计算脉冲在非线性耦合器中演化的Matlab 程序 r|l?2 eO~ xN*k&! 1& % This Matlab script file solves the coupled nonlinear Schrodinger equations of
1 iox0 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
4$iS @o| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Z]B v % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
lrJV"H VJ\q p% %fid=fopen('e21.dat','w');
:6Z2@9.}w N = 128; % Number of Fourier modes (Time domain sampling points)
3zB'AG3b M1 =3000; % Total number of space steps
O84:ejro J =100; % Steps between output of space
o9}\vN0F T =10; % length of time windows:T*T0
{dxFd-K3 T0=0.1; % input pulse width
1'/
[x(/]d MN1=0; % initial value for the space output location
iZG-ca dt = T/N; % time step
JtO}i{A n = [-N/2:1:N/2-1]'; % Index
b se`Xfg t = n.*dt;
T^4 dHG-( u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
dU9;sx u20=u10.*0.0; % input to waveguide 2
S${% T$> u1=u10; u2=u20;
n#6{K6}k~ U1 = u1;
GTLS0l) U2 = u2; % Compute initial condition; save it in U
Movm1*&= ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ZbC$Fk,,I& w=2*pi*n./T;
;j9%D`u< g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
]$drBk86bh L=4; % length of evoluation to compare with S. Trillo's paper
I/w;4!+) dz=L/M1; % space step, make sure nonlinear<0.05
AZ(zM.y!#_ for m1 = 1:1:M1 % Start space evolution
:#g.%& u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Tz)Ku u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
z]9 t 5I ca1 = fftshift(fft(u1)); % Take Fourier transform
85!]N F ca2 = fftshift(fft(u2));
=6U5^+|d c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
m}z6Bbis 0 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
jOT/ |k u2 = ifft(fftshift(c2)); % Return to physical space
lW5Lwy t8 u1 = ifft(fftshift(c1));
x _~_/&X5 if rem(m1,J) == 0 % Save output every J steps.
Y/J~M$9P, U1 = [U1 u1]; % put solutions in U array
D9TjjA|zS U2=[U2 u2];
(eF[nfM MN1=[MN1 m1];
)Lz
=[e z1=dz*MN1'; % output location
2V]a +Cgk end
EmaS/]X[ end
ng/h6
S hg=abs(U1').*abs(U1'); % for data write to excel
B:X%k /{ ha=[z1 hg]; % for data write to excel
MB;rxUbhe3 t1=[0 t'];
[z"E"_r~%Y hh=[t1' ha']; % for data write to excel file
%l8!p'a %dlmwrite('aa',hh,'\t'); % save data in the excel format
;"cQ)=s9Y figure(1)
{d<XDx4` waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
~IYR&GEaUG figure(2)
;.AMP$o`(Y waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
/ckk qk " Ye]K 74M. 非线性超快脉冲耦合的数值方法的Matlab程序 L*4"D4V x%s1)\^A 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。
Y:/p0 o 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
j5D Cc,s hY!ek;/Gc 7HVENj_b+M ~D@ YLW1z( % This Matlab script file solves the nonlinear Schrodinger equations
&Z > ??|f % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
+EjXoW7 V % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
CKH mJ]= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
oUn+tu: LpY{<:y C=1;
-ysNo4#e& M1=120, % integer for amplitude
Ej)7[ M3=5000; % integer for length of coupler
3\4e{3$ N = 512; % Number of Fourier modes (Time domain sampling points)
L+G0/G}O\ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
^;ZpK@Luk T =40; % length of time:T*T0.
]d[e dt = T/N; % time step
TgjjwcO Y n = [-N/2:1:N/2-1]'; % Index
c
$r"q :\ t = n.*dt;
OIj.K@Kr ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
c*B< -
l<5 w=2*pi*n./T;
x %`YV):* g1=-i*ww./2;
:l"B NT[/ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ilQ}{ p6I g3=-i*ww./2;
L4 B/
g)K P1=0;
.`~?w+ ~ P2=0;
cY5;~lO P3=1;
Rd7U5MBEF P=0;
;Q, t65+Am for m1=1:M1
C) R hld p=0.032*m1; %input amplitude
S'^ q s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
kJl^,q s1=s10;
ML'y `S s20=0.*s10; %input in waveguide 2
DzMg^Kp s30=0.*s10; %input in waveguide 3
UUDH knm" s2=s20;
C{$iuus 0 s3=s30;
,9d]-CuP; p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
?o.d FKUe %energy in waveguide 1
B-_b.4ND) p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
V*PL_|Q5 %energy in waveguide 2
xDU \mfeGj p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Wk7E&?-:6 %energy in waveguide 3
fZ & for m3 = 1:1:M3 % Start space evolution
~C^:SND7 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
;G} s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
O >+=cg s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
,ja!OZ0$ sca1 = fftshift(fft(s1)); % Take Fourier transform
pTi7Xy!Cw sca2 = fftshift(fft(s2));
^%zhj3# sca3 = fftshift(fft(s3));
L ,.~VNy- sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
, d $"`W2 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
D|Q7dIZm sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
q=->) &D% s3 = ifft(fftshift(sc3));
pl3ap(/ s2 = ifft(fftshift(sc2)); % Return to physical space
#S9J9k s1 = ifft(fftshift(sc1));
e`b #,= end
VO eVS&} p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
s !?uLSEdb p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
^?H|RAp p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Dfzj/spFV P1=[P1 p1/p10];
@%x2d1FS P2=[P2 p2/p10];
Lfi6b %/z P3=[P3 p3/p10];
B VeMV4 P=[P p*p];
UA*VqK)Y end
ws9IO ?|&G figure(1)
SWx: -< plot(P,P1, P,P2, P,P3);
JMt*GFd R+ NiIoa 转自：
http://blog.163.com/opto_wang/
