计算脉冲在非线性耦合器中演化的Matlab 程序 izw}25SW aVb]H0 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
#+G2ZJxL| % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
+ NY4j-O % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Ss:,#| % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
K_aN7?#.v` {|%O)fr, %fid=fopen('e21.dat','w');
,W-0qN&%/ N = 128; % Number of Fourier modes (Time domain sampling points)
<j#Ey GAV M1 =3000; % Total number of space steps
#.)>geLC>9 J =100; % Steps between output of space
a< EC]-nw T =10; % length of time windows:T*T0
F~AS(sk T0=0.1; % input pulse width
r;C \eN MN1=0; % initial value for the space output location
EHHxCq? dt = T/N; % time step
"=(;l3-o n = [-N/2:1:N/2-1]'; % Index
E-D5iiF t = n.*dt;
_ XZ=4s u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
B`aAvD`7 u20=u10.*0.0; % input to waveguide 2
NjxW A&[ng u1=u10; u2=u20;
SS~Q ;9o U1 = u1;
sdWl5 " U2 = u2; % Compute initial condition; save it in U
xNkY'4% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
"BRE0Ir: w=2*pi*n./T;
Z]f2& g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
>B
L=4; % length of evoluation to compare with S. Trillo's paper
OpLSjr dz=L/M1; % space step, make sure nonlinear<0.05
nS4S[|w" for m1 = 1:1:M1 % Start space evolution
obq}# u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
p'qH [<s u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
)mdNvb[*n ca1 = fftshift(fft(u1)); % Take Fourier transform
s>\g03= ca2 = fftshift(fft(u2));
pG6-. F; c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
BT3O_X`u c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
hhGpB$A u2 = ifft(fftshift(c2)); % Return to physical space
.}N^AO= u1 = ifft(fftshift(c1));
;l ()3 ; if rem(m1,J) == 0 % Save output every J steps.
0Q >|s_ U1 = [U1 u1]; % put solutions in U array
_vH!0@QFU U2=[U2 u2];
WZ&@
J B MN1=[MN1 m1];
0)5Sx /5' z1=dz*MN1'; % output location
VWy:U#;+8 end
9 Zm<1Fw end
e,&%Z
hg=abs(U1').*abs(U1'); % for data write to excel
7V
(7JV<> ha=[z1 hg]; % for data write to excel
x Ui!|c t1=[0 t'];
R+0 " B hh=[t1' ha']; % for data write to excel file
)`mF.87b&h %dlmwrite('aa',hh,'\t'); % save data in the excel format
P AV2w_X~ figure(1)
r5!M;hU1j waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
(H+[ ^(3d2 figure(2)
Vor9
?F&w waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
X&.$/xaT yQ{_\t 1Wd 非线性超快脉冲耦合的数值方法的Matlab程序 J. 2]km ,jsx]U/^ 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。
Ko)T>8: 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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1+% T1HiHvJ y%bqeo
L~ }#*zjMOz % This Matlab script file solves the nonlinear Schrodinger equations
a=.db&;vY % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
n "KJB % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
!a(qqZ|s % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
14 'x-w^~k 9 ~'Ip7X,! C=1;
5qQ( V)ah M1=120, % integer for amplitude
n UCk0:{ M3=5000; % integer for length of coupler
-^Km}9g N = 512; % Number of Fourier modes (Time domain sampling points)
u6I0<i_KZ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
/{ MH' T =40; % length of time:T*T0.
JS?l?~ dt = T/N; % time step
< VR&= YJ n = [-N/2:1:N/2-1]'; % Index
h;UdwmT t = n.*dt;
x ETVt q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
"rDzrz w=2*pi*n./T;
[I<'E
LX g1=-i*ww./2;
q\ y# g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
T>Rf?%o g3=-i*ww./2;
1 qKxg P1=0;
sFM>gG P2=0;
1fhK {9# P3=1;
f9XO9N,hE: P=0;
h9w^7MbO for m1=1:M1
)7 "DR+;: p=0.032*m1; %input amplitude
Y1_6\zpA s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
h8= MVh(I s1=s10;
VueQP| s20=0.*s10; %input in waveguide 2
$CwTNm ? s30=0.*s10; %input in waveguide 3
pkV\D s2=s20;
27 YLg c s3=s30;
4U
a~*58 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
GlgOR y=> %energy in waveguide 1
vu a1iN1 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
p C2c(4 %energy in waveguide 2
;7^ j-6 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
`Y({#U %energy in waveguide 3
3g#=sd!0O@ for m3 = 1:1:M3 % Start space evolution
9EA
!j} s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
aU]O$Pg{ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
g yH7 ((#i s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
a0/n13c?G sca1 = fftshift(fft(s1)); % Take Fourier transform
t"bPKFRy9E sca2 = fftshift(fft(s2));
>;&V~q:di sca3 = fftshift(fft(s3));
S}p&\w H sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
-f;j1bQ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
[F V=@NI sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
)>X|o$2 s3 = ifft(fftshift(sc3));
# pjyhH@ s2 = ifft(fftshift(sc2)); % Return to physical space
p5# P
r s1 = ifft(fftshift(sc1));
~iR!3+yg4 end
)av'u.]%c p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
0jJ28.kOp p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
0@e}hv; p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
am'p^Z @ P1=[P1 p1/p10];
)4F/T, {;m P2=[P2 p2/p10];
0O['-x P3=[P3 p3/p10];
qfP"UAc{/ P=[P p*p];
d,J<SG&L& end
$7gB&T.x figure(1)
SL\y\G aV plot(P,P1, P,P2, P,P3);
hzu MTKH9 7MuK/q. 转自：
http://blog.163.com/opto_wang/
