计算脉冲在非线性耦合器中演化的Matlab 程序 an0@EkZ tH17Z % This Matlab script file solves the coupled nonlinear Schrodinger equations of
;2#H M^Mu % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
d=N5cCqq % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
kX5v!pm[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
yd#4b`8U` P8z++h %fid=fopen('e21.dat','w');
x\I9J4Q N = 128; % Number of Fourier modes (Time domain sampling points)
0`,a@Q4 M1 =3000; % Total number of space steps
oV,>u5:B J =100; % Steps between output of space
pd>EUdbrp& T =10; % length of time windows:T*T0
h#;fBQ]
T0=0.1; % input pulse width
n3~xiQ' MN1=0; % initial value for the space output location
~A>3k2N/e dt = T/N; % time step
Vu;tU. n = [-N/2:1:N/2-1]'; % Index
~cU,3g t = n.*dt;
Gd:fWz( u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
/`:5#O u20=u10.*0.0; % input to waveguide 2
F RS@-P u1=u10; u2=u20;
k<8: U1 = u1;
#H M0s~^w& U2 = u2; % Compute initial condition; save it in U
9~Q.[ A ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
qhL e[[> w=2*pi*n./T;
EDL<J1% g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
,i,f1XJ| L=4; % length of evoluation to compare with S. Trillo's paper
yd`.Rb&V dz=L/M1; % space step, make sure nonlinear<0.05
evu @uq for m1 = 1:1:M1 % Start space evolution
<Pg.N u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
\HTXl] u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
GMB%A ca1 = fftshift(fft(u1)); % Take Fourier transform
CNfeHMT ca2 = fftshift(fft(u2));
G)'cd D1 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
{Qlvj.Xw c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
HO&#Lv u2 = ifft(fftshift(c2)); % Return to physical space
vseuk@> u1 = ifft(fftshift(c1));
A%%WPBk{O if rem(m1,J) == 0 % Save output every J steps.
7&l U1 = [U1 u1]; % put solutions in U array
_oe2pL& U2=[U2 u2];
!oM1 MN1=[MN1 m1];
*gVRMSrx4 z1=dz*MN1'; % output location
3 T&m end
Jw"'ZW#W end
vIz~B2%x hg=abs(U1').*abs(U1'); % for data write to excel
YujhpJ< ha=[z1 hg]; % for data write to excel
tw\/1wa. t1=[0 t'];
"d%":F( hh=[t1' ha']; % for data write to excel file
o`h F1*yp %dlmwrite('aa',hh,'\t'); % save data in the excel format
%UgyGQeo figure(1)
g%[lUxL waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
spd>.Cm` figure(2)
YadyRUE waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
m|=/|Hm ]7c715@ 非线性超快脉冲耦合的数值方法的Matlab程序 NWb,$/7T =,,!a/U 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。
v=9:N/sW 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
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lHSMFw bBC3% H^
.* VZY &7JCPw % This Matlab script file solves the nonlinear Schrodinger equations
[ V/*{Z % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Ko2{[% % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
VY Va8[} % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
e"[o2=v;5 SP5/K3t-* C=1;
A2*z M1=120, % integer for amplitude
N[ E
t M3=5000; % integer for length of coupler
PL%_V ?z N = 512; % Number of Fourier modes (Time domain sampling points)
>k
kuw?O@ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
umSbxEZU@ T =40; % length of time:T*T0.
NC@OmSR\0 dt = T/N; % time step
G|IO~o0+ n = [-N/2:1:N/2-1]'; % Index
vMj"% t = n.*dt;
V.\do"m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
!W .ooy5( w=2*pi*n./T;
3%!d&j>v g1=-i*ww./2;
|brl<*: g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
PgxD?Oi8 g3=-i*ww./2;
97'*Xq P1=0;
/<
h~d P2=0;
$(.[b][S P3=1;
yH@W6' . P=0;
"P"~/<:) for m1=1:M1
|f?tyQ p=0.032*m1; %input amplitude
0rjxWPc s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
1+.(N:) + s1=s10;
&37QUdp+p s20=0.*s10; %input in waveguide 2
![{> f6{J s30=0.*s10; %input in waveguide 3
%R-"5?eTtu s2=s20;
|*i0h`a s3=s30;
.K XpB7: p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
'-S^z"ZrI %energy in waveguide 1
yA
\C3r' p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
YPFjAQ %energy in waveguide 2
@/E5$mX` p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
u])N^AY"sj %energy in waveguide 3
aQ46euth for m3 = 1:1:M3 % Start space evolution
Ef:.)!;jy s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
8;-a_VjA) s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
!T#~.QP4 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
?b:l.0m sca1 = fftshift(fft(s1)); % Take Fourier transform
11Pm lzy sca2 = fftshift(fft(s2));
4}gqtw: sca3 = fftshift(fft(s3));
.@gv}`> sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
w=e~
M sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Qpe&_.&RE sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Ca0~K42~ s3 = ifft(fftshift(sc3));
K
p~x s2 = ifft(fftshift(sc2)); % Return to physical space
~OAS T s1 = ifft(fftshift(sc1));
1|q$Wn:* end
NYm2fFPc p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
E,>/6AU p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
TmvI+AY/ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
\%K< S P1=[P1 p1/p10];
4b,N"w{v P2=[P2 p2/p10];
zdlysr# P3=[P3 p3/p10];
w|OMT>. P=[P p*p];
AQDT6E: end
:1PT`:Y figure(1)
^Z$%OM, plot(P,P1, P,P2, P,P3);
)k.;.7dXe nX7{09 转自:
http://blog.163.com/opto_wang/