7k `_# end
3 :UA<&=s hg=abs(U1').*abs(U1'); % for data write to excel
^b= XV&{q ha=[z1 hg]; % for data write to excel
K${} r0 t1=[0 t'];
VQ2Fnb4 hh=[t1' ha']; % for data write to excel file
=: 4?>2) %dlmwrite('aa',hh,'\t'); % save data in the excel format
r ] 9 e^ figure(1)
q?yMa9ZZky waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
_D -5 }a " figure(2)
@.k5MOn waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ovz# zHV|- R 非线性超快脉冲耦合的数值方法的Matlab程序 > =Jsv
P&mtA2 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。
^PC\E} 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
va^0JfQ x:qr \Rz wk@yTTnb i *B:El1 % This Matlab script file solves the nonlinear Schrodinger equations
l]$40 j % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Y[ ?`\c| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
)=Zsv40O % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
AeaPK <Pio Q >~ C=1;
!_dR' M1=120, % integer for amplitude
]% Y\ZIS M3=5000; % integer for length of coupler
9\>sDSCx N = 512; % Number of Fourier modes (Time domain sampling points)
) \ 4
| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
x<@kjfm 5 T =40; % length of time:T*T0.
fe';b[q)# dt = T/N; % time step
x<s|vgl| n = [-N/2:1:N/2-1]'; % Index
AFm,CINa t = n.*dt;
\6:>{0\ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
gfm;xT/y w=2*pi*n./T;
V!xw b:J g1=-i*ww./2;
*> KHRR<N g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
\B&6TeR g3=-i*ww./2;
<BP RV> 0X P1=0;
wyzOcx>M P2=0;
GmbIFOT~
P3=1;
]`d2_mu P=0;
ZBJ3 VK for m1=1:M1
JOHR mfqR p=0.032*m1; %input amplitude
`NSy"6{Z s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
2e.N"eLNt s1=s10;
~.6 |dw\p! s20=0.*s10; %input in waveguide 2
+#s;yc#=2 s30=0.*s10; %input in waveguide 3
1ef'7a7e8 s2=s20;
7 2, "Cj s3=s30;
q@kOTkHv) p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
_q)!B,y-/N %energy in waveguide 1
AK *N p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
4\6: \ %energy in waveguide 2
9 mPIykAj8 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
~{M @?8wi %energy in waveguide 3
j o_
sAb for m3 = 1:1:M3 % Start space evolution
KDD@% E s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Sl>>SP s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
j V^C19 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Hbk&6kS sca1 = fftshift(fft(s1)); % Take Fourier transform
C(o.Cy6 sca2 = fftshift(fft(s2));
rN" Xz sca3 = fftshift(fft(s3));
2xn<E>] sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
^i'y6J sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
@Tr&`Hi sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
V7C1FV2 s3 = ifft(fftshift(sc3));
:}9j^}"c3 s2 = ifft(fftshift(sc2)); % Return to physical space
o@/xPo| s1 = ifft(fftshift(sc1));
SY1GR n end
`c(\i$1JY) p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
%8w 9E= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
jK3\K/ob( p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Tn A?u (R% P1=[P1 p1/p10];
cJ/]+|PQ P2=[P2 p2/p10];
[M:S`{SbY P3=[P3 p3/p10];
#hJQbv=B" P=[P p*p];
Au5rR>W end
U =cWmH figure(1)
a2yE:16o6 plot(P,P1, P,P2, P,P3);
^u)rB<#BR OOB^gf}$' 转自：
http://blog.163.com/opto_wang/
