计算脉冲在非线性耦合器中演化的Matlab 程序 ~!2fUewEu /3rNX}tOMH % This Matlab script file solves the coupled nonlinear Schrodinger equations of
wG7>2*( % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
>KP,67 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
gsEcvkj* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
&dWGa+e tbR %fid=fopen('e21.dat','w');
(M1YOK) I N = 128; % Number of Fourier modes (Time domain sampling points)
gl`J( M1 =3000; % Total number of space steps
KWjhkRK4] J =100; % Steps between output of space
\W TKw x T =10; % length of time windows:T*T0
j7Y7&x" T0=0.1; % input pulse width
=oh%-Sh: MN1=0; % initial value for the space output location
C{^I}p dt = T/N; % time step
U`EOun, n = [-N/2:1:N/2-1]'; % Index
|hi,]D^Kc t = n.*dt;
J|^XD<Y u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
CC"a2Hu/ u20=u10.*0.0; % input to waveguide 2
DMsqTB` u1=u10; u2=u20;
}T\.;$f U1 = u1;
gt.F[q3
U2 = u2; % Compute initial condition; save it in U
?t6wozib2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
tF-l=ph}` w=2*pi*n./T;
;qUB[Kw g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
j0~c2 L=4; % length of evoluation to compare with S. Trillo's paper
9#hp]0S6 dz=L/M1; % space step, make sure nonlinear<0.05
H<fi,"X^ for m1 = 1:1:M1 % Start space evolution
2bw), W u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
O%>*=h`P u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
@|t]9 ca1 = fftshift(fft(u1)); % Take Fourier transform
^swj!da ca2 = fftshift(fft(u2));
f'5
6IT
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
1,OkuyXy!> c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
%>9L}OAm u2 = ifft(fftshift(c2)); % Return to physical space
:NWIUN u1 = ifft(fftshift(c1));
Wp:vz']V if rem(m1,J) == 0 % Save output every J steps.
d`flYNg4 U1 = [U1 u1]; % put solutions in U array
;8&/JS N M U2=[U2 u2];
?0KIM*
. MN1=[MN1 m1];
d
oEuKT z1=dz*MN1'; % output location
KGc.YUoE end
Iq,h}7C8' end
2(~Zl\ hg=abs(U1').*abs(U1'); % for data write to excel
H{N},B ha=[z1 hg]; % for data write to excel
PknKzrEG:> t1=[0 t'];
~4Fz A,, hh=[t1' ha']; % for data write to excel file
2BF455e %dlmwrite('aa',hh,'\t'); % save data in the excel format
yevJA?C4 v figure(1)
t, /8U waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
2!W[ff@~7 figure(2)
>\:GFD{z waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Ths~8{dMb <Rn-B).3bs 非线性超快脉冲耦合的数值方法的Matlab程序 +UX~'t_'v _U4@W+lhX_ 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的
论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
O9?.J,,mVh Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
P* &0HbJ l"`VvW[ P/WGB~NH S~fP$L5 % This Matlab script file solves the nonlinear Schrodinger equations
m(9I+` % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
^;s/4 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
l8+)Xk> % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
rf]z5; JtMl/h C=1;
NhNd+SCZ@ M1=120, % integer for amplitude
Qt>kythi M3=5000; % integer for length of coupler
5+oY c- N = 512; % Number of Fourier modes (Time domain sampling points)
\P":V dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
pYAKA1F T =40; % length of time:T*T0.
Rm)hgmZ dt = T/N; % time step
)jUPMIo n = [-N/2:1:N/2-1]'; % Index
1oiSmW\ t = n.*dt;
gk?H@b* ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
X|!@%wuGC w=2*pi*n./T;
w<h8`K`3 g1=-i*ww./2;
~J~R.r/ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ZQ`4'|" g3=-i*ww./2;
z(.,BB[ P1=0;
: 4-pnn P2=0;
MxX)&327 P3=1;
-W@nc
QL} P=0;
[Rq|;p for m1=1:M1
`DSFaBj, p=0.032*m1; %input amplitude
{%k[Z9*tO s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
`~lG5| s1=s10;
D'ZUbAh! s20=0.*s10; %input in waveguide 2
lg
)xQV s30=0.*s10; %input in waveguide 3
~(tt.l# s2=s20;
2g5 4<G*e s3=s30;
8q6Le{G p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
FwB xag:u %energy in waveguide 1
)Kl@dj p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
gG.+3= %energy in waveguide 2
0(u}z p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
!UPB4I %energy in waveguide 3
k^;/@: for m3 = 1:1:M3 % Start space evolution
u^]Gc p s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
b W/T}FND s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
=Xid"$ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
l'2vo=IQ sca1 = fftshift(fft(s1)); % Take Fourier transform
Df2$2VU sca2 = fftshift(fft(s2));
W;!V_-: sca3 = fftshift(fft(s3));
iKaS7lWH sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
3rN}iSF^ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
@sZ' --Y sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
"^{Hta s3 = ifft(fftshift(sc3));
9)=bBQyr: s2 = ifft(fftshift(sc2)); % Return to physical space
:TKx>~` s1 = ifft(fftshift(sc1));
g%^/^<ei end
KkzG#'I1 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
(NfB+Ue} p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
iDgc$'%? p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
In:V.'D/>t P1=[P1 p1/p10];
mrKIiaU<J P2=[P2 p2/p10];
4T$jY}U P3=[P3 p3/p10];
*Ev8f11i& P=[P p*p];
wpQp1){%Q end
x+'Ea.^ figure(1)
4XiQ8"C plot(P,P1, P,P2, P,P3);
9|@5eN:N -cn`D2RP 转自:
http://blog.163.com/opto_wang/