计算脉冲在非线性耦合器中演化的Matlab 程序 eiOAbO#U w2 (}pz: % This Matlab script file solves the coupled nonlinear Schrodinger equations of
7 HL
Uk3 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
^38k xwh % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
!U5Cwq % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
s!09cS r_ 9"^Er %fid=fopen('e21.dat','w');
aG" N = 128; % Number of Fourier modes (Time domain sampling points)
M AqETjB M1 =3000; % Total number of space steps
p ^{yA"MQ J =100; % Steps between output of space
t re`iCH~ T =10; % length of time windows:T*T0
Y edF% T0=0.1; % input pulse width
4u p7 :? MN1=0; % initial value for the space output location
l h0G/8+C dt = T/N; % time step
?~^p:T n = [-N/2:1:N/2-1]'; % Index
%,N-M]Jf t = n.*dt;
KPK`C0mg@k u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
WVyq$p/V u20=u10.*0.0; % input to waveguide 2
D S|x*w'I u1=u10; u2=u20;
pdQaVe7tRo U1 = u1;
2Sy:wt U2 = u2; % Compute initial condition; save it in U
f:t5`c. ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
>&Ye(3w& w=2*pi*n./T;
dg N #" g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
kad$Fp39 L=4; % length of evoluation to compare with S. Trillo's paper
/KiaLS dz=L/M1; % space step, make sure nonlinear<0.05
dZ,7q_r,~ for m1 = 1:1:M1 % Start space evolution
l 9 rN!Q| u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
q<g!bW% u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
<1V>0[[e ca1 = fftshift(fft(u1)); % Take Fourier transform
>]bS"S ca2 = fftshift(fft(u2));
,E(M<n|. c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
5',b~P p c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
CwEb ? u2 = ifft(fftshift(c2)); % Return to physical space
sGMn m u1 = ifft(fftshift(c1));
)A;jBfr if rem(m1,J) == 0 % Save output every J steps.
f`J[u!Ja U1 = [U1 u1]; % put solutions in U array
IgF#f%|Q U2=[U2 u2];
\iwUsv>SB MN1=[MN1 m1];
^^Q> AfTR. z1=dz*MN1'; % output location
A.P*@}9 end
n
u>6UjV end
-fz( ]d hg=abs(U1').*abs(U1'); % for data write to excel
j;rxr1 +w ha=[z1 hg]; % for data write to excel
~b jT,i t1=[0 t'];
t 1l4mdp hh=[t1' ha']; % for data write to excel file
# b= *hi`E %dlmwrite('aa',hh,'\t'); % save data in the excel format
1 rmN) figure(1)
p_sqw~)^% waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
3V/|" R2s figure(2)
L!W5H2Mc waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
X`} 4=> (5^SL Y 非线性超快脉冲耦合的数值方法的Matlab程序 x A ZRl IC . R4- 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。
MB5X$ 5it 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
HtI>rj/\
x H,1 I z@W1 |VX0o2 hniTMO % This Matlab script file solves the nonlinear Schrodinger equations
Z5 >} % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
<C7/b#4>\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
p["20 ?^ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
=$%_asQJ Q"{Q]IT C=1;
k$K>ml/h M1=120, % integer for amplitude
771r(X?Fa M3=5000; % integer for length of coupler
'~Gk{'Nx" N = 512; % Number of Fourier modes (Time domain sampling points)
cNRe > dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
q}7(w$& T =40; % length of time:T*T0.
V^p XbDRl dt = T/N; % time step
w 259': n = [-N/2:1:N/2-1]'; % Index
(@u" t = n.*dt;
Ds%~J ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T`^LWc" w=2*pi*n./T;
;h U~nj+{ g1=-i*ww./2;
=Cr
F(wVO" g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
+QFY. >KH g3=-i*ww./2;
h|&qWv P1=0;
k'Z$# P2=0;
V}"w8i+D? P3=1;
[kg*BaG: P=0;
p[gq^5WuC for m1=1:M1
5},kXXN{ + p=0.032*m1; %input amplitude
ig,v6lqhM s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
E@ $HO_;& s1=s10;
s a v s20=0.*s10; %input in waveguide 2
)SFy Q s30=0.*s10; %input in waveguide 3
%L;'C
v s2=s20;
R a?0jcSQ$ s3=s30;
Q" an6ht| p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Ej6 4^* %energy in waveguide 1
g JMv p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
@8 GW?R %energy in waveguide 2
ns1@=f cO p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
4wQ>HrS)( %energy in waveguide 3
ZnYoh/ for m3 = 1:1:M3 % Start space evolution
8a4&}^| s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
|G]M"3^ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
[ 6t!}q s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
k%?A= h sca1 = fftshift(fft(s1)); % Take Fourier transform
rn8t<=ptH3 sca2 = fftshift(fft(s2));
r6eApKZ>f6 sca3 = fftshift(fft(s3));
}7jg>3ng( sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Arb-,[kwN sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Fs EPM"&?h sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Syj7K*,%bZ s3 = ifft(fftshift(sc3));
u0& dDZ s2 = ifft(fftshift(sc2)); % Return to physical space
K2R[u#Q s1 = ifft(fftshift(sc1));
V|8`]QW@ end
GiN \ @F! p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
%@Ty,d:;= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
*6e 5T p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
w_!]_6%{b P1=[P1 p1/p10];
+b]+5 ! P2=[P2 p2/p10];
*aF<#m v P3=[P3 p3/p10];
(GdL(H#IL P=[P p*p];
x GHS end
WSW,}tFp" figure(1)
4h[^!up.7 plot(P,P1, P,P2, P,P3);
/P /S0 c);(+b 转自：
http://blog.163.com/opto_wang/
