计算脉冲在非线性耦合器中演化的Matlab 程序 Q`{2 yU:r nA)KRCi % This Matlab script file solves the coupled nonlinear Schrodinger equations of
&4R -5i2a % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
)' 3V4Z& % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
e_v_y$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
vkgAI< V[RsSZx
= %fid=fopen('e21.dat','w');
/nas~{B N = 128; % Number of Fourier modes (Time domain sampling points)
u4QBD5T" M1 =3000; % Total number of space steps
_Q=h3(ZI J =100; % Steps between output of space
n=8DC& T =10; % length of time windows:T*T0
px>g T0=0.1; % input pulse width
&o]ic(74c? MN1=0; % initial value for the space output location
qQ
T ^d dt = T/N; % time step
5%K(t Rc| n = [-N/2:1:N/2-1]'; % Index
(S)jV 0 t = n.*dt;
*<"#1H/q u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
:5,
k64'D u20=u10.*0.0; % input to waveguide 2
! 0DOj[" u1=u10; u2=u20;
}xG~ a=, U1 = u1;
W#sCvI@ U2 = u2; % Compute initial condition; save it in U
sb"h:i>O4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
=f\BAi w=2*pi*n./T;
sG K7Uy g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
59X'-fg , L=4; % length of evoluation to compare with S. Trillo's paper
mDX
UF~G[ dz=L/M1; % space step, make sure nonlinear<0.05
H2oD0f| for m1 = 1:1:M1 % Start space evolution
.;,` bH0 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
uJ9
hU`h u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
;cD &qheDV ca1 = fftshift(fft(u1)); % Take Fourier transform
1 h,m ca2 = fftshift(fft(u2));
(D~NW*, 9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
3^-yw ` c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
}h=}!R'm u2 = ifft(fftshift(c2)); % Return to physical space
t}x^*I$* u1 = ifft(fftshift(c1));
l`(pV ;{W if rem(m1,J) == 0 % Save output every J steps.
-?Kd[Ma U1 = [U1 u1]; % put solutions in U array
trm-&e7q?; U2=[U2 u2];
D wtvtglqV MN1=[MN1 m1];
gWLhO|y z1=dz*MN1'; % output location
5JggU end
DR
c-L$bD end
A=bBI>GEYP hg=abs(U1').*abs(U1'); % for data write to excel
2'T uS? ha=[z1 hg]; % for data write to excel
=Yt)b/0b9 t1=[0 t'];
g7@.Fa.u'! hh=[t1' ha']; % for data write to excel file
|:)ARH6l# %dlmwrite('aa',hh,'\t'); % save data in the excel format
k+;XQEH figure(1)
g t|:K)[,6 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
''3b[< figure(2)
d*tn&d~k, waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
JK9 J;c#T o%_Hmd;_' 非线性超快脉冲耦合的数值方法的Matlab程序 ]!'9Y}9a DC+l3 N 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。
u81@vEK:_ 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
P`TJqJiY~ 7?W 1i{( :/~TV >^ TcO % This Matlab script file solves the nonlinear Schrodinger equations
i=AQ1X\s % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
uB>OS 1= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7L !$hk % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'8V>:dy> F*J@O Y8i C=1;
mr<camL5 M1=120, % integer for amplitude
<BX'Owbs!O M3=5000; % integer for length of coupler
'Fr"96C $ N = 512; % Number of Fourier modes (Time domain sampling points)
?CSv ;: dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
WNcJ710k27 T =40; % length of time:T*T0.
" gQJeMU dt = T/N; % time step
{2=f,,| +f n = [-N/2:1:N/2-1]'; % Index
r9y(j
z t = n.*dt;
X3Yi|dyn T ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
}zy h! w=2*pi*n./T;
=kDh: &u% g1=-i*ww./2;
H tAO9 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
bD4 aSubN g3=-i*ww./2;
CA]u3bf~ P1=0;
(K `@OwD P2=0;
&[qJ=HMm I P3=1;
T))F
r : P=0;
qj:\ )#I for m1=1:M1
+Z1y1%a p=0.032*m1; %input amplitude
B*&HQW *u s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
..;e p2jSs s1=s10;
$9rQ w1#e s20=0.*s10; %input in waveguide 2
~jDf ,a2 s30=0.*s10; %input in waveguide 3
_ 0 h)O s2=s20;
v/[*Pze,C s3=s30;
cllnYvr3 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Y0xn}:%K %energy in waveguide 1
0}qnq" p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
u}eLf'^ZCe %energy in waveguide 2
<Wa7$ h F p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
-W.bOr %energy in waveguide 3
h)pYV>!d for m3 = 1:1:M3 % Start space evolution
e!oL!Zg s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
YES-,;ZQ' s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
6YF<GF{ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
J?_-Dg(= sca1 = fftshift(fft(s1)); % Take Fourier transform
G6q*U, sca2 = fftshift(fft(s2));
f?W" ^6Df sca3 = fftshift(fft(s3));
-h%1rw sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
>^J sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
@BoZZ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
$5N\sdyZxg s3 = ifft(fftshift(sc3));
g[ O6WZ!F_ s2 = ifft(fftshift(sc2)); % Return to physical space
{VT**o s1 = ifft(fftshift(sc1));
6oy[0hj end
3S{3AmKj? p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
NEW0dF&) p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
G0b##-.'^ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
*^i"q\n5( P1=[P1 p1/p10];
V#TNv 0&0 P2=[P2 p2/p10];
4M PR P3=[P3 p3/p10];
(o518fmR P=[P p*p];
~'VVCtA end
{+jO/ZQu5 figure(1)
9O|k|FD plot(P,P1, P,P2, P,P3);
+@qIDUiF3 sOhKMz 转自：
http://blog.163.com/opto_wang/
