计算脉冲在非线性耦合器中演化的Matlab 程序 o.Rv<a5.L /KX+'@ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
/1v9U|j % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
tV`=o$` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
^a_a%ws % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*;]}`r L/r_MtN %fid=fopen('e21.dat','w');
WA"~6U* N = 128; % Number of Fourier modes (Time domain sampling points)
L"%SU M1 =3000; % Total number of space steps
<y] 67:"<v J =100; % Steps between output of space
|Rz.Pt6 T =10; % length of time windows:T*T0
{\(MMTQ T0=0.1; % input pulse width
F{!pii5O9 MN1=0; % initial value for the space output location
8>,w8(Nt dt = T/N; % time step
sqtz^K ROM n = [-N/2:1:N/2-1]'; % Index
w|-3X t = n.*dt;
- ~|Gwr" u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Leb|YX u20=u10.*0.0; % input to waveguide 2
;//9,x9;t u1=u10; u2=u20;
*H/3xPh,* U1 = u1;
twq~.:<o U2 = u2; % Compute initial condition; save it in U
NFZ(*v1U ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
[i/!ovcY w=2*pi*n./T;
ZQ_6I}i") g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
T5."3i L=4; % length of evoluation to compare with S. Trillo's paper
L|T?,^ dz=L/M1; % space step, make sure nonlinear<0.05
R-S<7Q3E0= for m1 = 1:1:M1 % Start space evolution
hc[ K
VLpS u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Qk:Lo*! u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
[jzsB:;XB& ca1 = fftshift(fft(u1)); % Take Fourier transform
GQn:lu3j: ca2 = fftshift(fft(u2));
PY.K_(D c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
{h7 vJ^ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
31a,i2Q4 u2 = ifft(fftshift(c2)); % Return to physical space
"mW'tm1+ u1 = ifft(fftshift(c1));
L^
J|cgmNw if rem(m1,J) == 0 % Save output every J steps.
dA~:L`A|X U1 = [U1 u1]; % put solutions in U array
]=qauf>3 U2=[U2 u2];
^w\22 Q MN1=[MN1 m1];
bGH#s {'5 z1=dz*MN1'; % output location
wW@e#: end
\D? '.Wo% end
|(3y09 hg=abs(U1').*abs(U1'); % for data write to excel
$u!(F]^ ha=[z1 hg]; % for data write to excel
2!J#XzR0W t1=[0 t'];
Nrr})
g hh=[t1' ha']; % for data write to excel file
sv%X8 %dlmwrite('aa',hh,'\t'); % save data in the excel format
7Ed0BJTa figure(1)
THp_ dTD waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
FBNLszT{L figure(2)
^?`fN'!p waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
RW. qw4
0Idek 非线性超快脉冲耦合的数值方法的Matlab程序 't5ufAT 6DHK&<=D8 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。
Yub}AuU`v 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
G;G*!nlWf 0!\C@wnH ;`78h?` wf\"&xwh? % This Matlab script file solves the nonlinear Schrodinger equations
Sv n7.Ivep % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
\34vE@V* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
BV~J*e % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
bkV<ZUW|; ]<>cjk.ya C=1;
rv*{[K M1=120, % integer for amplitude
pux IJ M3=5000; % integer for length of coupler
|u>(~6 N = 512; % Number of Fourier modes (Time domain sampling points)
'@t$3
hk dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
kw#X,hP T =40; % length of time:T*T0.
1&=)Bxg4 dt = T/N; % time step
IgX &aW n = [-N/2:1:N/2-1]'; % Index
+;KUL6 t = n.*dt;
Ib# -M;{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
*-nO,K>y` w=2*pi*n./T;
!/XNp QP g1=-i*ww./2;
@Lnv g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
}
{1IB g3=-i*ww./2;
PEf yHf7` P1=0;
w \b+OW P2=0;
M}\h?s P3=1;
O+}py{ st P=0;
|U|>YA1[b for m1=1:M1
u9hd%}9Qd? p=0.032*m1; %input amplitude
,UY1.tR( s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
i/9iM\2 s1=s10;
c;VqEpsbl s20=0.*s10; %input in waveguide 2
y8k8Hd1<f s30=0.*s10; %input in waveguide 3
6'Q{xJe? s2=s20;
=0ZRGp s3=s30;
#rkq
?:Q p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
[H}>
2Q %energy in waveguide 1
&u>dKf)5 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
PILpWhjL$9 %energy in waveguide 2
:V'99Esv` p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
"2cOS PpQL %energy in waveguide 3
q?}C`5%D for m3 = 1:1:M3 % Start space evolution
#r'MfTr s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Q@W/~~N s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
2RkW/)A9 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
&i5@4,p y9 sca1 = fftshift(fft(s1)); % Take Fourier transform
E_ns4k#uG sca2 = fftshift(fft(s2));
Ehx9-*] sca3 = fftshift(fft(s3));
bJ^h{] sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
iOk;o= sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
h=#w< @ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
>rd#,r s3 = ifft(fftshift(sc3));
xb;{<~`71 s2 = ifft(fftshift(sc2)); % Return to physical space
b#_RZ s1 = ifft(fftshift(sc1));
0g?)j- end
;st0Ekni) p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
7:jLZ!mgi p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
{kpF etXt? p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
*ub2dH4/ P1=[P1 p1/p10];
gNCS*a P2=[P2 p2/p10];
=)Xj[NNRT P3=[P3 p3/p10];
%O\@rws P=[P p*p];
E 2nz end
/|?$C7%a\D figure(1)
5BVvT
`< plot(P,P1, P,P2, P,P3);
*] ihc u &,&+p0CSI! 转自:
http://blog.163.com/opto_wang/