计算脉冲在非线性耦合器中演化的Matlab 程序 .jLMl*6%: 9*7Hoi4Ji % This Matlab script file solves the coupled nonlinear Schrodinger equations of
x:=0.l# % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
%H 8A= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ev)rOcOU % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
',L{CQA?c cZCGnzy %fid=fopen('e21.dat','w');
)RpqZe/h4 N = 128; % Number of Fourier modes (Time domain sampling points)
J(3gT }z- M1 =3000; % Total number of space steps
NvEm,E\| J =100; % Steps between output of space
Jsl k T =10; % length of time windows:T*T0
/ c4;3>I S T0=0.1; % input pulse width
N8Rm}) MN1=0; % initial value for the space output location
i5ajM,i/K dt = T/N; % time step
5xG|35Pj n = [-N/2:1:N/2-1]'; % Index
5HWwl.D t = n.*dt;
E.?E~ }z u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
UY ?i E= u20=u10.*0.0; % input to waveguide 2
e {^:/WcYB u1=u10; u2=u20;
[] GthF U1 = u1;
z Y$X|= f U2 = u2; % Compute initial condition; save it in U
8o*\W $K@ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
L?Kz
P.(t+ w=2*pi*n./T;
|@T5$Xg]5 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
[0mFy) 6 L=4; % length of evoluation to compare with S. Trillo's paper
?Zc/upd:$N dz=L/M1; % space step, make sure nonlinear<0.05
j |^-1X for m1 = 1:1:M1 % Start space evolution
2N8rM}?90 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
c n\k`8 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Oz4,Y+[# ca1 = fftshift(fft(u1)); % Take Fourier transform
%igFHh? ca2 = fftshift(fft(u2));
6Tm
Rc c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Q0
uP8I}n c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
|_hioMVz u2 = ifft(fftshift(c2)); % Return to physical space
I_"Hg x< u1 = ifft(fftshift(c1));
+cPE4(d if rem(m1,J) == 0 % Save output every J steps.
~8KF<2c U1 = [U1 u1]; % put solutions in U array
3{2^G@j U2=[U2 u2];
8 o8b'tW^ MN1=[MN1 m1];
p=mCK@ z1=dz*MN1'; % output location
E<X{72fb> end
1Pw(.8P end
:Y}Y&mA4 hg=abs(U1').*abs(U1'); % for data write to excel
Rye ~w6 ha=[z1 hg]; % for data write to excel
rL!_&| t1=[0 t'];
UX-_{I
QW hh=[t1' ha']; % for data write to excel file
!I~ C\$^U %dlmwrite('aa',hh,'\t'); % save data in the excel format
AHp830 \ figure(1)
z*NC?\ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
=|qt !gY)Y figure(2)
RTPq8S" waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
w (vE2Y ? d'lr:=GQ 非线性超快脉冲耦合的数值方法的Matlab程序 'XZI{q2i S:2u 3th7 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。
yL.PGF1( 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
0gwm gc/# g~ppPAH > hDsm;,/ Z uFV tW@ % This Matlab script file solves the nonlinear Schrodinger equations
&.+n
L
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
cKi^C % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@aqd'O % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
?' ez. a} =x='<{jtgW C=1;
')~Y M1=120, % integer for amplitude
nyl8=F:V M3=5000; % integer for length of coupler
-A-hxK*^ N = 512; % Number of Fourier modes (Time domain sampling points)
8XS {6< dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
w$(0V$l_ T =40; % length of time:T*T0.
9J2q`/6~e dt = T/N; % time step
3j=%D e n = [-N/2:1:N/2-1]'; % Index
ATMogxh t = n.*dt;
/]MB 6E7& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
R[>;_}5"> w=2*pi*n./T;
@sg T[P*ut g1=-i*ww./2;
!CVBG *E^l g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
]9KQP-p' g3=-i*ww./2;
bD-/ZZz P1=0;
)D" G3g. P2=0;
*Sz{DE1U P3=1;
\AtwO P=0;
xT=kxyu for m1=1:M1
t6h`WAZV p=0.032*m1; %input amplitude
Tk v s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
i w~V_y4 s1=s10;
${I@YSU s20=0.*s10; %input in waveguide 2
QGbD=c7 s30=0.*s10; %input in waveguide 3
K9I,Q$&xX s2=s20;
eUKl
Co s3=s30;
_;J9q} X p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
+2au
;^N %energy in waveguide 1
u7Y'3x,` p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
@aiLG wh %energy in waveguide 2
-' H+lrmv p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
?D~SHcBaN %energy in waveguide 3
,@'){V for m3 = 1:1:M3 % Start space evolution
-t~B@% s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
i9EMi_% s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Zs5I?R1e8 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
{Y* ]Qc sca1 = fftshift(fft(s1)); % Take Fourier transform
evmEX <N sca2 = fftshift(fft(s2));
#Z=)= sca3 = fftshift(fft(s3));
J6["j sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
kX ,FQG> sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
d-N"m I- sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
@+CSY-g$ s3 = ifft(fftshift(sc3));
Q@ ) rw0$ s2 = ifft(fftshift(sc2)); % Return to physical space
NKUI! [ s1 = ifft(fftshift(sc1));
5KH '|z end
mZ5K hPvf8 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
+/>YH-P= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
MMA@J p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
=<'iLQb1 P1=[P1 p1/p10];
a] wcA P2=[P2 p2/p10];
k>0cTBY& P3=[P3 p3/p10];
rIFC#Jd/ P=[P p*p];
D N 8pJa end
V\M!]Nnxr figure(1)
V+a%,sI plot(P,P1, P,P2, P,P3);
'3u]-GU2_ pTX'5 转自：
http://blog.163.com/opto_wang/
