计算脉冲在非线性耦合器中演化的Matlab 程序 3h4>edM O @l `D` % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Agl[Z>Q % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
4u<oe_n % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
(*|hlD~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
k?_Miqr "2 Kh2[K %fid=fopen('e21.dat','w');
O:1YG$uKa N = 128; % Number of Fourier modes (Time domain sampling points)
o/Z?/alt4 M1 =3000; % Total number of space steps
smSUo / J =100; % Steps between output of space
w L:3RZB T =10; % length of time windows:T*T0
!4|7U\; T0=0.1; % input pulse width
%zWtPxAf MN1=0; % initial value for the space output location
-gzk,ymp dt = T/N; % time step
_Ab|<!a /R n = [-N/2:1:N/2-1]'; % Index
o0AREZ+I t = n.*dt;
$ } ~:x_[ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
K(hqDif*6 u20=u10.*0.0; % input to waveguide 2
'E6)6N u1=u10; u2=u20;
"BK&C6 ] U1 = u1;
^)X^Pcx U2 = u2; % Compute initial condition; save it in U
0%v
p'v ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<CeDIX t w=2*pi*n./T;
4 /$]wK` g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
QH+Oi&xH L=4; % length of evoluation to compare with S. Trillo's paper
9Czc$fSS t dz=L/M1; % space step, make sure nonlinear<0.05
D{ c`H}/ ` for m1 = 1:1:M1 % Start space evolution
Mwi T1sB~ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
0rF{"HM~ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
~/QzL.S;p ca1 = fftshift(fft(u1)); % Take Fourier transform
=*}|y;I ca2 = fftshift(fft(u2));
9kT U|py c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
k5|h8%h8 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
[gU z9iU u2 = ifft(fftshift(c2)); % Return to physical space
KN5.2pp u1 = ifft(fftshift(c1));
E: #VS~ if rem(m1,J) == 0 % Save output every J steps.
B+,Z 3* U1 = [U1 u1]; % put solutions in U array
;|66AIwDe U2=[U2 u2];
s2q#D.f MN1=[MN1 m1];
gzxLHPiw z1=dz*MN1'; % output location
^ygN/a>rr end
Z>'.+OW end
{um~] hg=abs(U1').*abs(U1'); % for data write to excel
EFhe`` ha=[z1 hg]; % for data write to excel
[@Y?'={qE t1=[0 t'];
V*LpO 8= hh=[t1' ha']; % for data write to excel file
#k*e> d$ %dlmwrite('aa',hh,'\t'); % save data in the excel format
" J$vt` figure(1)
^[!LU waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
jrG@
+" } figure(2)
jf@#&%AC9 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
m;k' j@: |K7JU^"OQ 非线性超快脉冲耦合的数值方法的Matlab程序 YaDr6) d -lC|5U% 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
Jv a&"}Cb Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
B usxg?= 0fwo8NgX J1hc :I<; QXn iWJJ % This Matlab script file solves the nonlinear Schrodinger equations
] =7}Y%6 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
\f05(l d % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
?=-18@:.ss % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
u+kXJ !'[f!vsyM{ C=1;
?FxxH*>" M1=120, % integer for amplitude
BNnGtVAbZ M3=5000; % integer for length of coupler
C&D!TR!K N = 512; % Number of Fourier modes (Time domain sampling points)
vaW, O/F dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
&dH/V-te T =40; % length of time:T*T0.
}]'Z~5T dt = T/N; % time step
]W]o6uo7 n = [-N/2:1:N/2-1]'; % Index
8 W79 t = n.*dt;
"o+<
\B~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
A7 C+-N w=2*pi*n./T;
vm_+ U*%c g1=-i*ww./2;
IR(qjm \V g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
iG!tRNQ{y g3=-i*ww./2;
?Bno?\ P1=0;
/q0[T{Wz$ P2=0;
ia?{]!7$ P3=1;
= ]K;" P=0;
S=*rWh8)%< for m1=1:M1
<-D>^p9 p=0.032*m1; %input amplitude
<j+DY@* s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
gG!L#J? s1=s10;
:?S1#d_ s20=0.*s10; %input in waveguide 2
~xer ZQgc s30=0.*s10; %input in waveguide 3
5hF
iK
K7 s2=s20;
4"nb>tA s3=s30;
%wzDBsX p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
<%Zg; ]2H` %energy in waveguide 1
J^m#984 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
wM9HZraB< %energy in waveguide 2
{N42z0c p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
W2 ? 6f: %energy in waveguide 3
;'~U5 Po8 for m3 = 1:1:M3 % Start space evolution
]%>7OH' s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
hd^?mZ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
M_lQ^7/ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
N_Q)AXr) sca1 = fftshift(fft(s1)); % Take Fourier transform
(NR8B9qLN sca2 = fftshift(fft(s2));
^lud2x$O^C sca3 = fftshift(fft(s3));
ND $m|V-C sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
SaceIV %( sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
{]B PSj{B sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
VRV *\*~$ s3 = ifft(fftshift(sc3));
|Ii[WfFA|J s2 = ifft(fftshift(sc2)); % Return to physical space
jeXP|;#Una s1 = ifft(fftshift(sc1));
Aq nDsr! end
/
Vy pN, p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
(&t741DN| p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Fjch<gAofS p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
n,/eT,48` P1=[P1 p1/p10];
50kjX} P2=[P2 p2/p10];
Jmg<mjq/G P3=[P3 p3/p10];
Yz7H@Y2i P=[P p*p];
{BPNb{dBKr end
3>asl5 4 figure(1)
v8
r K \ plot(P,P1, P,P2, P,P3);
m.!n|_}] >n3w'b 转自：
http://blog.163.com/opto_wang/
