计算脉冲在非线性耦合器中演化的Matlab 程序 0 b6jGa J9eOBom8e< % This Matlab script file solves the coupled nonlinear Schrodinger equations of
G%^jgr) % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
9u R+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
waI?X2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
g%Bh-O9\ Wip@MGtJ %fid=fopen('e21.dat','w');
? lq N = 128; % Number of Fourier modes (Time domain sampling points)
B|pO2d e M1 =3000; % Total number of space steps
#(swVo:+E J =100; % Steps between output of space
ze2%#< T =10; % length of time windows:T*T0
0t*e#,y T0=0.1; % input pulse width
Lh%z2 5t MN1=0; % initial value for the space output location
EP,j+^RVf dt = T/N; % time step
xfoQx_]$Im n = [-N/2:1:N/2-1]'; % Index
9$[6\jMh t = n.*dt;
Ak3cE_*Y/ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
_ PT5 u20=u10.*0.0; % input to waveguide 2
cq]JD6937 u1=u10; u2=u20;
p3r("\Za, U1 = u1;
aIt Q(+y U2 = u2; % Compute initial condition; save it in U
'
`
_TFTO ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
GWFF.Mo^ w=2*pi*n./T;
` _aX>fw g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
F!7dGa$ L=4; % length of evoluation to compare with S. Trillo's paper
ezimQ dz=L/M1; % space step, make sure nonlinear<0.05
(P!r^87 for m1 = 1:1:M1 % Start space evolution
Vu.VH([b]Q u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
O6*2oUKqK u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
&1 /OwTI4J ca1 = fftshift(fft(u1)); % Take Fourier transform
"DaE(S& ca2 = fftshift(fft(u2));
Zt_~Zxn3 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
m`i_O0T c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
u7&q(Z&&O u2 = ifft(fftshift(c2)); % Return to physical space
&Va="HNKt u1 = ifft(fftshift(c1));
.~$!BWP if rem(m1,J) == 0 % Save output every J steps.
U!d|5W.{Q U1 = [U1 u1]; % put solutions in U array
.RNY}bbk U2=[U2 u2];
Pi+pQFz5 MN1=[MN1 m1];
R2 Es~T z1=dz*MN1'; % output location
T@wgWE<0y_ end
>|X ) end
vB7 4r]'F hg=abs(U1').*abs(U1'); % for data write to excel
|I[/Fl: ha=[z1 hg]; % for data write to excel
yPrF2@#XZ/ t1=[0 t'];
6VUs:iO1j5 hh=[t1' ha']; % for data write to excel file
\?v?%}x %dlmwrite('aa',hh,'\t'); % save data in the excel format
E5aRTDLq figure(1)
vtq$@#?~ b waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Mj& G5R~_ figure(2)
u Mx6: waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
xX f,j#`" 0=0,ix7?# 非线性超快脉冲耦合的数值方法的Matlab程序 8)lrQvZ dGyrzuPJ 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。
lArKfs/ 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
dI%?uk 1=Z!ZY}}e ;NOmI+t0w& .k:heN2-x % This Matlab script file solves the nonlinear Schrodinger equations
},n? % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
? g\e mhG % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;6 eBfMhL % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
rD+mI/ _J` h1t~hrq C=1;
wz '= M1=120, % integer for amplitude
({ O~O5k M3=5000; % integer for length of coupler
7fI2b,~ N = 512; % Number of Fourier modes (Time domain sampling points)
0G31Kou dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
NbC2N)L4 T =40; % length of time:T*T0.
:8K}e]!c1 dt = T/N; % time step
q<j9l'dHG n = [-N/2:1:N/2-1]'; % Index
\TZSn1isZX t = n.*dt;
@9eN\b%I^H ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
2 x>7>;> w=2*pi*n./T;
U9ZuD40\ g1=-i*ww./2;
M8V c5 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
6Df*wi!jI g3=-i*ww./2;
k".kbwcaF P1=0;
<UF0Xc&X' P2=0;
(3Q$) 0t P3=1;
qA;Gl"HF P=0;
;4U"y8PVTh for m1=1:M1
LSo*JO6 p=0.032*m1; %input amplitude
)s,LFIy<A s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
@DIEENiM s1=s10;
GE`1j'^- s20=0.*s10; %input in waveguide 2
3. @LAF s30=0.*s10; %input in waveguide 3
y XKddD s2=s20;
EK=
y!> s3=s30;
RC}m]!Uz p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
#i . ,+Q %energy in waveguide 1
"u]&~$ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
C6EG M/m8 %energy in waveguide 2
,{mv6?_ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
D Qz+t %energy in waveguide 3
Vpne-PW for m3 = 1:1:M3 % Start space evolution
"={* 0P s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
.%y'q!? s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
pHuR_U5*? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
}K8 e(i6z sca1 = fftshift(fft(s1)); % Take Fourier transform
|_ +#&x sca2 = fftshift(fft(s2));
cF 4 ,dnI sca3 = fftshift(fft(s3));
JO*/UC>" sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
z 3]W # sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
?m5E Xe sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
]Zt ]wnL+ s3 = ifft(fftshift(sc3));
63 'X#S s2 = ifft(fftshift(sc2)); % Return to physical space
7UY4* j|[C s1 = ifft(fftshift(sc1));
^D5Jqh)
end
(8aj`> y p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
#M{qMJHDo p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
`3 i<jZMG p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
,cL; ,YN P1=[P1 p1/p10];
)l$}plT4 P2=[P2 p2/p10];
y+T[="W P3=[P3 p3/p10];
;}iB9 Tl P=[P p*p];
nj0sh"~+ end
m3BL figure(1)
O >pv/Ns plot(P,P1, P,P2, P,P3);
Yb-{+H8{ J oz>2P.7 转自：
http://blog.163.com/opto_wang/
