计算脉冲在非线性耦合器中演化的Matlab 程序 - |mWi [B9'/: % This Matlab script file solves the coupled nonlinear Schrodinger equations of
r]eeKV,{p % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
$ WA Fr % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
.$+]N[-=
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
OKfJ (#* 7LdZ %fid=fopen('e21.dat','w');
kVs'>H@FY N = 128; % Number of Fourier modes (Time domain sampling points)
>{i/ LC^S M1 =3000; % Total number of space steps
b:.aZ7+4 J =100; % Steps between output of space
A87JPX#R? T =10; % length of time windows:T*T0
n(.y_NEgV! T0=0.1; % input pulse width
I0 a,mO;m MN1=0; % initial value for the space output location
U'S}7gya dt = T/N; % time step
u2
a
U0k: n = [-N/2:1:N/2-1]'; % Index
*6~ODiB t = n.*dt;
FjIS:9^)t5 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
5Qhu5~,K u20=u10.*0.0; % input to waveguide 2
][- N< u1=u10; u2=u20;
FblwQ-D U1 = u1;
Tl=cn iy] U2 = u2; % Compute initial condition; save it in U
e L l+F%@ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`e]L.P_e? w=2*pi*n./T;
O(;K ]8 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Y - 6
?x L=4; % length of evoluation to compare with S. Trillo's paper
?)x>GB(9ZN dz=L/M1; % space step, make sure nonlinear<0.05
6> v`6 for m1 = 1:1:M1 % Start space evolution
/W'GX n u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
XnrOC|P$ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
@cdd ~9w ca1 = fftshift(fft(u1)); % Take Fourier transform
n aCPSsei ca2 = fftshift(fft(u2));
`m?%{ \ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
IbC(/i#%` c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Ed ,`1+ u2 = ifft(fftshift(c2)); % Return to physical space
Tx?,]c,(u u1 = ifft(fftshift(c1));
pfgFHNH: if rem(m1,J) == 0 % Save output every J steps.
\|nF55W [ U1 = [U1 u1]; % put solutions in U array
*@=in7*c U2=[U2 u2];
mh]'/C_*<w MN1=[MN1 m1];
o^;$-O!/ z1=dz*MN1'; % output location
- 4`Wkkhu end
+[*VU2f t end
yC !`6$ hg=abs(U1').*abs(U1'); % for data write to excel
1VK ?Svnd ha=[z1 hg]; % for data write to excel
:#58m0YLA: t1=[0 t'];
Pcut#8?
hh=[t1' ha']; % for data write to excel file
9@
[R>C %dlmwrite('aa',hh,'\t'); % save data in the excel format
I&]d6, figure(1)
aYr?J
Ol waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
3}=r.\]U figure(2)
{8UYu2t waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
b {<qt} ) D_
xPa 非线性超快脉冲耦合的数值方法的Matlab程序 9{|JmgO! GqumH/; 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。
9Y!N\-x` 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
1o)@{x/pd Ov"]&e(I[ \#.,@g LnIl n[g: % This Matlab script file solves the nonlinear Schrodinger equations
8A}w}h % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
q 65KxOf` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
6s\niro2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
XJy~uks, fyP p zA0 C=1;
HQ~`ha. M1=120, % integer for amplitude
:8aa #bA M3=5000; % integer for length of coupler
gR v5l3k N = 512; % Number of Fourier modes (Time domain sampling points)
e5KsKzu a dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
5ckL=q"+/ T =40; % length of time:T*T0.
{'VP_ZS1v dt = T/N; % time step
bVmHUcR0 n = [-N/2:1:N/2-1]'; % Index
"a))TV%N t = n.*dt;
cH OtMPyQ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<+ UEM ~) w=2*pi*n./T;
xgHR;US H g1=-i*ww./2;
"V-k_d " g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Hs/
aU _ g3=-i*ww./2;
uc!j`G*] P1=0;
k8H@0p P2=0;
vdw5T&Q{{C P3=1;
^Gt&c_gH P=0;
i'9aQi" G for m1=1:M1
IvGQ7
VLr p=0.032*m1; %input amplitude
wBZ=IMDu\ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
LVKv Pi s1=s10;
-V0_%Smc s20=0.*s10; %input in waveguide 2
4-;"w; s30=0.*s10; %input in waveguide 3
Fw5|_@&k s2=s20;
|S.G# za s3=s30;
O 4zD
>O p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
|U{9Yy6p %energy in waveguide 1
li'h&!|] p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
G2
A#&86J{ %energy in waveguide 2
0$)s? \ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
FsQeyh> %energy in waveguide 3
.j?`U[V%a for m3 = 1:1:M3 % Start space evolution
873$EiyXR s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Cbu /7z s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
O b'B? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
!/] F.0 sca1 = fftshift(fft(s1)); % Take Fourier transform
su;u_rc, sca2 = fftshift(fft(s2));
U-Ia$b-5! sca3 = fftshift(fft(s3));
-^sW{s0Rc sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
X[/>{rK sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
d: D`rpcC sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
gGF]Dq s3 = ifft(fftshift(sc3));
"fK` F/ s2 = ifft(fftshift(sc2)); % Return to physical space
{gh41G;n s1 = ifft(fftshift(sc1));
Z9 X<W` end
Fp'qn'){:# p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
@>`+eg][?P p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
|dIP &9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
\kSoDY`l& P1=[P1 p1/p10];
$pW6a %7 P2=[P2 p2/p10];
;pe1tp P3=[P3 p3/p10];
Z] ?Tx2|7 P=[P p*p];
O/g|E47 end
PWeCk2 xH figure(1)
ZK:dhwe r plot(P,P1, P,P2, P,P3);
iMG)zPj od~^''/b 转自：
http://blog.163.com/opto_wang/
