计算脉冲在非线性耦合器中演化的Matlab 程序 `a%MD>R_Lg >%ovL8F % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Cz)&R^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
v \[+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1< Sg@ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<iA\ZS: Z5E; FGPb %fid=fopen('e21.dat','w');
P6&%`$ N = 128; % Number of Fourier modes (Time domain sampling points)
1uO2I&B M1 =3000; % Total number of space steps
!
,bQ;p3g| J =100; % Steps between output of space
ftG3!} T =10; % length of time windows:T*T0
;=7K*npT T0=0.1; % input pulse width
au04F]-|j8 MN1=0; % initial value for the space output location
e P,bFc dt = T/N; % time step
lm6hFvEZ n = [-N/2:1:N/2-1]'; % Index
/Kd7# @ t = n.*dt;
8IA1@0n& u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
0-uw3U< u20=u10.*0.0; % input to waveguide 2
f1]zsn: u1=u10; u2=u20;
f~F{@),acZ U1 = u1;
P}]o$nWT U2 = u2; % Compute initial condition; save it in U
AN:yL
a! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
@ 5^nrB w=2*pi*n./T;
!b"?l"C +u g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
qVKd c*R- L=4; % length of evoluation to compare with S. Trillo's paper
%@Z;;5 L dz=L/M1; % space step, make sure nonlinear<0.05
1X[^^p~^ for m1 = 1:1:M1 % Start space evolution
,sIC=V + u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
<sw@P":F u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
<|3%}? ca1 = fftshift(fft(u1)); % Take Fourier transform
\"1>NJn&k) ca2 = fftshift(fft(u2));
<^\rv42'(2 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
m`9nDiV c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
<)p.GAZ u2 = ifft(fftshift(c2)); % Return to physical space
w`;HwK$ , u1 = ifft(fftshift(c1));
qXg&E}]:= if rem(m1,J) == 0 % Save output every J steps.
*68 TTBq( U1 = [U1 u1]; % put solutions in U array
)Xh }N U2=[U2 u2];
HeO:=OE~> MN1=[MN1 m1];
CVW T >M < z1=dz*MN1'; % output location
g"Y _!)X end
+4.s4&f) end
!( rAI hg=abs(U1').*abs(U1'); % for data write to excel
4 WJY+) ha=[z1 hg]; % for data write to excel
>UMxlvTg& t1=[0 t'];
4/Y?e UQ hh=[t1' ha']; % for data write to excel file
$8)XN-%( %dlmwrite('aa',hh,'\t'); % save data in the excel format
X3\PVsH$K figure(1)
"~5cz0
H3v waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
F)(^c figure(2)
X>Vc4n<} waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
R7/S SuG6\ vY-CXWC 7 非线性超快脉冲耦合的数值方法的Matlab程序 `^V d * n&njSj/ 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。
=nGFLH6) 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
;NR |Hi] _Xt/U>N `UTPX'Vz mUa#sTm % This Matlab script file solves the nonlinear Schrodinger equations
&h0LWPl % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
b)< W C$" % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
N< 9 c/V % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^o{{kju q1T)H2S C=1;
z_!IA
] v M1=120, % integer for amplitude
=P]Z "Ok M3=5000; % integer for length of coupler
{+WBi(=W N = 512; % Number of Fourier modes (Time domain sampling points)
-67Z!N dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
=I `S7oF T =40; % length of time:T*T0.
|n/;x$Cb dt = T/N; % time step
8f9wUPr n = [-N/2:1:N/2-1]'; % Index
#NW+t|E t = n.*dt;
UZI :st
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-Cs( 3[ w=2*pi*n./T;
Jh 3 g1=-i*ww./2;
+6 #$6 hG g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
zr /v .$< g3=-i*ww./2;
i%-yR DIX P1=0;
|%C2 cx P2=0;
gsbr8zwG, P3=1;
^eh.Iml'@ P=0;
ENZym for m1=1:M1
ryL1 <u
~ p=0.032*m1; %input amplitude
~HB#7+b s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
5vyg-' s1=s10;
V: D;? $Jl s20=0.*s10; %input in waveguide 2
w7Yu} JY^ s30=0.*s10; %input in waveguide 3
p^pd7)sBr s2=s20;
e *2^ s3=s30;
zMv`<m% p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
nQ\` ] _C %energy in waveguide 1
H?=W]<!W{y p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
O>' }q/ %energy in waveguide 2
8"j $=T6;W p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
\J+a7N8m, %energy in waveguide 3
x4I!f)8Q for m3 = 1:1:M3 % Start space evolution
,<U =
7<NU s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
g{V(Wy T@ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
[ P
&B s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
G'\[dwD,u sca1 = fftshift(fft(s1)); % Take Fourier transform
.o/|]d`% sca2 = fftshift(fft(s2));
l zFiZx sca3 = fftshift(fft(s3));
[c3!xHt5O sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
8g0 #WV sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
3gUY13C}:p sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
>%tP"x{ s3 = ifft(fftshift(sc3));
R4'.QZ-x s2 = ifft(fftshift(sc2)); % Return to physical space
G<?RH"RZr s1 = ifft(fftshift(sc1));
b-_l&;NWg end
rr
tMd p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
G3_7e A#; p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
N |yA]dg[ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
h"1}j'2>@ P1=[P1 p1/p10];
}k VC ]+ P2=[P2 p2/p10];
d~aTj f P3=[P3 p3/p10];
p%$r\G-x P=[P p*p];
GJB+] b- end
!0l|[c4 e> figure(1)
16 AlmegDk plot(P,P1, P,P2, P,P3);
+S~ u ,= <.ZIhDiE l 转自：
http://blog.163.com/opto_wang/
