计算脉冲在非线性耦合器中演化的Matlab 程序 El<*) f?sm~PwC- % This Matlab script file solves the coupled nonlinear Schrodinger equations of
:9UgERjra % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
8J(j}</>a % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
:uo1QavO@, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
tf~B,? 29RP$$gR %fid=fopen('e21.dat','w');
_K~h?
\u N = 128; % Number of Fourier modes (Time domain sampling points)
AYA{_^#+3 M1 =3000; % Total number of space steps
$5&%X'jk J =100; % Steps between output of space
Ocx"s\q (
T =10; % length of time windows:T*T0
lj Nwt T0=0.1; % input pulse width
%f1%9YH MN1=0; % initial value for the space output location
z5fE<=<X_W dt = T/N; % time step
f)/Z7*Z n = [-N/2:1:N/2-1]'; % Index
V|MGG t = n.*dt;
XA2Ld u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
1XSnnkJm u20=u10.*0.0; % input to waveguide 2
:*''ci u1=u10; u2=u20;
QF"7.~~2 U1 = u1;
V^2_]VFj U2 = u2; % Compute initial condition; save it in U
n(F!t,S1i ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
@N>7+
4 w=2*pi*n./T;
.zO2g8(VR g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
l/X_CM8y~ L=4; % length of evoluation to compare with S. Trillo's paper
AatSN@,~z dz=L/M1; % space step, make sure nonlinear<0.05
+NPL. b| for m1 = 1:1:M1 % Start space evolution
E Jk HPn u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
w X "hUu u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Ht
Fr(g\"$ ca1 = fftshift(fft(u1)); % Take Fourier transform
~$ HB}/ ca2 = fftshift(fft(u2));
X1|
+9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
EU?qL j': c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
I@'[ > t u2 = ifft(fftshift(c2)); % Return to physical space
K&L!O3#( u1 = ifft(fftshift(c1));
? gE=h h if rem(m1,J) == 0 % Save output every J steps.
") |/\ w, U1 = [U1 u1]; % put solutions in U array
h:%,>I%{ U2=[U2 u2];
e% \^V\L MN1=[MN1 m1];
+lym8n~-O z1=dz*MN1'; % output location
NfgXOLthM end
QHk\ Z end
*'/, hg=abs(U1').*abs(U1'); % for data write to excel
Bs~~C 8+ ha=[z1 hg]; % for data write to excel
O sgPNy0 t1=[0 t'];
?*fa5=ql hh=[t1' ha']; % for data write to excel file
q#K{~: %dlmwrite('aa',hh,'\t'); % save data in the excel format
_\WR3Q!V figure(1)
A WR : ~{ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
>f]/VaMH{ figure(2)
AjVC{\Ik waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
B5lwQp] nh} Xu~#_ 非线性超快脉冲耦合的数值方法的Matlab程序 R}&?9tVRR MKHnA|uQ]( 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。
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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
8 1,N92T5 G ]K1X"W? iiPVqU% ;s B=f % This Matlab script file solves the nonlinear Schrodinger equations
l;; 2\m L? % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
E'AR.! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
*QC6zJ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
my 'nDi -c`xeuzK' C=1;
%F*9D3^h M1=120, % integer for amplitude
m xv ?PP M3=5000; % integer for length of coupler
(Z ) ,gxt N = 512; % Number of Fourier modes (Time domain sampling points)
BhJ>G% dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
E)v~kC}7. T =40; % length of time:T*T0.
voa)V 1A/] dt = T/N; % time step
0,Ds1y^ n = [-N/2:1:N/2-1]'; % Index
-^@FZ R^Y t = n.*dt;
!dqC6 a ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Wg-m Ju( w=2*pi*n./T;
}a]`"_i;[ g1=-i*ww./2;
VE\L&d2S g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
%_!/4^smE g3=-i*ww./2;
x@ - K P1=0;
`Y&`2WZ ~ P2=0;
S:xXD^n#H P3=1;
BZeE Z2" P=0;
~;"eNg{ T for m1=1:M1
[OC( ~b p=0.032*m1; %input amplitude
y 1V}c , s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
TFSdb\g s1=s10;
&h5Vhzq(< s20=0.*s10; %input in waveguide 2
r:QLU]
s30=0.*s10; %input in waveguide 3
A*h8 o9M s2=s20;
b_x!m{ s3=s30;
E?w#$HS p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
8F sQLeOE %energy in waveguide 1
ndSu-8?L p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
RD`|Z~:q:K %energy in waveguide 2
A c_ P^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
3D|Lb]= %energy in waveguide 3
x\yM|WGL for m3 = 1:1:M3 % Start space evolution
> X~\(|EM s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
_}{KS, f]0 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
# qd!_oN s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
u Kx:7"KD sca1 = fftshift(fft(s1)); % Take Fourier transform
,N$Q']Td sca2 = fftshift(fft(s2));
7 [Us.V@ sca3 = fftshift(fft(s3));
[@K'}\U^+ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Y>$5j}K sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
rZI63S sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
%`C e#b()' s3 = ifft(fftshift(sc3));
@&*TGU s2 = ifft(fftshift(sc2)); % Return to physical space
OTy!Q,0$. s1 = ifft(fftshift(sc1));
|~9jO/&r end
Dl!0Hl p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
wSR|uh p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
VwR\"8r3 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
m[%356u P1=[P1 p1/p10];
:!i=g +e] P2=[P2 p2/p10];
X}#vt?mu P3=[P3 p3/p10];
8@3=SO P=[P p*p];
`^#Rwn# end
;MfqI/B{ figure(1)
}s2CN D plot(P,P1, P,P2, P,P3);
^B.Z 3Y e1[ReZW 转自：
http://blog.163.com/opto_wang/
