计算脉冲在非线性耦合器中演化的Matlab 程序 QYbB\Y [+o{0o> % This Matlab script file solves the coupled nonlinear Schrodinger equations of
G`l\R:Q % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
1"y !wsM% % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Rs=Fcvl % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1>e30Ri,g jV2H61d %fid=fopen('e21.dat','w');
4r$ #- N = 128; % Number of Fourier modes (Time domain sampling points)
Xy(QK2| M1 =3000; % Total number of space steps
0$|VkMq ( J =100; % Steps between output of space
3#t9pI4 T =10; % length of time windows:T*T0
<.)= CK T0=0.1; % input pulse width
Yh9 5W MN1=0; % initial value for the space output location
~) ;4O8~. dt = T/N; % time step
`sm Cfh}j6 n = [-N/2:1:N/2-1]'; % Index
b%lB&}uw} t = n.*dt;
I7vP*YE 7F u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
437Wy+Q|e u20=u10.*0.0; % input to waveguide 2
{v*4mT u1=u10; u2=u20;
k5< n:dS U1 = u1;
+c _AAMe U2 = u2; % Compute initial condition; save it in U
o'lG9ePM| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Z0&^(Fb w=2*pi*n./T;
zh) &6'S\ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
~ n<|f L=4; % length of evoluation to compare with S. Trillo's paper
^ X&`YXjuN dz=L/M1; % space step, make sure nonlinear<0.05
b=Nsz$[ for m1 = 1:1:M1 % Start space evolution
4PVg? u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
$2Wk#F2c= u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
ftY&Q#[ ca1 = fftshift(fft(u1)); % Take Fourier transform
R"OT&:0/ ca2 = fftshift(fft(u2));
4&NB xe c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Mg\588cI c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
lB27Z} u2 = ifft(fftshift(c2)); % Return to physical space
Qb@j8Xa4[ u1 = ifft(fftshift(c1));
) , {3LIr if rem(m1,J) == 0 % Save output every J steps.
#N`'hPD} U1 = [U1 u1]; % put solutions in U array
ai?uJ} U2=[U2 u2];
Q3>qT84 MN1=[MN1 m1];
"dCIg{j z1=dz*MN1'; % output location
4 AhF E@ end
$MasYi end
q<\r}1Dm hg=abs(U1').*abs(U1'); % for data write to excel
@Xoh@:j\ ha=[z1 hg]; % for data write to excel
.U(6])%;@ t1=[0 t'];
-v9 (43 hh=[t1' ha']; % for data write to excel file
>> cW0I/` %dlmwrite('aa',hh,'\t'); % save data in the excel format
xLIyh7$t figure(1)
eQQVfEvS waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Jha*BaD~N figure(2)
tgBA(2/Co waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
}|h-=T ' {Q/@ Y.~< 非线性超快脉冲耦合的数值方法的Matlab程序
!& c%!* g S(JgN 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。
c Mi9 Z] 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
K/( LF} Ty b_'|?rW Yaq0mef0 Z2{ $FN % This Matlab script file solves the nonlinear Schrodinger equations
j 1 'H| 4 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
-6 v?iiZr % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
z*nztvY@e % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Nj6Np ^@sH akw:3 +` C=1;
M/V"Ke"N M1=120, % integer for amplitude
.~'q
yD2V M3=5000; % integer for length of coupler
@lB1t=
D N = 512; % Number of Fourier modes (Time domain sampling points)
>pt I!\ i} dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
,S(_YS^m T =40; % length of time:T*T0.
:%Z)u:~': dt = T/N; % time step
.WOF:Nu4
n = [-N/2:1:N/2-1]'; % Index
MS SHMR t = n.*dt;
;$a|4_U$m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
m";8 nm w=2*pi*n./T;
nb5%a g1=-i*ww./2;
O'S xTwO g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
p38s&\-kEN g3=-i*ww./2;
T5 ~Qfl?Y P1=0;
-'W:P'B G P2=0;
hQSJt[8My P3=1;
EI9Yv>7 d{ P=0;
17Q*
<iCs for m1=1:M1
UIQ=b;J9 p=0.032*m1; %input amplitude
#l2WRw_t s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
,38bT#p:,r s1=s10;
I |D]NY^ s20=0.*s10; %input in waveguide 2
fv3)#>Dgp> s30=0.*s10; %input in waveguide 3
Y!E| X 3 s2=s20;
jM@@N. s3=s30;
8/34{2048 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Q[O U` %energy in waveguide 1
S4O:?^28 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Qzk/oH s %energy in waveguide 2
J! eVw\6 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
WY ~}sE %energy in waveguide 3
9aqFdlbY for m3 = 1:1:M3 % Start space evolution
FH H2 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
$0iN43WSQ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
sEfGf. s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
~w%Z Bp sca1 = fftshift(fft(s1)); % Take Fourier transform
PzTTL=G + sca2 = fftshift(fft(s2));
[laX~(ND{ sca3 = fftshift(fft(s3));
b OmM~pD sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
w1A&p sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
K[ TMTn sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
=09j1:''<d s3 = ifft(fftshift(sc3));
s?K4::@ Fv s2 = ifft(fftshift(sc2)); % Return to physical space
El&pu x2 s1 = ifft(fftshift(sc1));
' *p-` end
Pq7tNM E p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
!r!Mq~X<= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
I0jEhg%J Z p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
zZh`go02E P1=[P1 p1/p10];
1y 8:tri>N P2=[P2 p2/p10];
v:T` D P3=[P3 p3/p10];
kAk,:a;P P=[P p*p];
.y[K =p3 end
z06pX$Q.< figure(1)
:* / `` plot(P,P1, P,P2, P,P3);
:U[_V4? 7 yZ)ScB ^ 转自：
http://blog.163.com/opto_wang/
