计算脉冲在非线性耦合器中演化的Matlab 程序
D+8d^-: jA? #!lx_ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
\lL[08G % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
y48]|%73 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
N k~} aj % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
c0Ug5Vr owVvbC2<b( %fid=fopen('e21.dat','w');
\j)Evjw N = 128; % Number of Fourier modes (Time domain sampling points)
K/4@ 2vF M1 =3000; % Total number of space steps
vwR_2u J =100; % Steps between output of space
>WLPE6E T =10; % length of time windows:T*T0
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,!iK` T0=0.1; % input pulse width
_sjS'*] MN1=0; % initial value for the space output location
!U`&a=k dt = T/N; % time step
{f*Y}/@ n = [-N/2:1:N/2-1]'; % Index
AZ:7_4jz t = n.*dt;
F<4rn u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
I-v}
DuM u20=u10.*0.0; % input to waveguide 2
` X c7b u1=u10; u2=u20;
:XKYfc_y U1 = u1;
[%IOB/{N U2 = u2; % Compute initial condition; save it in U
/i+z#q5' ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
4^_6~ YP7 w=2*pi*n./T;
,CE/o7.FG g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
=4y gbk L=4; % length of evoluation to compare with S. Trillo's paper
LPs%^*8(2 dz=L/M1; % space step, make sure nonlinear<0.05
?2<Q oS for m1 = 1:1:M1 % Start space evolution
$0* sj XV u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
_S!^=9bJ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
}"Y<<e<z: ca1 = fftshift(fft(u1)); % Take Fourier transform
Bz+oM N#XJ ca2 = fftshift(fft(u2));
.X g.,k W c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
HC0juT OiO c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
(qcFGM22U u2 = ifft(fftshift(c2)); % Return to physical space
zI88IM7 / u1 = ifft(fftshift(c1));
J_s`G if rem(m1,J) == 0 % Save output every J steps.
UG 1<Xfu| U1 = [U1 u1]; % put solutions in U array
aRd~T6I U2=[U2 u2];
bC&A@.g{ MN1=[MN1 m1];
b[%@3 }E z1=dz*MN1'; % output location
T2{e 1 =Z7 end
FT).$h~+4 end
x 0 7 = hg=abs(U1').*abs(U1'); % for data write to excel
M-WSdG[AJ ha=[z1 hg]; % for data write to excel
B =Hd:P| t1=[0 t'];
h*%p%t< hh=[t1' ha']; % for data write to excel file
dT`nR" %dlmwrite('aa',hh,'\t'); % save data in the excel format
Z bRRDXk! figure(1)
F`}'^> waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
yoE- a
figure(2)
DJ ru|2 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
(6%T~|a ~tUZQ 5" 非线性超快脉冲耦合的数值方法的Matlab程序 ^} j~:EZb |N,^*xP(6 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。
/Qgb t 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
q 4BXrEOw g$(Y\`zw b"g^Jm! j 0%xk tf % This Matlab script file solves the nonlinear Schrodinger equations
j /V_h'} % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
D5zc{) / % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
k-$Acv( % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
e\)%<G5 Aez2n(yac C=1;
[*% lm9 x M1=120, % integer for amplitude
6v@Prw@.b M3=5000; % integer for length of coupler
& -/J~b)" N = 512; % Number of Fourier modes (Time domain sampling points)
/ Pjd " dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
[bLKjD T =40; % length of time:T*T0.
~B< \#oO dt = T/N; % time step
{/[@uMS_6] n = [-N/2:1:N/2-1]'; % Index
O"9t,B>=i t = n.*dt;
} $?FR ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
lw=kTY bq w=2*pi*n./T;
bbL\ xq^ g1=-i*ww./2;
ff9 m_P g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ZllmaI g3=-i*ww./2;
d% EdvM|) P1=0;
J~x]~}V& P2=0;
fb
f&bJT P3=1;
o sc8;B/ P=0;
I!zoo[/)% for m1=1:M1
+;,{`*W+N p=0.032*m1; %input amplitude
74_ ?@Z( s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-=-^rQx9 s1=s10;
<h(AJX7wsD s20=0.*s10; %input in waveguide 2
`JI p$ s30=0.*s10; %input in waveguide 3
PvKGB01_ s2=s20;
2e6P?pX~2 s3=s30;
6>?qBWW p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
NbWEP\dS'z %energy in waveguide 1
AyJl:aN^ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
|E13W %energy in waveguide 2
(U\o0LI p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
6@aH2+4+ %energy in waveguide 3
n%r>W^2j for m3 = 1:1:M3 % Start space evolution
'[r: pwE s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
~'*23]j s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
,]wab6sY s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Vc\g"1 x sca1 = fftshift(fft(s1)); % Take Fourier transform
CfOyHhhKX sca2 = fftshift(fft(s2));
d 6Y9D=O
sca3 = fftshift(fft(s3));
->#wDL!6 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
%>&~?zrq sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
J5b3r1~D"[ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
eg~
Dm>Es s3 = ifft(fftshift(sc3));
'
!huU s2 = ifft(fftshift(sc2)); % Return to physical space
ZW M:Wj192 s1 = ifft(fftshift(sc1));
h5{//0 y end
P]"@3Z&w p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
:] Wn26z) p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
)t~ad]oM p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
+@$VJM%^7b P1=[P1 p1/p10];
7]@M P2=[P2 p2/p10];
3SM'vV0 [ P3=[P3 p3/p10];
%n]jsdE^| P=[P p*p];
]:ca=&> end
9f['TG," figure(1)
t:dvgRJt* plot(P,P1, P,P2, P,P3);
?23 J(;)s DN9x<%/- 转自：
http://blog.163.com/opto_wang/
