计算脉冲在非线性耦合器中演化的Matlab 程序 m%(JRh H+&w 7ER % This Matlab script file solves the coupled nonlinear Schrodinger equations of
q9(}wvtr % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
v@s`l# % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5BO!K$6 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
F"TI 9ib ~u& O %fid=fopen('e21.dat','w');
{O oNhN9 N = 128; % Number of Fourier modes (Time domain sampling points)
Sqt" G6< M1 =3000; % Total number of space steps
q5?mP6 J =100; % Steps between output of space
[bVP2j T =10; % length of time windows:T*T0
&Gwh<%=U T0=0.1; % input pulse width
:DpK{$eCb MN1=0; % initial value for the space output location
0J-ux"kfI dt = T/N; % time step
X}FF4jE]D( n = [-N/2:1:N/2-1]'; % Index
*
rANf&y t = n.*dt;
0x/V1?gm u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
H#` ?t oS u20=u10.*0.0; % input to waveguide 2
J+|V[E<x u1=u10; u2=u20;
Ym2m1 U1 = u1;
iDxg AV f* U2 = u2; % Compute initial condition; save it in U
OHvzK8 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
& .4a w=2*pi*n./T;
li
XD2N g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
`8bp6} OD, L=4; % length of evoluation to compare with S. Trillo's paper
vt=S0X^$yc dz=L/M1; % space step, make sure nonlinear<0.05
:6iq{XV^ for m1 = 1:1:M1 % Start space evolution
m:7bynT{ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
U}Fk%Jj u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
G ~\$ Oq8 ca1 = fftshift(fft(u1)); % Take Fourier transform
'Em($A ( ca2 = fftshift(fft(u2));
},ZL8l{ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
N VPYv#uK c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
w2V E_ u2 = ifft(fftshift(c2)); % Return to physical space
V1qHl5" u1 = ifft(fftshift(c1));
.}>[ Kr if rem(m1,J) == 0 % Save output every J steps.
JPzPL\ U1 = [U1 u1]; % put solutions in U array
@"2-tn@q_ U2=[U2 u2];
HWZ*Htr MN1=[MN1 m1];
u8=|{)yL z1=dz*MN1'; % output location
h*%1Jkxu end
2yc\A3ft# end
Y [,C1, hg=abs(U1').*abs(U1'); % for data write to excel
5to NEDN ha=[z1 hg]; % for data write to excel
w $ HC! t1=[0 t'];
qm_E/B hh=[t1' ha']; % for data write to excel file
jGPs!64f) %dlmwrite('aa',hh,'\t'); % save data in the excel format
% m$ Mn x figure(1)
_< Tz 1>j= waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
014 !~ c figure(2)
GM I >$$< waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
@#">~P|Hp dGN*K} 5 非线性超快脉冲耦合的数值方法的Matlab程序 `Y9@ ?s Q D1a2|^zt
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。
H^0KNMf( 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
v4^VYi,.- #=m 5 *}= =p:6u_@XWj lPP7w`[ PA % This Matlab script file solves the nonlinear Schrodinger equations
(Zkt2[E` % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
.kV/ 0!q? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
KDk^)zv%! % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
wDzS <mm 0KE l + C=1;
Jr
zU-g M1=120, % integer for amplitude
"
8v M3=5000; % integer for length of coupler
wvY$ s; N = 512; % Number of Fourier modes (Time domain sampling points)
3f
x!\ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
5@\<:Zmi T =40; % length of time:T*T0.
Zs)9O Ju dt = T/N; % time step
MI 3_<[ n = [-N/2:1:N/2-1]'; % Index
{fs(+
0ei t = n.*dt;
Dc5XU3Eu` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
lC{m;V2 w=2*pi*n./T;
N0NMRU]zT g1=-i*ww./2;
n$9!G g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
:mL.Y em*' g3=-i*ww./2;
x8t1g,QA P1=0;
p+Xz9A" P2=0;
q_)DY
f7V} P3=1;
Zf! 7pM P=0;
LE"xZxe for m1=1:M1
Y|bGd_j p=0.032*m1; %input amplitude
~V 4|DN[I s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Fej$`2mRH s1=s10;
w1Kyd?~%] s20=0.*s10; %input in waveguide 2
oz--gA:g s30=0.*s10; %input in waveguide 3
F);C?SW" s2=s20;
^;e`ZtcI s3=s30;
mj pH)6aD0 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
O`4X[r1LD %energy in waveguide 1
qW9|&GuZ$ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
2 q>4nN %energy in waveguide 2
7e4\BzCC
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
l"64w>, %energy in waveguide 3
p O.8>C% for m3 = 1:1:M3 % Start space evolution
Aka `L:k s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
>ObpOFb% s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
7u; B[qH s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
=KMck=#B sca1 = fftshift(fft(s1)); % Take Fourier transform
7G(X:! sca2 = fftshift(fft(s2));
i*3_ivc) sca3 = fftshift(fft(s3));
G{<wXxq% sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
^ gy(~u sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
q\\J9`Q$J sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
94+#6jd e s3 = ifft(fftshift(sc3));
+KZc"0? s2 = ifft(fftshift(sc2)); % Return to physical space
+oc}kv,h] s1 = ifft(fftshift(sc1));
6
J#C end
ZD*>i=S p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
c?|/c9f p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
(N P=5lLH p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
^^Y0 \3. P1=[P1 p1/p10];
cI H`,bR P2=[P2 p2/p10];
'7$v@Tvnre P3=[P3 p3/p10];
q?6Zu :': P=[P p*p];
p^2pv{by end
qsLsyi |zG figure(1)
}r N" H4) plot(P,P1, P,P2, P,P3);
7}xKiHh: zx^)Qb/EL6 转自：
http://blog.163.com/opto_wang/
