计算脉冲在非线性耦合器中演化的Matlab 程序 N}#Rw2Vl bUcp8 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
s )WA9PiC % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
^iONC&r % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
`t /j6 e] % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
C+' -TLeu aL:|Dr3SX %fid=fopen('e21.dat','w');
1%_RXQVG N = 128; % Number of Fourier modes (Time domain sampling points)
3(o MASf M1 =3000; % Total number of space steps
J$6WU z:? J =100; % Steps between output of space
d92Z;FWb T =10; % length of time windows:T*T0
BWxfY^,'&6 T0=0.1; % input pulse width
?kR1T0lKkE MN1=0; % initial value for the space output location
OJu>#
dt = T/N; % time step
/xUF@%rT n = [-N/2:1:N/2-1]'; % Index
E3 % ~!ZC t = n.*dt;
tMw65Xei6b u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
93*d:W8Vr u20=u10.*0.0; % input to waveguide 2
g-K;J4 K% u1=u10; u2=u20;
},d^y:m U1 = u1;
[;wJM|Z J0 U2 = u2; % Compute initial condition; save it in U
;B@#,6t/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_&] 7 w=2*pi*n./T;
s?HK2b^;D g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
PE5*]+lW. L=4; % length of evoluation to compare with S. Trillo's paper
'1D $ ; dz=L/M1; % space step, make sure nonlinear<0.05
P%:?"t+J`; for m1 = 1:1:M1 % Start space evolution
lG-B)
F u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
*OA(v^@tx7 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
kSV(T'#x ca1 = fftshift(fft(u1)); % Take Fourier transform
)n)AmNpq
ca2 = fftshift(fft(u2));
wn@~80)$ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
(kR
NqfX c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
+(= -95qZ u2 = ifft(fftshift(c2)); % Return to physical space
<%YW/k"o u1 = ifft(fftshift(c1));
E2 M<I;:EA if rem(m1,J) == 0 % Save output every J steps.
E#_/#J]UQn U1 = [U1 u1]; % put solutions in U array
|fKT@2( U2=[U2 u2];
4^r6RS@z MN1=[MN1 m1];
/Pe x tj< z1=dz*MN1'; % output location
z6)N![ X end
)P7ep end
DY#195H hg=abs(U1').*abs(U1'); % for data write to excel
K+|XI|1p ha=[z1 hg]; % for data write to excel
F^/KD<cgK t1=[0 t'];
2V]a +Cgk hh=[t1' ha']; % for data write to excel file
1 ?BLL;[a8 %dlmwrite('aa',hh,'\t'); % save data in the excel format
ng/h6
S figure(1)
B:X%k /{ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
6/ 5c| figure(2)
y7/4u-_c waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Sj I,v+ 2->Lz 非线性超快脉冲耦合的数值方法的Matlab程序 CmXLD} L_x R]yce2w" z 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。
S(CkA\[rz 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
&Y^4>y% v@]SddP,? lD0a<L 3 Gx$m"Jeq\ % This Matlab script file solves the nonlinear Schrodinger equations
Qw5-/p=t % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
=CO Qv= GT % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
mn03KF=n] % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
2 T} >9X =~J VU C=1;
,y'6vW`%g9 M1=120, % integer for amplitude
s7n7u7$j M3=5000; % integer for length of coupler
gs!'*U ) N = 512; % Number of Fourier modes (Time domain sampling points)
DTH }= r- dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
T%oJmp?0 T =40; % length of time:T*T0.
Sed 8Q-m dt = T/N; % time step
/RJ]MQ\*O n = [-N/2:1:N/2-1]'; % Index
U\ Y0v.11 t = n.*dt;
}J6:D]Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
?{aC-3VAT w=2*pi*n./T;
~]?s A{ g1=-i*ww./2;
QOK,- g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
$1 B?@~& g3=-i*ww./2;
x*:VE57,z P1=0;
`uMc.:5\ P2=0;
V|@bITJ?7 P3=1;
"Y^j=?1k P=0;
LU;zpXg\ for m1=1:M1
=v^#MU{k? p=0.032*m1; %input amplitude
`Y.~e E s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
|pS]zD s1=s10;
[K,P)V> K s20=0.*s10; %input in waveguide 2
@5wc 3y s30=0.*s10; %input in waveguide 3
)NhC+=N s2=s20;
im9 w|P 5 s3=s30;
LZ_0=Xx% p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Dqo#+_v %energy in waveguide 1
ROn@tW p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
"p3<-06 %energy in waveguide 2
5?H wM[` p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
tz2=l.1 %energy in waveguide 3
'*L6@e#U for m3 = 1:1:M3 % Start space evolution
w>cqsTq s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
#8M?y*<I s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
hDTC~~J/ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
x# 3*C|A sca1 = fftshift(fft(s1)); % Take Fourier transform
z/"*-+j sca2 = fftshift(fft(s2));
- 5 sca3 = fftshift(fft(s3));
UFT JobU sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
RtR@wZ2\s sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
9tv,,I;iU sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
sgi5dQ s3 = ifft(fftshift(sc3));
jZ-s6r2= s2 = ifft(fftshift(sc2)); % Return to physical space
$.C-_L s1 = ifft(fftshift(sc1));
al}J^MJ end
TW>GYGz p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
$adZ|Q\ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
czIAx1 R9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
&~+QPnI>Pm P1=[P1 p1/p10];
^CLQs;zXE P2=[P2 p2/p10];
hsrf 2Xw[ P3=[P3 p3/p10];
mrR id}2 P=[P p*p];
g/f6N
z end
aOd#f:{y figure(1)
]w>o=<?b plot(P,P1, P,P2, P,P3);
v[|W\y@H/3 ^wWbW&<Tg 转自：
http://blog.163.com/opto_wang/
