计算脉冲在非线性耦合器中演化的Matlab 程序 %J~8a _vO dE/Vl/ : % This Matlab script file solves the coupled nonlinear Schrodinger equations of
;Jv)J3y % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Z0b1E % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
',m,wp ` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)c]GgPH >@ h0@ N %fid=fopen('e21.dat','w');
<JF78MD\ N = 128; % Number of Fourier modes (Time domain sampling points)
" o;l8$)VL M1 =3000; % Total number of space steps
@8n0GCv J =100; % Steps between output of space
zr8 4%_^ T =10; % length of time windows:T*T0
RTLu]Bry T0=0.1; % input pulse width
_f^q!tP&d MN1=0; % initial value for the space output location
m]7Y
)&3 dt = T/N; % time step
UO<uG#FB n = [-N/2:1:N/2-1]'; % Index
ik7#Og~ 3 t = n.*dt;
MI',E?#yB u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
yq6!8OkF u20=u10.*0.0; % input to waveguide 2
s![=F}ck u1=u10; u2=u20;
={={ W U1 = u1;
XR P/E_4 U2 = u2; % Compute initial condition; save it in U
\&ERSk2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
G\jr^d\ w=2*pi*n./T;
hl6al:Y g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
|06J4H~k L=4; % length of evoluation to compare with S. Trillo's paper
8ru@ 8|r dz=L/M1; % space step, make sure nonlinear<0.05
LO# { for m1 = 1:1:M1 % Start space evolution
cpu +"/\ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
*Vv ;NA/ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
.N/4+[2p( ca1 = fftshift(fft(u1)); % Take Fourier transform
PeT A:MW ca2 = fftshift(fft(u2));
P4R.~J ;8 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
!l.Rv_o<O c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
;E* ^AW u2 = ifft(fftshift(c2)); % Return to physical space
zs[t<` 2 u1 = ifft(fftshift(c1));
m='+->O*'l if rem(m1,J) == 0 % Save output every J steps.
cf0em! U1 = [U1 u1]; % put solutions in U array
Z# 7HuAF{] U2=[U2 u2];
{'>X6: MN1=[MN1 m1];
7@+0E 2' z1=dz*MN1'; % output location
?em )om end
Z U
f<s? end
Nm OQ7T hg=abs(U1').*abs(U1'); % for data write to excel
$Cc4Sggq ha=[z1 hg]; % for data write to excel
[m}x t1=[0 t'];
1REq.%/= hh=[t1' ha']; % for data write to excel file
6D 0uLh %dlmwrite('aa',hh,'\t'); % save data in the excel format
r)U9u 0 figure(1)
ag|d_; waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
K{ q(/>: figure(2)
szmjp{g0 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
z81I2?v[Jr ~)oC+H@{ 非线性超快脉冲耦合的数值方法的Matlab程序 %\:.rs^ 4fP>;9[F 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
jWP(7}U Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%[ NefA( `pII-dSC% >A2&
Mjo 2Q1* Xq{ % This Matlab script file solves the nonlinear Schrodinger equations
Y`lC4 * g % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Hb!Q}V+Kb8 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
xu&
v(C9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%pTbJaM\U 5
0~L(< C=1;
He j0l^ M1=120, % integer for amplitude
6@Eip[e M3=5000; % integer for length of coupler
8&`s wu& N = 512; % Number of Fourier modes (Time domain sampling points)
EWH'x$ z_q dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
p9l&K/ T =40; % length of time:T*T0.
j
q1qj9KZ dt = T/N; % time step
E.6^~'/ n = [-N/2:1:N/2-1]'; % Index
m#%5 H t = n.*dt;
b3Y9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Z)6bqU<LQE w=2*pi*n./T;
nNBxT+3*i g1=-i*ww./2;
9J2% 9,^ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
LR9dQ=fHS g3=-i*ww./2;
V4V TP]'n P1=0;
3z ~zcQ^\ P2=0;
/V&$SRdL* P3=1;
vcV=9q8P1 P=0;
1*>a for m1=1:M1
nSd?P'PFg p=0.032*m1; %input amplitude
To=1B`@- s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Zu~ #d)l3N s1=s10;
/xf %Rp4} s20=0.*s10; %input in waveguide 2
2! &:V] s30=0.*s10; %input in waveguide 3
^f3F~XhY3 s2=s20;
3f M s3=s30;
7 F+w o p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
B;G|2um:$ %energy in waveguide 1
QD"V=}'? p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
=>S5}6 %energy in waveguide 2
A!iV iX &y p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
~rn82an@G %energy in waveguide 3
2psI\7UjA] for m3 = 1:1:M3 % Start space evolution
LuQ=i`eXx s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Qj 0@^LA s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
??1V__w s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
#kma)_X sca1 = fftshift(fft(s1)); % Take Fourier transform
; [dcbyu@ sca2 = fftshift(fft(s2));
4fpz;2% sca3 = fftshift(fft(s3));
oVmGZhkA@' sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
UXIq>[2Z1 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
S' TF7u sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
]9A9q<lZ s3 = ifft(fftshift(sc3));
8 wC3}U s2 = ifft(fftshift(sc2)); % Return to physical space
;Iv)J|* s1 = ifft(fftshift(sc1));
K mL
PWj end
&x;v& p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Fz>J7(Y.j p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Z;??j+`Eo p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
gX6'!}G8] P1=[P1 p1/p10];
w_\niqm<y P2=[P2 p2/p10];
ULQ*cW&;? P3=[P3 p3/p10];
,|T
P=[P p*p];
fdp/c wd end
2/>AmVM figure(1)
VCvuZU{< plot(P,P1, P,P2, P,P3);
p^~lQ8t O`|'2x{[O 转自：
http://blog.163.com/opto_wang/
