计算脉冲在非线性耦合器中演化的Matlab 程序 ZliJc7lss CBVL/pxy % This Matlab script file solves the coupled nonlinear Schrodinger equations of
ZSUbPz % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
;4!,19AT % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
3Aqw )B'"_ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
d<@SRHP( REj<2Lo %fid=fopen('e21.dat','w');
lO>9Q]S< N = 128; % Number of Fourier modes (Time domain sampling points)
DMc H, _( M1 =3000; % Total number of space steps
u@{z
xYn J =100; % Steps between output of space
FD+y?UF T =10; % length of time windows:T*T0
$ncJc T0=0.1; % input pulse width
[2 yxTK MN1=0; % initial value for the space output location
NhgzU+)+ dt = T/N; % time step
K!\$ M BI n = [-N/2:1:N/2-1]'; % Index
H E'1Wa0r t = n.*dt;
xX5EhVR u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
3R=R k u20=u10.*0.0; % input to waveguide 2
?}tWI7KI u1=u10; u2=u20;
W|yF jE&dr U1 = u1;
ALOS>Bi& U2 = u2; % Compute initial condition; save it in U
'Wv`^{y <^ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
6
#vc"5@M w=2*pi*n./T;
m,"N 4a@ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
V(5=-8k L=4; % length of evoluation to compare with S. Trillo's paper
b;K]; o-/f dz=L/M1; % space step, make sure nonlinear<0.05
d HUcu@, for m1 = 1:1:M1 % Start space evolution
cj5; X K u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
D J:N u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
%!vgAH4 ca1 = fftshift(fft(u1)); % Take Fourier transform
JR_s-& GaM ca2 = fftshift(fft(u2));
@_L:W1[ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Ny6 daf3f c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
:1 Y *&s u2 = ifft(fftshift(c2)); % Return to physical space
g:yUZ;U u1 = ifft(fftshift(c1));
3%N bT if rem(m1,J) == 0 % Save output every J steps.
M`=bJO: U1 = [U1 u1]; % put solutions in U array
O9_S"\8]@ U2=[U2 u2];
dZ"B6L!^( MN1=[MN1 m1];
'cpO"d?{ z1=dz*MN1'; % output location
p[&6hXTd end
9w B}EDZ end
S
Y7'S# hg=abs(U1').*abs(U1'); % for data write to excel
XoZw8cY ha=[z1 hg]; % for data write to excel
2=[de Qs t1=[0 t'];
OZ9ud ]@\ hh=[t1' ha']; % for data write to excel file
J: T %dlmwrite('aa',hh,'\t'); % save data in the excel format
dPtQ
Sa figure(1)
ee7{5 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
:-.K.Ch|: figure(2)
CB1AL]|3 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
D sI{*# i=ztWKwKf 非线性超快脉冲耦合的数值方法的Matlab程序 r'GD 5IsRIz[`TK 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。
IdzrQP 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
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`n{yls7. MUeS8:q-N !K~L&.\T % This Matlab script file solves the nonlinear Schrodinger equations
Og8'K=O# % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
aglW\L T^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
4YmN3i % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0nDlqy6b1b +=qazE<:0 C=1;
;Bs^+R7 M1=120, % integer for amplitude
F: P&hK M3=5000; % integer for length of coupler
Bv)4YU N = 512; % Number of Fourier modes (Time domain sampling points)
} XJZw|n dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
5V( $| 3PI T =40; % length of time:T*T0.
dl%KD8 dt = T/N; % time step
}_A#O|d xO n = [-N/2:1:N/2-1]'; % Index
k\~A\UIYo t = n.*dt;
&M6cCT]&M ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
)iiwxpdw w=2*pi*n./T;
4 <&8`Q g1=-i*ww./2;
`B4Px|3 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
G|"`k Aa g3=-i*ww./2;
c/g"/ICs P1=0;
cHG>iW 9C P2=0;
@6~OQN P3=1;
~Xf&<&5d T P=0;
!N:: 1c@C for m1=1:M1
u{@b_7 5Y p=0.032*m1; %input amplitude
~H0WHqcy s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
G#~6a%VW s1=s10;
o3mxtE] s20=0.*s10; %input in waveguide 2
luEP5l2& s30=0.*s10; %input in waveguide 3
KT5"/fv s2=s20;
9kk YD s3=s30;
09RJc3XE9 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
~
3HI; %energy in waveguide 1
sT^^#$ub p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
w Jb \Q %energy in waveguide 2
1HBdIWhHv. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
4/rd r80 %energy in waveguide 3
#&hu-gM V for m3 = 1:1:M3 % Start space evolution
m9Z 3q ; s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
P]pVYX# m s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
gXR1nnK s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
j})6O! L. sca1 = fftshift(fft(s1)); % Take Fourier transform
`B ^ HW8 sca2 = fftshift(fft(s2));
54A ndyeA sca3 = fftshift(fft(s3));
Ff\U]g sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
~IB~>5U! sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
p:,(r{*? sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
f"0{e9O]2 s3 = ifft(fftshift(sc3));
-6+&?f s2 = ifft(fftshift(sc2)); % Return to physical space
^PCshb## s1 = ifft(fftshift(sc1));
ye9-%~sjX end
JQ*C F(9 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
9tnW: Nw~ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Cu%|}xq p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
CVi3nS5Yl P1=[P1 p1/p10];
@nJ#kd[ P2=[P2 p2/p10];
RyGce'
q P3=[P3 p3/p10];
XZaei\rUn) P=[P p*p];
27;t,Oq} end
!50Fue^JM figure(1)
S> f8j?n plot(P,P1, P,P2, P,P3);
C#5 z!z/:% ~6nq$( # 转自：
http://blog.163.com/opto_wang/
