计算脉冲在非线性耦合器中演化的Matlab 程序 faJ>,^V# #ivN-WKCl % This Matlab script file solves the coupled nonlinear Schrodinger equations of
oD=6D9c? % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
~l=Jx* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
>FRJvZ6 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Z%uDz3I\Q" ~=pAy>oV %fid=fopen('e21.dat','w');
g\n0v~T+ N = 128; % Number of Fourier modes (Time domain sampling points)
s,2gd' M1 =3000; % Total number of space steps
xr< .r4 J =100; % Steps between output of space
df$V C T =10; % length of time windows:T*T0
j Rv j:H9 T0=0.1; % input pulse width
[Tq\K ^!^ MN1=0; % initial value for the space output location
;%V%6 : 5 dt = T/N; % time step
+l,6}tV9 n = [-N/2:1:N/2-1]'; % Index
UFED*al# t = n.*dt;
fjh0Z i45 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
]mW) T0_ u20=u10.*0.0; % input to waveguide 2
?R ;K`f9< u1=u10; u2=u20;
wB0zFlP U1 = u1;
^:yg,cS|Be U2 = u2; % Compute initial condition; save it in U
NIQX?|;b{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Gw;[maM!%` w=2*pi*n./T;
/h!Y/\ kI g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Owa]ax5 L=4; % length of evoluation to compare with S. Trillo's paper
4GY:N6qe ' dz=L/M1; % space step, make sure nonlinear<0.05
Yiq8 >| for m1 = 1:1:M1 % Start space evolution
G \S >H u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
6a=Y_fma u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
%](H?'H ca1 = fftshift(fft(u1)); % Take Fourier transform
~D9VjXfL) ca2 = fftshift(fft(u2));
t#p*{S 3u c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Yom ,{;Bv c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
mO UIGlv u2 = ifft(fftshift(c2)); % Return to physical space
>;;tX3( u1 = ifft(fftshift(c1));
8#S}.|"?F if rem(m1,J) == 0 % Save output every J steps.
qC%[J:RwF U1 = [U1 u1]; % put solutions in U array
P 3CzX48^ U2=[U2 u2];
``:AF: MN1=[MN1 m1];
?xTh}Sky z1=dz*MN1'; % output location
R&Oqm hT! end
l5m5H ,` end
- -~m{qmy hg=abs(U1').*abs(U1'); % for data write to excel
zP|y3`. 52 ha=[z1 hg]; % for data write to excel
t!g9,xG<X t1=[0 t'];
Zy -&g: hh=[t1' ha']; % for data write to excel file
^lP_{ c %dlmwrite('aa',hh,'\t'); % save data in the excel format
wM^_pah#Y5 figure(1)
&y}nd
7o waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
:jFKTG
figure(2)
5G\CT&cQR waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
&dino #()u=) 非线性超快脉冲耦合的数值方法的Matlab程序 ma\UJz UI*^$7z1 + 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
WB=pR C@ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
sp0j2<$a Z(8'ki 4<['%7U_[ fCMH<}w % This Matlab script file solves the nonlinear Schrodinger equations
-bamNw>| % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
buXPeIo^VM % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
e$E~@{[1) % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
T/_JXK>W @[ qGoai C=1;
K$H>/*&'~ M1=120, % integer for amplitude
_/W[=c M3=5000; % integer for length of coupler
lD8&*5tDmP N = 512; % Number of Fourier modes (Time domain sampling points)
nC3U%*l dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
vu%:0p` K T =40; % length of time:T*T0.
[\ M=w7 dt = T/N; % time step
.Z!!x n = [-N/2:1:N/2-1]'; % Index
r 3@Q(Rb t = n.*dt;
j;tT SNF ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
QL>G-Rp w=2*pi*n./T;
G36}4 g1=-i*ww./2;
7-oH >OF^ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ZwLD7j*) g3=-i*ww./2;
(O
N
\-* P1=0;
Dj<]e G] P2=0;
>+[uV ^2[ P3=1;
Ty"OJ P=0;
!9!kb for m1=1:M1
Y2
&N#~l* p=0.032*m1; %input amplitude
9 59i2z s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
1@nGD<,. s1=s10;
~HwY?[}!m s20=0.*s10; %input in waveguide 2
w$9aTL7 s30=0.*s10; %input in waveguide 3
oRM,_ s2=s20;
LF'M!C9| s3=s30;
fq){?hk~O p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
j b' hqz %energy in waveguide 1
y(K?mtQ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
.(Gq9m[~8H %energy in waveguide 2
d9XX^nY. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
y)W.x R %energy in waveguide 3
gY],
(*v for m3 = 1:1:M3 % Start space evolution
!*:Zcg?7n s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
kU8V,5 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
;SzOa7 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
27-<q5q sca1 = fftshift(fft(s1)); % Take Fourier transform
H}NW? sca2 = fftshift(fft(s2));
r sP3?.E sca3 = fftshift(fft(s3));
"hU'o& sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
eH2.,wY1 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
)* @Oz sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
EO'[AU% ~ s3 = ifft(fftshift(sc3));
V8>%$O
sw s2 = ifft(fftshift(sc2)); % Return to physical space
>Au ]S ` s1 = ifft(fftshift(sc1));
'#SacJ\L7
end
]@o p p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
.`!|^h%0 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
|X9YVZC p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
4WnB{9
i`I P1=[P1 p1/p10];
"D7*en P2=[P2 p2/p10];
v7O &9a; P3=[P3 p3/p10];
uG\ +`[-{0 P=[P p*p];
"v -\nAu end
:K& figure(1)
w$H=GF?" plot(P,P1, P,P2, P,P3);
<CL0@?*i9 ]Au78Yom 转自：
http://blog.163.com/opto_wang/
