计算脉冲在非线性耦合器中演化的Matlab 程序 1;V5b+b P@#6.Bb#V % This Matlab script file solves the coupled nonlinear Schrodinger equations of
wwz< c5 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
=%p{ " < % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
3ssio-X % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
j? A +qk }{"\"Bn_ %fid=fopen('e21.dat','w');
hAdEq$ N = 128; % Number of Fourier modes (Time domain sampling points)
IcZ 'KV M1 =3000; % Total number of space steps
~S9nLb:O{ J =100; % Steps between output of space
Pcc%VQ N T =10; % length of time windows:T*T0
)d~Mag+ T0=0.1; % input pulse width
RWE%? ` MN1=0; % initial value for the space output location
.IgQn|N dt = T/N; % time step
aum,bm/0J n = [-N/2:1:N/2-1]'; % Index
{T9g\F* t = n.*dt;
yLP0w^Q u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
t
+_G%tv u20=u10.*0.0; % input to waveguide 2
\?Z d UY u1=u10; u2=u20;
6dh PqL U1 = u1;
5V0=-K U2 = u2; % Compute initial condition; save it in U
'"EOLr\Z, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<~3 a aO w=2*pi*n./T;
}|d:(* g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
@N$r'@ L=4; % length of evoluation to compare with S. Trillo's paper
<|4j<U dz=L/M1; % space step, make sure nonlinear<0.05
! Zr vko for m1 = 1:1:M1 % Start space evolution
x9= lN^/4 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
b#M<b.R) u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
h$!qb'| ca1 = fftshift(fft(u1)); % Take Fourier transform
jL# ak V ca2 = fftshift(fft(u2));
=% p"oj]: c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
{D@y-K5 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
7]Egu D4 u2 = ifft(fftshift(c2)); % Return to physical space
=cQw R:): u1 = ifft(fftshift(c1));
g 0L 4 if rem(m1,J) == 0 % Save output every J steps.
<j>@Fg#q U1 = [U1 u1]; % put solutions in U array
qhtc?A/0} U2=[U2 u2];
B@4#y9`5 MN1=[MN1 m1];
z(xvt> z1=dz*MN1'; % output location
]1K
&U5p end
;Cwn1N9S end
86Rit!ih hg=abs(U1').*abs(U1'); % for data write to excel
U;31}'b ha=[z1 hg]; % for data write to excel
YW5E
| z t1=[0 t'];
ms $o ,[ hh=[t1' ha']; % for data write to excel file
PQK_*hJG" %dlmwrite('aa',hh,'\t'); % save data in the excel format
;KhYh S(q figure(1)
W)l&4#__( waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
+0OQ"2^& figure(2)
xU&rUk /L waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
e#seqx ^Iz.O 非线性超快脉冲耦合的数值方法的Matlab程序 1Nz\3] - (Cq-8**dY 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
zb<+x(0y" Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
XEuv
aM %guot~S| @.0,k a,X yP-Dj
, % This Matlab script file solves the nonlinear Schrodinger equations
t!k 0n& P % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
H\S,^)drJ? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
`>*P(yIN % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
c]9OP9F kO4C^pl"v C=1;
ql4T@r3l}3 M1=120, % integer for amplitude
F,D & M3=5000; % integer for length of coupler
mB\5bSFY` N = 512; % Number of Fourier modes (Time domain sampling points)
R[Rs2eS_ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
dU\fC{1Z T =40; % length of time:T*T0.
1{wy%| H\ dt = T/N; % time step
~UnfS};U n = [-N/2:1:N/2-1]'; % Index
o
2DnkzpJ t = n.*dt;
B4b UcYk ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
G P[$&8\M w=2*pi*n./T;
ZpdM[\Q- g1=-i*ww./2;
t! ~mbx+ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
G{J9F b8 g3=-i*ww./2;
e0q a ~5 P1=0;
83dOS S2 P2=0;
>hXUq9;: P3=1;
U!Lws#\X P=0;
@.5Yb gn for m1=1:M1
us]ah~U6A p=0.032*m1; %input amplitude
."lY>(HJ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
u0x\5!?2 s1=s10;
/#X O!%=7 s20=0.*s10; %input in waveguide 2
K+7xjFoDIR s30=0.*s10; %input in waveguide 3
<ZocM v9gM s2=s20;
|k)u..k{> s3=s30;
2|T@ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
]*@7o^4i %energy in waveguide 1
* T-XslI p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
|X sW)/ %energy in waveguide 2
]/a?:24 [ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
R38
w!6{ %energy in waveguide 3
0+L5k !1D for m3 = 1:1:M3 % Start space evolution
HiWZ ?G s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
2q#$?qs_b s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
zJ\I%7h* s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Ywni2-)< sca1 = fftshift(fft(s1)); % Take Fourier transform
FPqgncBHK sca2 = fftshift(fft(s2));
LvR=uD sca3 = fftshift(fft(s3));
_WkK%RYV sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
T ^79p$ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
m r;WxxO5 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
ZHZ>YSqCS s3 = ifft(fftshift(sc3));
&K7g8x"x. s2 = ifft(fftshift(sc2)); % Return to physical space
ZF`ckWT:-N s1 = ifft(fftshift(sc1));
XnNK )dUT} end
f(3#5288 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
~E)I+$, p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
:s4CWE d p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
J/mLB7^R P1=[P1 p1/p10];
}3+(A`9h f P2=[P2 p2/p10];
-wO`o< P3=[P3 p3/p10];
j;'NJ~NZ$ P=[P p*p];
,7'l$-r l end
L'c4 i[~s figure(1)
0
xXAhv-)O plot(P,P1, P,P2, P,P3);
3U} z?gP[ V9MA)If> 转自：
http://blog.163.com/opto_wang/
