计算脉冲在非线性耦合器中演化的Matlab 程序
7-Rn{"5 OB3AZH$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
XboOvdt^| % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
GN{\ccej % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
R@>R@V>c % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Faa :h# T,(IdVlJ %fid=fopen('e21.dat','w');
Kbx (^f12 N = 128; % Number of Fourier modes (Time domain sampling points)
Wf_aEW&n M1 =3000; % Total number of space steps
YU76(S9 0# J =100; % Steps between output of space
&dvJg T =10; % length of time windows:T*T0
S$%/9^\jF T0=0.1; % input pulse width
u]E% R& MN1=0; % initial value for the space output location
G% ycA m dt = T/N; % time step
=pWpHbB. n = [-N/2:1:N/2-1]'; % Index
P;KbS~ SlC t = n.*dt;
h0n0Dc{4 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
W_8 FzXA u20=u10.*0.0; % input to waveguide 2
`(;d+fof u1=u10; u2=u20;
8!>uC&bE8 U1 = u1;
[k-7Kq U2 = u2; % Compute initial condition; save it in U
&m8B%9w ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
D]y6*Ha w=2*pi*n./T;
_KmpC>J+ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
K *vNv 4 L=4; % length of evoluation to compare with S. Trillo's paper
_1y|#o dz=L/M1; % space step, make sure nonlinear<0.05
g/+M&k$ for m1 = 1:1:M1 % Start space evolution
aC3\Hs u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
i BJ*6orz u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
/G[y
24 Q ca1 = fftshift(fft(u1)); % Take Fourier transform
xx;'WL,g ca2 = fftshift(fft(u2));
B>X+eK c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
NL&g/4A[a c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
+KFK.. u2 = ifft(fftshift(c2)); % Return to physical space
e /;Ui u1 = ifft(fftshift(c1));
E\m?0]W| if rem(m1,J) == 0 % Save output every J steps.
w])~m1yW U1 = [U1 u1]; % put solutions in U array
}J`{g/ U2=[U2 u2];
~R)w
9uq MN1=[MN1 m1];
.[cT3l/ t z1=dz*MN1'; % output location
2SG|] = end
BqZLqGO Ku end
.E;6Xx_+r hg=abs(U1').*abs(U1'); % for data write to excel
u .hnQsM ha=[z1 hg]; % for data write to excel
8GlH)J+kq t1=[0 t'];
.v1rrH ? hh=[t1' ha']; % for data write to excel file
MiRH i<g0 %dlmwrite('aa',hh,'\t'); % save data in the excel format
<S$y=>.9 figure(1)
aE{b65'Dt waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
i UI,r* figure(2)
L6 _Sc-sU waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
D@
=.4z jHz] 非线性超快脉冲耦合的数值方法的Matlab程序 KMbBow3o*~ *"zE,Bp" 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。
(/*- M]> 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
t&r?O dc&m
vN4X%^:( ' .kbXw0}
%;W8; % This Matlab script file solves the nonlinear Schrodinger equations
$^
>n@Q@&L % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
_R-#I % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0]HK (,/h % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
T3?kabbF i;dr(c/ft C=1;
UT{N ly8u M1=120, % integer for amplitude
& H+<uYV M3=5000; % integer for length of coupler
[e^i". N = 512; % Number of Fourier modes (Time domain sampling points)
@ ic s dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
"t\9@nzdX T =40; % length of time:T*T0.
ih Yf WG| dt = T/N; % time step
0?`#ko7~d n = [-N/2:1:N/2-1]'; % Index
a9qZI t = n.*dt;
#F{|G:\@[ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
s[s^z<4G w=2*pi*n./T;
pEaH^(I* g1=-i*ww./2;
5
+
Jy
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
l{pF^?K g3=-i*ww./2;
gTQ6B,`/8 P1=0;
ix/uV)]k` P2=0;
fsmH] ;"GD P3=1;
?t%5 / P=0;
bFJn-g n for m1=1:M1
{MEU|9@
Y p=0.032*m1; %input amplitude
>qgBu_ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
:-
5Mn3* s1=s10;
Wex4>J<`/ s20=0.*s10; %input in waveguide 2
Anm5Cvt;i s30=0.*s10; %input in waveguide 3
34l=U? s2=s20;
dJ;;l7":~ s3=s30;
E nUo B< p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
* lTu- %energy in waveguide 1
;kF p)*i p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
J *B`C^i %energy in waveguide 2
0y1t%C075 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
50Jr(OeU< %energy in waveguide 3
o . _^ for m3 = 1:1:M3 % Start space evolution
u}h'v&"e, s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
U! `'Qw; s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
DxD0iJ=W s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Zu hT \l sca1 = fftshift(fft(s1)); % Take Fourier transform
|% kK?!e+- sca2 = fftshift(fft(s2));
df)1} /* L sca3 = fftshift(fft(s3));
YS~x-5OE\ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
| UaI i^ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
N1$P6 ZF sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
FP Mk& s3 = ifft(fftshift(sc3));
Eg:p_F*lr s2 = ifft(fftshift(sc2)); % Return to physical space
>*(> %E~H s1 = ifft(fftshift(sc1));
%2+]3h >g end
LH8?0 N[ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
(M=Br p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
2u:j6ic p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
M#p,Z F P1=[P1 p1/p10];
RAxz+1JT P2=[P2 p2/p10];
]aR4U` P3=[P3 p3/p10];
C G 7 LF P=[P p*p];
X>4`{x ` end
[4t KJ+v figure(1)
Z8@]e}n plot(P,P1, P,P2, P,P3);
R}VL UL$ D^~g q`/) 转自：
http://blog.163.com/opto_wang/
