计算脉冲在非线性耦合器中演化的Matlab 程序 ,T&B.'cq ]4z? sk@ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
W&bh&KzCW % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
_v2FXm % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
(5G^"Srw % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
pOH_ CXw BT#'< !7! %fid=fopen('e21.dat','w');
Pi+, y N = 128; % Number of Fourier modes (Time domain sampling points)
Q3oVl^ q M1 =3000; % Total number of space steps
Q'Q+mt8u5 J =100; % Steps between output of space
(V e[FhA T =10; % length of time windows:T*T0
/3+7a\|mKr T0=0.1; % input pulse width
W*U\79H MN1=0; % initial value for the space output location
vkBng sS dt = T/N; % time step
?"sk" { n = [-N/2:1:N/2-1]'; % Index
2!" N9Adt t = n.*dt;
Keof{>V=CA u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
UTs0=:+,t u20=u10.*0.0; % input to waveguide 2
]Ff&zBJ u1=u10; u2=u20;
`+*
M r U1 = u1;
IS'=%qhC` U2 = u2; % Compute initial condition; save it in U
0Y!Bb2 m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
l|N 1u=Z w=2*pi*n./T;
\" .3x
PkE g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
iY*Xm, # L=4; % length of evoluation to compare with S. Trillo's paper
-{L[Wt{1 dz=L/M1; % space step, make sure nonlinear<0.05
$f C = v for m1 = 1:1:M1 % Start space evolution
*AxKV5[H u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
},[j+wx u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
XM8C {I1 ca1 = fftshift(fft(u1)); % Take Fourier transform
y4shW|>5_ ca2 = fftshift(fft(u2));
% C)U
F c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Q) FL| c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Xb;CY9 & u2 = ifft(fftshift(c2)); % Return to physical space
"t\r jFw u1 = ifft(fftshift(c1));
gQ/zk3?k if rem(m1,J) == 0 % Save output every J steps.
YTYYb#"Q U1 = [U1 u1]; % put solutions in U array
U'lrdc" Q U2=[U2 u2];
y l3iU:+V MN1=[MN1 m1];
J-I7K !B z1=dz*MN1'; % output location
RHB>svT^K> end
Ye1P5+W( end
`9 $?g|rB hg=abs(U1').*abs(U1'); % for data write to excel
i>e7 5`9 ha=[z1 hg]; % for data write to excel
S!g&&RDx t1=[0 t'];
XPX{c|]>. hh=[t1' ha']; % for data write to excel file
O'5( L9, %dlmwrite('aa',hh,'\t'); % save data in the excel format
'VF9j\a figure(1)
T]E$H, p waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Vwv O@G7A figure(2)
@rVmr{UE waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
1 k H >xH3*0 Lp 非线性超快脉冲耦合的数值方法的Matlab程序 9prG@ J.O;c5wL 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。
1` 9/[2z 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
q .?D{[2 y)(@ >GZF \ER "w_(p|c m= % This Matlab script file solves the nonlinear Schrodinger equations
zHx?-Q&3 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
&G'R{s&" % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
c"0CHrd % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
!TG"AW z2,rnm )Q C=1;
kW/ksz0) M1=120, % integer for amplitude
wePMBL1P* M3=5000; % integer for length of coupler
* W i(% N = 512; % Number of Fourier modes (Time domain sampling points)
g\6(ezUF* dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
A
7TP 1 T =40; % length of time:T*T0.
lUWjm%| dt = T/N; % time step
Y3-15: - n = [-N/2:1:N/2-1]'; % Index
~[,E
i k t = n.*dt;
/+66y=`UJ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
U;{VL! w=2*pi*n./T;
T>LtN g1=-i*ww./2;
Xv'64Nc!; g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
qP]Gl--q{ g3=-i*ww./2;
&, K;F' P1=0;
!X#=Pt[, P2=0;
+L X&1GX P3=1;
LTJ|EXYA P=0;
V: IoeQ]- for m1=1:M1
,',fO?Qv' p=0.032*m1; %input amplitude
h3JIiwv0! s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
}*+ca>K s1=s10;
UkeW2l`: s20=0.*s10; %input in waveguide 2
)DoY*'Cl s30=0.*s10; %input in waveguide 3
gE8>5_R| s2=s20;
242lR0#aY s3=s30;
= P2T&Gb p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
v'Lckw@G4 %energy in waveguide 1
6i&WF<%D p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
zzPgL E 55 %energy in waveguide 2
g:O VAA p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Bepl S %energy in waveguide 3
`cVG_= 2 for m3 = 1:1:M3 % Start space evolution
/~AajLxu3W s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
@3b0hi4 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
i;Gl-b\_h s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
D4
e)v% sca1 = fftshift(fft(s1)); % Take Fourier transform
BDcl1f T sca2 = fftshift(fft(s2));
(+T|B E3*# sca3 = fftshift(fft(s3));
TNiF l hq sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
^8We}bs-c sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
b /<n:*$
sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
GKm)wOb(*S s3 = ifft(fftshift(sc3));
hX[hR s2 = ifft(fftshift(sc2)); % Return to physical space
>5XE*9 s1 = ifft(fftshift(sc1));
od-N7lp# end
q?\3m3GM p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
v`no d I p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
=SLJkw&w6 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
u QCQ$ P1=[P1 p1/p10];
u* PN1E P2=[P2 p2/p10];
;2& (]1X P3=[P3 p3/p10];
!_zmm$bR
P=[P p*p];
[?]s((A~B end
}X }f X#[ figure(1)
a}%>i ~v< plot(P,P1, P,P2, P,P3);
uv._N6mj BcA:M\dK% 转自：
http://blog.163.com/opto_wang/
