计算脉冲在非线性耦合器中演化的Matlab 程序 m&fm<?| *;Sj&O % This Matlab script file solves the coupled nonlinear Schrodinger equations of
@<;0 h| % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
g&&5F>mF % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
B!6?+< J" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
/JJU-A( %I?uO(
@ %fid=fopen('e21.dat','w');
U }xRvNz N = 128; % Number of Fourier modes (Time domain sampling points)
GXf"a3 M1 =3000; % Total number of space steps
y 1z4qSeM J =100; % Steps between output of space
]Z6==+mCP T =10; % length of time windows:T*T0
jo/-'Lf{? T0=0.1; % input pulse width
kbiMqiPG MN1=0; % initial value for the space output location
jgbE@IA@!' dt = T/N; % time step
~:v" TuuK n = [-N/2:1:N/2-1]'; % Index
!Yd7&#s t = n.*dt;
"/g/Lc u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
i#=s_v8 u20=u10.*0.0; % input to waveguide 2
83e{rcs u1=u10; u2=u20;
,~> A>J U1 = u1;
7ZqC1 U2 = u2; % Compute initial condition; save it in U
CB:G4VqOT ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
.gzNdSE w=2*pi*n./T;
[ lW~v:W g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
gWL'Fl }H L=4; % length of evoluation to compare with S. Trillo's paper
C/U^8,6\n dz=L/M1; % space step, make sure nonlinear<0.05
|aIY for m1 = 1:1:M1 % Start space evolution
*\L\Bzm u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
5Z@OgR u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
AQ7w5}g+V ca1 = fftshift(fft(u1)); % Take Fourier transform
?@!dc6
ca2 = fftshift(fft(u2));
^U)xQD" c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
AT+7!UGL c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
/ p}^ Tpu u2 = ifft(fftshift(c2)); % Return to physical space
r I23e[ u1 = ifft(fftshift(c1));
`2.[8%6 if rem(m1,J) == 0 % Save output every J steps.
^Q0%_V, U1 = [U1 u1]; % put solutions in U array
B}Qpqa=_c U2=[U2 u2];
76Ho\}-U"> MN1=[MN1 m1];
Ahv %Q%m%2 z1=dz*MN1'; % output location
8 6y )+h` end
sT
]JDC6 end
nJC/y S | hg=abs(U1').*abs(U1'); % for data write to excel
+`'=K ;{U ha=[z1 hg]; % for data write to excel
{$ 5?[KD t1=[0 t'];
OTwIR<_B+ hh=[t1' ha']; % for data write to excel file
^} 8qPBz %dlmwrite('aa',hh,'\t'); % save data in the excel format
dTcrJ|/Y figure(1)
=Kqb
V{! waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
=n7QL QU figure(2)
}M*yE]LL;Z waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
tX)l_ ?jVH V 'alzw7# 非线性超快脉冲耦合的数值方法的Matlab程序 J B[n]| dX^ ^
@7 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。
y Ud>EnQna 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
\%[sv@P9s F/.nr p$. m=+K~ oU"!"t % This Matlab script file solves the nonlinear Schrodinger equations
t`%Xx xu % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
K;)(fc % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;@/^hk{A % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
# O<, {Qv Whf C=1;
v%^"N_ ] M1=120, % integer for amplitude
Z8 eB5!$ M3=5000; % integer for length of coupler
|YEq<wbQ N = 512; % Number of Fourier modes (Time domain sampling points)
wjEyU: dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
bSJ@
5qS T =40; % length of time:T*T0.
v_G1YC7TU dt = T/N; % time step
Fw.df< n = [-N/2:1:N/2-1]'; % Index
FqwH:Fcr: t = n.*dt;
X?f\j" v ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
}%) ]b*3 w=2*pi*n./T;
[8%R*} g1=-i*ww./2;
\k
9Ei mT} g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
dBRK6hFC g3=-i*ww./2;
?2q4dx 0 P1=0;
dQ#$(< v[ P2=0;
hlKM4JT\ P3=1;
yX7P5c. P=0;
H;w8[ImK for m1=1:M1
x ky +" p=0.032*m1; %input amplitude
H"5=z7w s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-}x( MZ s1=s10;
Lqa|9| ! s20=0.*s10; %input in waveguide 2
U, Q s30=0.*s10; %input in waveguide 3
" i !Xiy~ s2=s20;
9Ib#A s3=s30;
d QljG.PiK p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
i U"2uLgb %energy in waveguide 1
;X;q8J^_K_ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
}t%2giJ %energy in waveguide 2
BZP{{ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
[x[ nTIg %energy in waveguide 3
;M<R
e for m3 = 1:1:M3 % Start space evolution
z{m%^,Cs, s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Qo\+FkhYq s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
+d!"Zy2|B s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Bcl6n@{2f sca1 = fftshift(fft(s1)); % Take Fourier transform
[6cF#_)* sca2 = fftshift(fft(s2));
r7FFZNs! sca3 = fftshift(fft(s3));
JavSR1_ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
CpLLsp hy sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
2'U+QK@ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
2%_UOEayU s3 = ifft(fftshift(sc3));
FKWL{"y s2 = ifft(fftshift(sc2)); % Return to physical space
a 8}!9kL s1 = ifft(fftshift(sc1));
1| XC $0 end
2A&Y })D
p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
#Y<QEGb( p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
p >h&SD?b p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
4Ai#$SHLm P1=[P1 p1/p10];
;&9wG` P2=[P2 p2/p10];
v43FU3 P3=[P3 p3/p10];
{?uG] G7 P=[P p*p];
`xsU'Wd^< end
|2!cPf^8 figure(1)
|R3A$r#- plot(P,P1, P,P2, P,P3);
7N8a4 8$8 m {?uR.O 转自：
http://blog.163.com/opto_wang/
