计算脉冲在非线性耦合器中演化的Matlab 程序 #CM2FN:W IuPwFf) % This Matlab script file solves the coupled nonlinear Schrodinger equations of
?R" ;EnD % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
L./ UgeZ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
rK];2[U % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
zd r?1 = ifuVV Fov %fid=fopen('e21.dat','w');
.*8.{n5 N = 128; % Number of Fourier modes (Time domain sampling points)
-E.EI@" M1 =3000; % Total number of space steps
<.Pr+ g J =100; % Steps between output of space
1<lLE1fk T =10; % length of time windows:T*T0
J|s4c`= T0=0.1; % input pulse width
KnlVZn[3t MN1=0; % initial value for the space output location
U|,VH-# dt = T/N; % time step
3dXyKi n = [-N/2:1:N/2-1]'; % Index
" 4s ,a t = n.*dt;
m|'TPy u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
fuQ? @F u20=u10.*0.0; % input to waveguide 2
++ x EMP) u1=u10; u2=u20;
&}rh+z U1 = u1;
^ G15]Pyw U2 = u2; % Compute initial condition; save it in U
*K!V$8k=99 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
,rQznE1e w=2*pi*n./T;
/+%1Kq.hP g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
fY \QI
= L=4; % length of evoluation to compare with S. Trillo's paper
R7+k=DI dz=L/M1; % space step, make sure nonlinear<0.05
--y .q~d for m1 = 1:1:M1 % Start space evolution
o <sX6a9e u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
UA}k "uM u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
$BCqz! 4K ca1 = fftshift(fft(u1)); % Take Fourier transform
Dg \fjuK9 ca2 = fftshift(fft(u2));
jh9^5"vQ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
RoP z?,u c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
74QWGw`, u2 = ifft(fftshift(c2)); % Return to physical space
Ip|7JL0Z u1 = ifft(fftshift(c1));
(eHvp if rem(m1,J) == 0 % Save output every J steps.
C) Mh U1 = [U1 u1]; % put solutions in U array
6M F%$ K3 U2=[U2 u2];
eo"6 \3z MN1=[MN1 m1];
5WY..60K, z1=dz*MN1'; % output location
SI U"cO4 end
JQ!D8Ut end
s\ _
,aI hg=abs(U1').*abs(U1'); % for data write to excel
R:zjEhH ) ha=[z1 hg]; % for data write to excel
Q']:k}y t1=[0 t'];
zS]Yd9;X1 hh=[t1' ha']; % for data write to excel file
,E pg&)wC] %dlmwrite('aa',hh,'\t'); % save data in the excel format
(',G
Ako figure(1)
u
JGYXlLE waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
XswEAz0= figure(2)
%=%jy waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
[[ H XOPaV ^<7)w2ns 非线性超快脉冲耦合的数值方法的Matlab程序 $GPenQ~}, }B^KV#_{S 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
Jy{A1i@4~s Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
a'rN&*P | \ C{R j?#S M! f =" z\ % This Matlab script file solves the nonlinear Schrodinger equations
ZI-)' % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
P8piXG % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
OiZPL" Q(K % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
j'I$F1>Te mq do@ C=1;
JmtU>2z\ M1=120, % integer for amplitude
}r9f}yX9Q M3=5000; % integer for length of coupler
R@u6mMX{N, N = 512; % Number of Fourier modes (Time domain sampling points)
x4Y+? 2 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
W_ngB[ T =40; % length of time:T*T0.
Xq1n1_Z dt = T/N; % time step
{eMu"< n = [-N/2:1:N/2-1]'; % Index
ts
aD5B t = n.*dt;
`fj( xrI ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
2>_6b>9] w=2*pi*n./T;
kb Odg: g1=-i*ww./2;
v_En9~e^n g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
|U>BXX P g3=-i*ww./2;
1Hp0 ,R} P1=0;
@I _A\ U{ P2=0;
2( Vm 0E P3=1;
; P&K a P=0;
y/'2WO[ for m1=1:M1
0,{Dw9W: p=0.032*m1; %input amplitude
HFB2ep7N s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Zm4IN3FGLv s1=s10;
?S36)oZzg s20=0.*s10; %input in waveguide 2
[j`It4^nC s30=0.*s10; %input in waveguide 3
i\ X Ok! s2=s20;
u L1e? s3=s30;
3W 5|Y@0 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
pdngM 8n %energy in waveguide 1
b(&2/|hd p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
j_H{_Ug %energy in waveguide 2
k^:$ETW2
D p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
-yy&q 9 %energy in waveguide 3
?sfA/9" for m3 = 1:1:M3 % Start space evolution
z
AacX@ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
G!C2[:[g s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
u`xmF/jhQ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
!vHnMY~AG sca1 = fftshift(fft(s1)); % Take Fourier transform
yNoJrA sca2 = fftshift(fft(s2));
pn{Mj sca3 = fftshift(fft(s3));
Zm >Q-7r9 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
pLE|#58I sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
zQMsS sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
y+)][Wa0 s3 = ifft(fftshift(sc3));
)O#]W vr s2 = ifft(fftshift(sc2)); % Return to physical space
Zz'(!h Uy s1 = ifft(fftshift(sc1));
bN`oQ.Z 4 end
RF U(wek p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
:A g]^ot p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
f<=
#WV p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
EW%%W 6O6 P1=[P1 p1/p10];
`(vgBz`e[ P2=[P2 p2/p10];
O[+S/6uy P3=[P3 p3/p10];
tV<}!~0,* P=[P p*p];
dE7 kd=.o end
I,(m\Nal K figure(1)
DN2K4%cM%' plot(P,P1, P,P2, P,P3);
r :{2}nE 2Vxr 转自：
http://blog.163.com/opto_wang/
