计算脉冲在非线性耦合器中演化的Matlab 程序 u,f$cR B]C 9f % This Matlab script file solves the coupled nonlinear Schrodinger equations of
JPt0k % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
HT@/0MF{J % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
NR@n% p % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8t$w/#'@ +. ` I %fid=fopen('e21.dat','w');
]"DsZI-glW N = 128; % Number of Fourier modes (Time domain sampling points)
!JOM+P: M1 =3000; % Total number of space steps
12bt\ h9 J =100; % Steps between output of space
EWX!:BKf T =10; % length of time windows:T*T0
]>%M%B T0=0.1; % input pulse width
g5,Bj MN1=0; % initial value for the space output location
5kju{2`GF dt = T/N; % time step
due'c! wW n = [-N/2:1:N/2-1]'; % Index
<:gNx%R t = n.*dt;
UrhSX!g/A> u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
=u,8(:R]s u20=u10.*0.0; % input to waveguide 2
?--EIA8mfp u1=u10; u2=u20;
}-8ZSWog6f U1 = u1;
Z8yt8O U2 = u2; % Compute initial condition; save it in U
^<"^}Jh.M ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
\as^z!< w=2*pi*n./T;
PE7D)!d
T g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
X$4MpXx L=4; % length of evoluation to compare with S. Trillo's paper
FLE2]cL- dz=L/M1; % space step, make sure nonlinear<0.05
{G^f/% for m1 = 1:1:M1 % Start space evolution
#rs]5tx([ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
@$bEY#*C u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
LE1#pB3TG ca1 = fftshift(fft(u1)); % Take Fourier transform
| 5h ~&kA ca2 = fftshift(fft(u2));
sBuOKT/j c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
@|hn @!YK c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
UOwEA9q% u2 = ifft(fftshift(c2)); % Return to physical space
u#&ZD| u1 = ifft(fftshift(c1));
UW?(-_8 if rem(m1,J) == 0 % Save output every J steps.
BA
9c-Ay U1 = [U1 u1]; % put solutions in U array
/ ~\ I U2=[U2 u2];
),u)#`.l
G MN1=[MN1 m1];
Munal=wL z1=dz*MN1'; % output location
F=qG +T end
4sCzUvI~Y1 end
/eI]!a hg=abs(U1').*abs(U1'); % for data write to excel
m [t4XK ha=[z1 hg]; % for data write to excel
)^^Eh=Kbj t1=[0 t'];
ys#V_ysb hh=[t1' ha']; % for data write to excel file
rCTH 5" %dlmwrite('aa',hh,'\t'); % save data in the excel format
;94e figure(1)
[IgB78_ $ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
P
nxx W? figure(2)
-? |-ux waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
&~SPDiu.t MkCq$MA 非线性超快脉冲耦合的数值方法的Matlab程序 )8rN T cP
(?v 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
d>f.p"B.gj Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0M=U >g) AzmIS m eInx\/ k-`5T mW % This Matlab script file solves the nonlinear Schrodinger equations
6S 2u% -] % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
4-wCk=I % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
pg4J)<t# % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*co=<g]4KY ofu
{g C=1;
>n^| eAH M1=120, % integer for amplitude
q yx
' M3=5000; % integer for length of coupler
wACx}'+M N = 512; % Number of Fourier modes (Time domain sampling points)
~$PQ8[= dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
ha%3%O8Z T =40; % length of time:T*T0.
v j ?6,Ae dt = T/N; % time step
"{&?t}rj+ n = [-N/2:1:N/2-1]'; % Index
Z|h&Zd1z t = n.*dt;
\en}8r9cy ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:*`5|'G} w=2*pi*n./T;
M2.Pf s g1=-i*ww./2;
= DT7]fU g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ju AUeGT g3=-i*ww./2;
<A _L Zi P1=0;
mqx #N% P2=0;
wj'5D0 P3=1;
r/32pY P=0;
Y~j )B\^{ for m1=1:M1
0CTUcVM#9 p=0.032*m1; %input amplitude
<Kq4thR s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
;ZSJ-r s1=s10;
Pz/bne;= s20=0.*s10; %input in waveguide 2
>H*?ktcW s30=0.*s10; %input in waveguide 3
BJ]4j-^o s2=s20;
S\F;b{S1 s3=s30;
'rX!E,59 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
];vEj*jCX %energy in waveguide 1
i r-= @ @ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
%]zaX-2dm! %energy in waveguide 2
nisW<Q `uB p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
yd -r7iq %energy in waveguide 3
'}Tf9L% for m3 = 1:1:M3 % Start space evolution
}aPx28:/ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
y7s:Buyc s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
^D{!!)O s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
D(m2^\O[ sca1 = fftshift(fft(s1)); % Take Fourier transform
< ah!! sca2 = fftshift(fft(s2));
RO]Vn]qb sca3 = fftshift(fft(s3));
8w:A"" sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
{!$E\e^d sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
bw@"MF{ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
L*rND15 s3 = ifft(fftshift(sc3));
;Tn $c70 s2 = ifft(fftshift(sc2)); % Return to physical space
|fJpX5W-l s1 = ifft(fftshift(sc1));
m~LB0u$ac end
~BS Ip
. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
z^KMYvH
g p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
y" (-O%Pe p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
@-7h}2P Q P1=[P1 p1/p10];
&at ^~ o P2=[P2 p2/p10];
=lE_
Q[P P3=[P3 p3/p10];
O e-FI+7 P=[P p*p];
:$>Co\D end
(4 hCT* figure(1)
Y6>@zz nk plot(P,P1, P,P2, P,P3);
2]$
7 Jj_ t0" 转自：
http://blog.163.com/opto_wang/
