计算脉冲在非线性耦合器中演化的Matlab 程序 yA}nPXrd gV`S % % This Matlab script file solves the coupled nonlinear Schrodinger equations of
#M:B3C!ouY % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
RAOKZ~ ` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
iiN?\OO^~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
gvr]]}h:O Hdna{@~ %fid=fopen('e21.dat','w');
.f%vDBJS N = 128; % Number of Fourier modes (Time domain sampling points)
\E&th p M1 =3000; % Total number of space steps
s((b"{fFb J =100; % Steps between output of space
gix>DHq$k T =10; % length of time windows:T*T0
@Yarz1 T0=0.1; % input pulse width
J[o${^ MN1=0; % initial value for the space output location
&<t79d%{ dt = T/N; % time step
=W |vOfy n = [-N/2:1:N/2-1]'; % Index
"i(U t = n.*dt;
un&> u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
pLo;#e8'f u20=u10.*0.0; % input to waveguide 2
ec1Fg0Fa u1=u10; u2=u20;
`.`FgaJ
| U1 = u1;
wOM<X hZ U2 = u2; % Compute initial condition; save it in U
fv/v| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
~D_ rZ& w=2*pi*n./T;
U L ck g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
x3_,nl L=4; % length of evoluation to compare with S. Trillo's paper
*V<)p%l. dz=L/M1; % space step, make sure nonlinear<0.05
*Ji 9%IA for m1 = 1:1:M1 % Start space evolution
2X^iV09 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
/t5g"n3 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
YpiRF + G
ca1 = fftshift(fft(u1)); % Take Fourier transform
Uv'uqt ca2 = fftshift(fft(u2));
wvX"D0eVn c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
ec#_olG% c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
63SVIc~wT u2 = ifft(fftshift(c2)); % Return to physical space
4a1BGNI%SW u1 = ifft(fftshift(c1));
|&(H^<+Xp if rem(m1,J) == 0 % Save output every J steps.
k=FcPF" U1 = [U1 u1]; % put solutions in U array
Qdi rE 4W U2=[U2 u2];
(w}r7`n MN1=[MN1 m1];
R'r|E_ z1=dz*MN1'; % output location
a0)vvo=bz end
_3I3AG0e end
EO"=\C, hg=abs(U1').*abs(U1'); % for data write to excel
:nt}7Dn' ha=[z1 hg]; % for data write to excel
EI<"DB t1=[0 t'];
svF*@(- P# hh=[t1' ha']; % for data write to excel file
Qk|( EFQ9 %dlmwrite('aa',hh,'\t'); % save data in the excel format
Fr<Pe&d n figure(1)
s~/57S waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
rdFs?hO figure(2)
#qPV Qt waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
RlPjki"Mg xL|?(pQ/BK 非线性超快脉冲耦合的数值方法的Matlab程序 )!BB/'DRQ @f-0X1C."N 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。
20n%o&kG]8 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 z'O {f h=:*7>} bL+sN"Km 9'D8[p% % This Matlab script file solves the nonlinear Schrodinger equations
ozT._ C % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
XL= 2wh % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
hcj{%^p % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
twAw01". n}) C=1;
C zK%x?~] M1=120, % integer for amplitude
?exALv'B M3=5000; % integer for length of coupler
*
.oi3m N = 512; % Number of Fourier modes (Time domain sampling points)
Lqg7D\7j dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
x/pC%25 T =40; % length of time:T*T0.
VOD1xWrb dt = T/N; % time step
7l[t9ON n = [-N/2:1:N/2-1]'; % Index
A X/=}G t = n.*dt;
]eY Qio! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
jc3ExOH w=2*pi*n./T;
%
E<FB ;h g1=-i*ww./2;
9c#L{in g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
"X\q%%P=? g3=-i*ww./2;
bDxPgb7N= P1=0;
$[WN[J P2=0;
0^-z?Kb<} P3=1;
S^*(ALFPj P=0;
n\~"Wim<b for m1=1:M1
Z`e$~n(Bh p=0.032*m1; %input amplitude
E>o&GYc s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
t201ud2$ s1=s10;
,"4X&>_f s20=0.*s10; %input in waveguide 2
[R roHXdk+ s30=0.*s10; %input in waveguide 3
0:~gW#lD s2=s20;
5;r({ J s3=s30;
ZS07_6.~ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
eW<!^Aer %energy in waveguide 1
A0'tCq]?0 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
EuhF$L1 %energy in waveguide 2
Nj! R9N p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
bvt-leA= %energy in waveguide 3
] I N - for m3 = 1:1:M3 % Start space evolution
LA( f]Xmc s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
N9~'P-V s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
2d ,wrC<'$ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
% t,1_c0w sca1 = fftshift(fft(s1)); % Take Fourier transform
p8 E;[ sca2 = fftshift(fft(s2));
#$9U=^Z[ sca3 = fftshift(fft(s3));
i[ V,IP + sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
lk5_s@V
l sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
0~LnnD N sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
' eTpcrS3 s3 = ifft(fftshift(sc3));
*}50q9) / s2 = ifft(fftshift(sc2)); % Return to physical space
NpjsZcA s1 = ifft(fftshift(sc1));
/
r`Y'rm end
&k {t0> p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
nJnO/~| p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
D(W7O>5vQ2 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
KV3+}k P1=[P1 p1/p10];
|wl")|b% P2=[P2 p2/p10];
[bQ8A(u P3=[P3 p3/p10];
LS?` {E
P=[P p*p];
(]GY.(F{ end
U/~Zk@3j figure(1)
|G5=>W plot(P,P1, P,P2, P,P3);
c{ r6a=C {ILQ
CvP* 转自：
http://blog.163.com/opto_wang/
