计算脉冲在非线性耦合器中演化的Matlab 程序 co [ &)#bdt [ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
vK,.P:n % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
TOXZl3 s5# % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
rv;is=#1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Nr:%yvk%s Jyo(Etp %fid=fopen('e21.dat','w');
G> w+J'7 N = 128; % Number of Fourier modes (Time domain sampling points)
#5 }v ? M1 =3000; % Total number of space steps
fVx_]5jM J =100; % Steps between output of space
cSWn4-B@l T =10; % length of time windows:T*T0
1]] #HTwX T0=0.1; % input pulse width
9,G94.da MN1=0; % initial value for the space output location
.YxcXe3# dt = T/N; % time step
~sbn"OS + n = [-N/2:1:N/2-1]'; % Index
Y[Kpd[)[v t = n.*dt;
@bO/5"X, u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
l~*D
jr~ u20=u10.*0.0; % input to waveguide 2
1JWo~E' u1=u10; u2=u20;
r>3y87 U1 = u1;
KB6`OT^b{r U2 = u2; % Compute initial condition; save it in U
J\c\Ar : ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Q]<6i
w=2*pi*n./T;
|]'0z0> g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
' L=4; % length of evoluation to compare with S. Trillo's paper
J1gLT $ dz=L/M1; % space step, make sure nonlinear<0.05
?)L X4GY for m1 = 1:1:M1 % Start space evolution
$3je+ =ER u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
uhO-0H u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
JPGEE1!B{b ca1 = fftshift(fft(u1)); % Take Fourier transform
Yo;Mexo! ca2 = fftshift(fft(u2));
MZK%IC> c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
w!~85"" c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
>[ a&,gS u2 = ifft(fftshift(c2)); % Return to physical space
^U[yk'!Y u1 = ifft(fftshift(c1));
]0@
06G(y if rem(m1,J) == 0 % Save output every J steps.
Bl!R
bh\ U1 = [U1 u1]; % put solutions in U array
QDpzIj Jj U2=[U2 u2];
J'#R9NO< MN1=[MN1 m1];
mqk tM 6 z1=dz*MN1'; % output location
jpRC6b? end
d
gRTV<vM end
}hA h'*( hg=abs(U1').*abs(U1'); % for data write to excel
X w_6SR9C ha=[z1 hg]; % for data write to excel
#8;#)q_[u t1=[0 t'];
M&~cU{9c hh=[t1' ha']; % for data write to excel file
sTC hbks %dlmwrite('aa',hh,'\t'); % save data in the excel format
-5TMV#i
{ figure(1)
Xl\yOMfp waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
7zEpuw figure(2)
w6FV SU]sY waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
, J Z M%f 'ghwc:Og|% 非线性超快脉冲耦合的数值方法的Matlab程序 cN vh2JI #)
bqn|0l 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
-P[bA0N, Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
q;#:nf" A!.* eIV| G;Thz 5B,HJax % This Matlab script file solves the nonlinear Schrodinger equations
):pFI/iC % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
w;(B4 ^? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
JTI 'W % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]n$&|@ #uillSV C=1;
>S=,ype~G M1=120, % integer for amplitude
PHHX)xK M3=5000; % integer for length of coupler
Od @< L N = 512; % Number of Fourier modes (Time domain sampling points)
ZK8I f?SD dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
h(Ccm44 T =40; % length of time:T*T0.
os~}5QJ dt = T/N; % time step
qk=0ovUzg n = [-N/2:1:N/2-1]'; % Index
?Qfo mTT t = n.*dt;
Fl;!'1 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
c3G&)gU4q w=2*pi*n./T;
Sw^-@w=!U5 g1=-i*ww./2;
Ad ]oM] g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
SdOE^_@: g3=-i*ww./2;
Imm|5-qJ P1=0;
R4P$zB_< 2 P2=0;
3PU'd^ P3=1;
aB+B1YdY" P=0;
h&$,mbEoI for m1=1:M1
[tY+P7j9) p=0.032*m1; %input amplitude
$dgez#TPL s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
K`% I!Br s1=s10;
AiE\PMF~{P s20=0.*s10; %input in waveguide 2
H G)c\b s30=0.*s10; %input in waveguide 3
qc6eqE s2=s20;
h`HdM58CQ s3=s30;
.7 Lv p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
jYi{[* * %energy in waveguide 1
:U$U:e p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
;V"(! 'd %energy in waveguide 2
2lm{: tS p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
0nOp'Ky\k %energy in waveguide 3
<{yQNXf[ for m3 = 1:1:M3 % Start space evolution
- yn;Jo2- s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
q\gvX
76 a s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
UZq1qn@+ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Z 6XP .. sca1 = fftshift(fft(s1)); % Take Fourier transform
&$
/}HND sca2 = fftshift(fft(s2));
eg
vgi?y sca3 = fftshift(fft(s3));
| ~ I- sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
zu-1|X X sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
fW'U 7&O sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
F6h|AF|" s3 = ifft(fftshift(sc3));
' y9yx[P s2 = ifft(fftshift(sc2)); % Return to physical space
<DjFMTCN s1 = ifft(fftshift(sc1));
U%,N" ]` end
:5M7*s)e16 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
.0zN t p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
;
3WA-nn p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
kW=GFj)L P1=[P1 p1/p10];
t% f6P P2=[P2 p2/p10];
_^)<d$R< P3=[P3 p3/p10];
ugI9rxT]Kv P=[P p*p];
m+m,0Ey5H end
'9#O#I &J figure(1)
g@jAIy] plot(P,P1, P,P2, P,P3);
[Nn ?:5" *4tJ|m6"Y6 转自：
http://blog.163.com/opto_wang/
