计算脉冲在非线性耦合器中演化的Matlab 程序 cP`f\\c _W/s=pCh % This Matlab script file solves the coupled nonlinear Schrodinger equations of
a[]=*(AZI % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
GN?^7kI % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
di>"\On- % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
?P,z^ y/h~oGxy %fid=fopen('e21.dat','w');
z*>"I N = 128; % Number of Fourier modes (Time domain sampling points)
UGj!I M1 =3000; % Total number of space steps
@bOhnd#W J =100; % Steps between output of space
8]]uk=P T =10; % length of time windows:T*T0
#Z)e]4{!l T0=0.1; % input pulse width
LoSblV MN1=0; % initial value for the space output location
v*<hE>J0 dt = T/N; % time step
WW\u}z.QJ n = [-N/2:1:N/2-1]'; % Index
z4b2t} t = n.*dt;
d+rrb>-OU u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
\Pi\c~)Pr u20=u10.*0.0; % input to waveguide 2
oS0l Tf\ u1=u10; u2=u20;
U2 U1 = u1;
wUW^
O U2 = u2; % Compute initial condition; save it in U
Q4Zuz)r* ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
X#'DS&{ w=2*pi*n./T;
' 7+x,TszI g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
gPh; L=4; % length of evoluation to compare with S. Trillo's paper
,dhJ\cQ~ dz=L/M1; % space step, make sure nonlinear<0.05
:JH#*5%gQ: for m1 = 1:1:M1 % Start space evolution
K'%2 'd u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
f6vhW66:?x u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
ayfR{RYi ca1 = fftshift(fft(u1)); % Take Fourier transform
O;z:?
ca2 = fftshift(fft(u2));
{^=T&aCYdS c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
yhv(KI c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
1K?RA*aj u2 = ifft(fftshift(c2)); % Return to physical space
g>-pC a u1 = ifft(fftshift(c1));
]$Pl[Vegy if rem(m1,J) == 0 % Save output every J steps.
FM;NA{ U1 = [U1 u1]; % put solutions in U array
3u#bx1 U2=[U2 u2];
z/!LC;( MN1=[MN1 m1];
nNz1gV:0X z1=dz*MN1'; % output location
^MIF+/bQ end
cWjb149@) end
0gO_dyB hg=abs(U1').*abs(U1'); % for data write to excel
m0QE
S ha=[z1 hg]; % for data write to excel
k>E^FB= t1=[0 t'];
a?jUm. hh=[t1' ha']; % for data write to excel file
YbtsJ
<w %dlmwrite('aa',hh,'\t'); % save data in the excel format
|eykb?j` figure(1)
L#O1> waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
waI?X2 figure(2)
g%Bh-O9\ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Wip@MGtJ ?lq 非线性超快脉冲耦合的数值方法的Matlab程序 yJQ>u 2t 6m# 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的
论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
ze2%#< Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
fh_+M"Y0` Lh%z2 5t EP,j+^RVf xfoQx_]$Im % This Matlab script file solves the nonlinear Schrodinger equations
9$[6\jMh % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Ak3cE_*Y/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
_PT5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
9d&@;&al YBh|\ C=1;
"uCO?hv0 M1=120, % integer for amplitude
$B%wK`J M3=5000; % integer for length of coupler
hr$Wt?B N = 512; % Number of Fourier modes (Time domain sampling points)
3LGX ^J<f dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Drm#z05i[g T =40; % length of time:T*T0.
/2^"c+/'p dt = T/N; % time step
!LI6_Oq n = [-N/2:1:N/2-1]'; % Index
JLd-{}A""- t = n.*dt;
"5<:Dj/W ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
@$}Ct w=2*pi*n./T;
m)AF9#aT2 g1=-i*ww./2;
n*A?>NV g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
0JFS%Yjw[ g3=-i*ww./2;
riR(CJ}Ff P1=0;
+YZ*>ki P2=0;
E{;F4wT_@ P3=1;
[|".j#ZlK P=0;
Fn>KdoByN for m1=1:M1
}1fi# p=0.032*m1; %input amplitude
PRJ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
UQZl:DYa s1=s10;
+*RaX (&
s20=0.*s10; %input in waveguide 2
e5RF6roxO s30=0.*s10; %input in waveguide 3
&F-
\t5X=i s2=s20;
j,n\`7dD$ s3=s30;
O22Q
g p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
)ifjK6* %energy in waveguide 1
U$yy7}g p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
8Y4mTW %energy in waveguide 2
R
+
~b@ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
hrNB"W|?x %energy in waveguide 3
s$% t2UaV for m3 = 1:1:M3 % Start space evolution
!"2S'oQKS s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
.n n&K}h s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
|\zzOfaO s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
|v:oLgUdH sca1 = fftshift(fft(s1)); % Take Fourier transform
acrR sca2 = fftshift(fft(s2));
+7\d78U sca3 = fftshift(fft(s3));
6k_Uq.<X sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
6Hbu7r*tm sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
SZ29B sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
2FR+Z3&z s3 = ifft(fftshift(sc3));
SJB^dI**/d s2 = ifft(fftshift(sc2)); % Return to physical space
;6eBfMhL s1 = ifft(fftshift(sc1));
/#WvC;B end
@(bg# p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
aFaioE#h( p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
_9g-D9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
hkb&]XWi[ P1=[P1 p1/p10];
-MRX@ a^1 P2=[P2 p2/p10];
9X?RJ."J P3=[P3 p3/p10];
Ptz##o'{5 P=[P p*p];
FnKC|X end
Fc#Sn2p* figure(1)
^T:L6: plot(P,P1, P,P2, P,P3);
}DQTy.d;P Ol B9z 转自:
http://blog.163.com/opto_wang/