计算脉冲在非线性耦合器中演化的Matlab 程序 ;5q =/ \H*"UgS % This Matlab script file solves the coupled nonlinear Schrodinger equations of
jQj`GnN| % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
o D*h@yL % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
kR TT
~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
O6YYOmt3 teg LGp@_ %fid=fopen('e21.dat','w');
T,!?+# N = 128; % Number of Fourier modes (Time domain sampling points)
&xj?MgdNL M1 =3000; % Total number of space steps
bv4lgRE6Y J =100; % Steps between output of space
0V}%'Ec<e T =10; % length of time windows:T*T0
i ?A4uyYwS T0=0.1; % input pulse width
,+oQ 5c(f MN1=0; % initial value for the space output location
3EI$tP @4 dt = T/N; % time step
Z '/:
n = [-N/2:1:N/2-1]'; % Index
|*fGG?} t = n.*dt;
WDP$w ( M u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
wZ0$ylEX u20=u10.*0.0; % input to waveguide 2
5 4-sb~] u1=u10; u2=u20;
y7u"a)T U1 = u1;
> IJH#>i U2 = u2; % Compute initial condition; save it in U
H .JA)*b- ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Zyu4! w=2*pi*n./T;
38 tRb"3zP g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
dArg'Dc4 L=4; % length of evoluation to compare with S. Trillo's paper
T5=3 jPQ dz=L/M1; % space step, make sure nonlinear<0.05
~N;kF.q&>& for m1 = 1:1:M1 % Start space evolution
[as\ > @o u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
`&LPqb u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
$GSn#} yz ca1 = fftshift(fft(u1)); % Take Fourier transform
q$yTG!q* ca2 = fftshift(fft(u2));
sPyq.o G c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
G yvEc3|@ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
}Cvf[H1+ u2 = ifft(fftshift(c2)); % Return to physical space
mcP]k8?C u1 = ifft(fftshift(c1));
f 0~<qT?:n if rem(m1,J) == 0 % Save output every J steps.
q3z<v:=1y U1 = [U1 u1]; % put solutions in U array
Q = )$ U2=[U2 u2];
~5N0=) MN1=[MN1 m1];
K63OjR >H z1=dz*MN1'; % output location
dAh&Z:86\ end
Y^M3m' d? end
wI'T J e, hg=abs(U1').*abs(U1'); % for data write to excel
C?fd.2#U ha=[z1 hg]; % for data write to excel
|e! %6Qq3 t1=[0 t'];
NoB)tAvw hh=[t1' ha']; % for data write to excel file
3,8<5)ds* %dlmwrite('aa',hh,'\t'); % save data in the excel format
*?zmo@- figure(1)
~Y7>P$G) waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
6U Q~Fv`] figure(2)
]u?|3y^ ( waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
- ,)&? S _ho9}7 > 非线性超快脉冲耦合的数值方法的Matlab程序 E z?O
gE{ 5/F1| N4 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。
C< 3` ]l 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
[_Fj2nb* $Ypt
/` l+HmG< P E#[_"^n % This Matlab script file solves the nonlinear Schrodinger equations
oCg|*
c|+ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
_ I"}3* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
J&CA#Bg:w % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
e{EKM4 H*51GxK C=1;
O`j1~o<{ M1=120, % integer for amplitude
`d2
r5*< M3=5000; % integer for length of coupler
mM0VUSy N = 512; % Number of Fourier modes (Time domain sampling points)
BCMQ^hP}t dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
T1%_sq T =40; % length of time:T*T0.
F$.h+v dt = T/N; % time step
_JNSl2 n = [-N/2:1:N/2-1]'; % Index
td JA? t = n.*dt;
', ~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/*Iq,"kGz w=2*pi*n./T;
$ha,DlN g1=-i*ww./2;
6l]jm j)/ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
OIJNOu I g3=-i*ww./2;
~ES6Qw`Oe P1=0;
N!!=9'fGF P2=0;
7IkNS P3=1;
;O8'vp P=0;
"`g5iUHqUl for m1=1:M1
Jx@_OE_vp p=0.032*m1; %input amplitude
IJ\4S s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
+lC?Vpi^ s1=s10;
4FQB%3>* s20=0.*s10; %input in waveguide 2
qQjd@J}^ s30=0.*s10; %input in waveguide 3
nl<TM96 s2=s20;
;$, b
w5 s3=s30;
[ GQn1ZLc p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
7}#zF]vHNi %energy in waveguide 1
j/ [V< p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
^E~F,]dV= %energy in waveguide 2
|ht:_l
8 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
AS4mJ UU9 %energy in waveguide 3
{z#!3a for m3 = 1:1:M3 % Start space evolution
+xNV1bM s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
":@\kw s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
OFe-e(c1 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
IVSOSl| sca1 = fftshift(fft(s1)); % Take Fourier transform
HpP82X xj sca2 = fftshift(fft(s2));
DwmK?5 p sca3 = fftshift(fft(s3));
Sf*1Z~P | sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
^+p7\D/E( sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
)OHGg sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
mqj]=F q* s3 = ifft(fftshift(sc3));
)iX2r { s2 = ifft(fftshift(sc2)); % Return to physical space
}TQa<;Q s1 = ifft(fftshift(sc1));
r)S:-wP end
tNoPpIu p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
"w&IO}j;= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
or,:5Z p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
4SVId S A P1=[P1 p1/p10];
+[vI ocu P2=[P2 p2/p10];
{ty)2 P3=[P3 p3/p10];
ylm # Xa P=[P p*p];
fHK.q({Qc end
:a/l9 m( figure(1)
r[g plot(P,P1, P,P2, P,P3);
,I6li7V y0f:N
U 转自：
http://blog.163.com/opto_wang/
