计算脉冲在非线性耦合器中演化的Matlab 程序 0EJ(.8hwm .UoOO'1K % This Matlab script file solves the coupled nonlinear Schrodinger equations of
' H7x L % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
.G o{1[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
L4L2O7 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
z4 E|Ai h~wi6^{&Y %fid=fopen('e21.dat','w');
I}2P>)K N = 128; % Number of Fourier modes (Time domain sampling points)
,Z S6jZ M1 =3000; % Total number of space steps
n&A'C \ J =100; % Steps between output of space
Su 5>$ T =10; % length of time windows:T*T0
@Tfl>/% T0=0.1; % input pulse width
upvS|KUil MN1=0; % initial value for the space output location
&QNWL] dt = T/N; % time step
(RtueEb.~E n = [-N/2:1:N/2-1]'; % Index
P=1I<Pe w t = n.*dt;
y< C<_2 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
k=GG>]<i u20=u10.*0.0; % input to waveguide 2
H:H6b u1=u10; u2=u20;
; +1RU v U1 = u1;
^*~;k|;& U2 = u2; % Compute initial condition; save it in U
M,}|tsL ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ps$7bN C w=2*pi*n./T;
!`bio cA g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Z0De!?ALV\ L=4; % length of evoluation to compare with S. Trillo's paper
sE{ pzPq! dz=L/M1; % space step, make sure nonlinear<0.05
5'a3huRtV for m1 = 1:1:M1 % Start space evolution
#P#-xz u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
&Z?ut *%S u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
a?YCn! ca1 = fftshift(fft(u1)); % Take Fourier transform
m ?HZ; ca2 = fftshift(fft(u2));
OGiV{9U c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
$BmmNn# c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
,<DB&&EV8 u2 = ifft(fftshift(c2)); % Return to physical space
_lW+>xQ u1 = ifft(fftshift(c1));
a(]`F(L if rem(m1,J) == 0 % Save output every J steps.
.Wi{lt U1 = [U1 u1]; % put solutions in U array
`pd&se'p U2=[U2 u2];
g]UB Z33y MN1=[MN1 m1];
PCn Q_A-Q z1=dz*MN1'; % output location
aCV4Ay G end
9z?oB&5 end
0u lt7s} hg=abs(U1').*abs(U1'); % for data write to excel
,&U4a1%i#c ha=[z1 hg]; % for data write to excel
!se0F.K t1=[0 t'];
fA48 (0p hh=[t1' ha']; % for data write to excel file
oPc\<$ %dlmwrite('aa',hh,'\t'); % save data in the excel format
) rLMIk figure(1)
BK,sc'b waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
.k4W_9 figure(2)
5BR 5X\f0 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
63?)K s 6a}"6d/sTL 非线性超快脉冲耦合的数值方法的Matlab程序 x ]5@>5
wiX ~D
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。
FI8Oz, 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
0tk#Gs[ 56hA]O 29O M\b")Tu{0 ]aCk_*U % This Matlab script file solves the nonlinear Schrodinger equations
p#f+P? % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
(yo;NKq,@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7 1W5.! % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1 p`+ Pag63njg? C=1;
C} IbxKl M1=120, % integer for amplitude
8&" (WuZ@ M3=5000; % integer for length of coupler
#sKWd N = 512; % Number of Fourier modes (Time domain sampling points)
Kt>X[o3m, dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
mmw^{MK! T =40; % length of time:T*T0.
1G~S |,8p dt = T/N; % time step
!S%6Uzsj n = [-N/2:1:N/2-1]'; % Index
( wRBd t = n.*dt;
g= }v>[k E ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
0%s|Zbo!> w=2*pi*n./T;
pO<-., g1=-i*ww./2;
O$`UCq g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
%[<Y9g,:Q g3=-i*ww./2;
5s de P1=0;
IGX:H)&* P2=0;
"%8A :^1 P3=1;
v}J;ZIb P=0;
V@=V5bZLs for m1=1:M1
PU9`<3z5 p=0.032*m1; %input amplitude
XC15 K@K s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
M4Z@O3OI E s1=s10;
z1 i &Ge s20=0.*s10; %input in waveguide 2
'k&?DZ! s30=0.*s10; %input in waveguide 3
V[pvJ( s2=s20;
o?Sla_D s3=s30;
bAxTLIf p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Bd bJ< Is %energy in waveguide 1
O}Ui`eWU p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
r0m)j %energy in waveguide 2
47 u@ 4"M p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
]Gc3Ea;4 %energy in waveguide 3
-'rj&x{Q)U for m3 = 1:1:M3 % Start space evolution
dTEJ=d40 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
fm1X1T . s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
SP
2 8 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
;Hm'6TR! sca1 = fftshift(fft(s1)); % Take Fourier transform
+-068k( sca2 = fftshift(fft(s2));
ST1Ts 5I sca3 = fftshift(fft(s3));
Mj0Cat= sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
?SY<~i<K- sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Q F-)^`N sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
}F`beoMAkM s3 = ifft(fftshift(sc3));
|U[y_Y\ a s2 = ifft(fftshift(sc2)); % Return to physical space
!^U6Z@&/ R s1 = ifft(fftshift(sc1));
0/]_n d end
urY`^lX~ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
2xmk,&s p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
g j G2 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
tw qFs P1=[P1 p1/p10];
i% (yk#=V P2=[P2 p2/p10];
[j6~}zu@ P3=[P3 p3/p10];
!"4w&bQ P=[P p*p];
9+CFR YC end
YaFcz$GE_ figure(1)
.+#Lx;}) plot(P,P1, P,P2, P,P3);
qc!xW ,I KS!yT_O 转自：
http://blog.163.com/opto_wang/
