计算脉冲在非线性耦合器中演化的Matlab 程序 b_ 88o-*/ F@Bh>Vb % This Matlab script file solves the coupled nonlinear Schrodinger equations of
TTjj.fq6 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
J/(3:
a> % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
:UjHP}s % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
vUa~PN+Iy `q Sfo` %fid=fopen('e21.dat','w');
sW%U3, j N = 128; % Number of Fourier modes (Time domain sampling points)
[\N,ow,n M1 =3000; % Total number of space steps
1_vaSEov J =100; % Steps between output of space
#"|Y"#@k T =10; % length of time windows:T*T0
(1e;7sNG@ T0=0.1; % input pulse width
5=CL R MN1=0; % initial value for the space output location
a&YD4DQ05 dt = T/N; % time step
NJ8QI(^" n = [-N/2:1:N/2-1]'; % Index
dtJaQ` t = n.*dt;
w- Zb($_ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
4xLU15C u20=u10.*0.0; % input to waveguide 2
9 k.LV/Y u1=u10; u2=u20;
?8 wFT!J U1 = u1;
e* gCc7zz U2 = u2; % Compute initial condition; save it in U
e9r#r~Qq| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_%Q\G,a; w=2*pi*n./T;
rtcY(5Q g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
.v [8ie L=4; % length of evoluation to compare with S. Trillo's paper
[sG=(~BU dz=L/M1; % space step, make sure nonlinear<0.05
8.D$J for m1 = 1:1:M1 % Start space evolution
@
?y(\> u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
31mY]Jve" u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
T 1m097 ca1 = fftshift(fft(u1)); % Take Fourier transform
L+Q"z*W ca2 = fftshift(fft(u2));
jYKs| J)[ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
btb-MSkO c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
C`OdMM>D u2 = ifft(fftshift(c2)); % Return to physical space
JBQ,rX_Hw u1 = ifft(fftshift(c1));
i}Ea>bi{N if rem(m1,J) == 0 % Save output every J steps.
]dk44,EL U1 = [U1 u1]; % put solutions in U array
2GECcx53 U2=[U2 u2];
_QCspPT' c MN1=[MN1 m1];
Q%4>okj, z1=dz*MN1'; % output location
$oK, &_ end
}8 A] end
7 ]a6dMh hg=abs(U1').*abs(U1'); % for data write to excel
'3=[xVnv ha=[z1 hg]; % for data write to excel
(PU0\bGA t1=[0 t'];
z<_{m 4I; hh=[t1' ha']; % for data write to excel file
'LIJpk3J %dlmwrite('aa',hh,'\t'); % save data in the excel format
`.n kC_d figure(1)
s9)
@$3\ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
[ >#?C*s figure(2)
' U {?"FP waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
B&|F9Z6D k{Yj!C>
# 非线性超快脉冲耦合的数值方法的Matlab程序 k <ds7k1m 7QL>f5Q 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
J!%Yy\G Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Lu}oC2 a
#?% I# mJ0nyjX^ \Oh9)X: I % This Matlab script file solves the nonlinear Schrodinger equations
T#?KY % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
k7)H %31; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
fKIwdk%!- % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Zeyhr\T 7 }(LO^,A C=1;
Ac<V!v71 M1=120, % integer for amplitude
j y{T=Nb M3=5000; % integer for length of coupler
(.7_`T6QG N = 512; % Number of Fourier modes (Time domain sampling points)
u*`acmS>N dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Wfkm'BnV T =40; % length of time:T*T0.
VztalwI dt = T/N; % time step
]OZZPo n = [-N/2:1:N/2-1]'; % Index
laqKP+G t = n.*dt;
AS`0.RC- ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
GEfX,9LF & w=2*pi*n./T;
/lDW5 ;d g1=-i*ww./2;
RvV4SlZz g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
=K{$?%"
g3=-i*ww./2;
y.5mYQA4=[ P1=0;
K,%H*1YKK P2=0;
( :]. ?o P3=1;
vG#|CO9 P=0;
wlBdA for m1=1:M1
2fTkHBhn& p=0.032*m1; %input amplitude
~ C6< 75 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
UZMo(rG.]{ s1=s10;
qO[6?q=c: s20=0.*s10; %input in waveguide 2
d z &| 3o s30=0.*s10; %input in waveguide 3
yAR'' > s2=s20;
g"(
vl-Uw s3=s30;
cH'*J/ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
:h0as!2@dp %energy in waveguide 1
IPa08/ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
neJNMdv@T %energy in waveguide 2
;r >?V2,tm p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
=| S8.|r+ %energy in waveguide 3
z,}1K! for m3 = 1:1:M3 % Start space evolution
)y'`C@ijI s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
oP5G*AFUq s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
i;*c|ma1> s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
$&nF1HBI4 sca1 = fftshift(fft(s1)); % Take Fourier transform
Pk [f_%0 sca2 = fftshift(fft(s2));
j{>E.F2. sca3 = fftshift(fft(s3));
Fp4eGuWH# sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
M kko1T=6 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
inZMq(_@$ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
!tv3.:eT s3 = ifft(fftshift(sc3));
2:MB u5** s2 = ifft(fftshift(sc2)); % Return to physical space
YTQ|Hg6jO s1 = ifft(fftshift(sc1));
s
,\w00-: end
X_+`7yCi"x p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
mJ<rzX p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
l!Z >QE`.S p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
[ =u8$5/a P1=[P1 p1/p10];
j#Ly!%dp P2=[P2 p2/p10];
T,Cq;|g5E P3=[P3 p3/p10];
U }MU>kzb P=[P p*p];
+`u]LOAyP= end
468LVe?0 figure(1)
>p O[ S[ plot(P,P1, P,P2, P,P3);
RPP xiYU^ tz
j]c 转自：
http://blog.163.com/opto_wang/
