计算脉冲在非线性耦合器中演化的Matlab 程序 :I)WSXP9h }5I+VY7a % This Matlab script file solves the coupled nonlinear Schrodinger equations of
.0gF&>I} % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
o/6 'g)r* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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7^PTgcO %fid=fopen('e21.dat','w');
*$4 EXwt' N = 128; % Number of Fourier modes (Time domain sampling points)
H`XE5Hk)P% M1 =3000; % Total number of space steps
@ 7WWoy J =100; % Steps between output of space
oRbG6Vv/ T =10; % length of time windows:T*T0
<Y9 L3O`[ T0=0.1; % input pulse width
%xH2jf MN1=0; % initial value for the space output location
];n 3H~2 dt = T/N; % time step
7"iUyZ( n = [-N/2:1:N/2-1]'; % Index
)uJu .foE t = n.*dt;
]l~TI8gC u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
z(yJ/~m u20=u10.*0.0; % input to waveguide 2
oOj7y>Nm u1=u10; u2=u20;
"G+g(?N]j U1 = u1;
h>A~. . U2 = u2; % Compute initial condition; save it in U
;]/emw=a ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ZjEc\{ s w=2*pi*n./T;
rda/ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
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L=4; % length of evoluation to compare with S. Trillo's paper
j-% vLL/ dz=L/M1; % space step, make sure nonlinear<0.05
`wzb}"gLsM for m1 = 1:1:M1 % Start space evolution
z3\WcW7| u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
63EwV p /| u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
n*Q~< `T ca1 = fftshift(fft(u1)); % Take Fourier transform
Qel2OI `b ca2 = fftshift(fft(u2));
LZ ?z5U: c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
vs`"BQYf c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
*T+Bjj;w u2 = ifft(fftshift(c2)); % Return to physical space
Wvg+5Q u1 = ifft(fftshift(c1));
vfn _Nq; if rem(m1,J) == 0 % Save output every J steps.
LMF@ -j% U1 = [U1 u1]; % put solutions in U array
\@3B%RW0 U2=[U2 u2];
p;P"mp\' MN1=[MN1 m1];
^^O @ [_ z1=dz*MN1'; % output location
zP
F0M( end
Xv~v=.HNhk end
LxcC5/@\~( hg=abs(U1').*abs(U1'); % for data write to excel
-{^I T` ha=[z1 hg]; % for data write to excel
Tgf#I*(^] t1=[0 t'];
%O=U|tuc$ hh=[t1' ha']; % for data write to excel file
d [p-zn. %dlmwrite('aa',hh,'\t'); % save data in the excel format
.d4L@{V figure(1)
D #`o waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
U i^~A figure(2)
wd
4]Z0; waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
}r+(Z.BHM vzr?#FG 非线性超快脉冲耦合的数值方法的Matlab程序 I 19 / ;E!(W=]*F 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。
!P_8D*^9 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
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W%Bsqn \E!a=cL ! 'UW(0 P Xw % This Matlab script file solves the nonlinear Schrodinger equations
.:`+4n % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
"IjCuR;# % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;a Y.CgX % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)37 .H^7 pK nM= N1f C=1;
W`q iPLk M1=120, % integer for amplitude
r&MHww1i M3=5000; % integer for length of coupler
?3 #W 7sF N = 512; % Number of Fourier modes (Time domain sampling points)
Y%i=u:}fm dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
vq.~8c1 T =40; % length of time:T*T0.
Ub(8ko :8$ dt = T/N; % time step
C,; hNg[ n = [-N/2:1:N/2-1]'; % Index
>R9_ ; t = n.*dt;
HZG^o^o1l+ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
j .b7<Vr4; w=2*pi*n./T;
QXQ'QEG g1=-i*ww./2;
sM4Qu./ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
n'
XvPV| g3=-i*ww./2;
@jKiE%OP P1=0;
YV6@SXy P2=0;
,D6hJ_: P3=1;
^h c&rD )_ P=0;
ptCF W_UV for m1=1:M1
Qh0tU<jG p=0.032*m1; %input amplitude
|SO?UIWp s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
(O v{gj^ s1=s10;
L,m '/} $ s20=0.*s10; %input in waveguide 2
+5zLQ>]z s30=0.*s10; %input in waveguide 3
XMR$I&;G8 s2=s20;
"5 /i s3=s30;
~)Z MGx p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
7jj.maK %energy in waveguide 1
:Z}d#Rbl p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Xf4 %energy in waveguide 2
gH0'
Ok' p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
DaA9fJ7a
%energy in waveguide 3
FuWMVT`Y for m3 = 1:1:M3 % Start space evolution
HFtl4P s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
z vM=k-Ec s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
MM+xm{4l s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
go6XUe sca1 = fftshift(fft(s1)); % Take Fourier transform
Ve]ufn6 sca2 = fftshift(fft(s2));
efc<lSUR sca3 = fftshift(fft(s3));
f>*D@TrU sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
k2"DFXsv sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
h~!KNF*XW sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
(9"w{pnlLc s3 = ifft(fftshift(sc3));
%gd {u\h^ s2 = ifft(fftshift(sc2)); % Return to physical space
3? R56$-+ s1 = ifft(fftshift(sc1));
_F2 R
x@Y end
\),D W) p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
5- =&4R\k p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
#><P28m p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
I 3ZlKI P1=[P1 p1/p10];
r
I- A)b4 P2=[P2 p2/p10];
V!|:rwG2 P3=[P3 p3/p10];
/K@_O\+;Q P=[P p*p];
UdIl5P end
!LG 5q/}& figure(1)
feSj3,<! plot(P,P1, P,P2, P,P3);
y7x& /2 ;Sc}e/WJj 转自：
http://blog.163.com/opto_wang/
