计算脉冲在非线性耦合器中演化的Matlab 程序 q5S 9C%b \'j|BJ~L f % This Matlab script file solves the coupled nonlinear Schrodinger equations of
8q7b_Pq1U % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
e+K^A q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
sDV Q#}a % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
}<:}XlwT% g9F?z2^ %fid=fopen('e21.dat','w');
2:ylv<\$ N = 128; % Number of Fourier modes (Time domain sampling points)
C7AUsYM M1 =3000; % Total number of space steps
N {>n$ v}
J =100; % Steps between output of space
`r_/Wt{g T =10; % length of time windows:T*T0
FVBYo%Ap T0=0.1; % input pulse width
Oow2>F%_# MN1=0; % initial value for the space output location
jc9y<{~x/ dt = T/N; % time step
U
m+8"W n = [-N/2:1:N/2-1]'; % Index
<a+Z;> t = n.*dt;
%8x#rohP u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
0m ? )ROaJ u20=u10.*0.0; % input to waveguide 2
E_LN]v u1=u10; u2=u20;
zx7{U8*`< U1 = u1;
@lph)A Nk U2 = u2; % Compute initial condition; save it in U
T[A 69O]v ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
F6dP,( w=2*pi*n./T;
[ikOb8 G# g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
jZ;
=so L=4; % length of evoluation to compare with S. Trillo's paper
"zy7C*)>r dz=L/M1; % space step, make sure nonlinear<0.05
gZ1?G-Q for m1 = 1:1:M1 % Start space evolution
@=kSo
-S X u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
)dSi/ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
H>@+om ca1 = fftshift(fft(u1)); % Take Fourier transform
n(]-y@X0_ ca2 = fftshift(fft(u2));
uW3!Yg@ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
,7b[!#?8 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
>F&47Yn u2 = ifft(fftshift(c2)); % Return to physical space
sp`Dvqx0 u1 = ifft(fftshift(c1));
S21,VpW\ if rem(m1,J) == 0 % Save output every J steps.
X\ F|Tk3_ U1 = [U1 u1]; % put solutions in U array
*uvQ\. U2=[U2 u2];
\nqS+on] MN1=[MN1 m1];
t&DEb_"De z1=dz*MN1'; % output location
WMg~Y"W end
KY] C6kh end
iG?[<1~ hg=abs(U1').*abs(U1'); % for data write to excel
sn>~O4" ha=[z1 hg]; % for data write to excel
O|UC ?]6 t1=[0 t'];
&iV s0 R hh=[t1' ha']; % for data write to excel file
HUO j0T %dlmwrite('aa',hh,'\t'); % save data in the excel format
7J&4akT{9 figure(1)
M&
CqSd waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
+d-NL?c figure(2)
G owH]MO waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
2)~> R ei5~& 非线性超快脉冲耦合的数值方法的Matlab程序 D|#E9OQzs da ~],MN 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。
&Y eA:i? 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
W+1^4::+ *4_Bd=5(U /|#fejPh D7qOZlX16 % This Matlab script file solves the nonlinear Schrodinger equations
:p6M = % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
0Fr?^3h % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
IdxzE_@ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
!$>R j xi; `ecqS< C=1;
bK-N:8Z M1=120, % integer for amplitude
i(+p0: < 0 M3=5000; % integer for length of coupler
_t}WsEQ+P N = 512; % Number of Fourier modes (Time domain sampling points)
{2 "zVt#h dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
e64 ^ChCoV T =40; % length of time:T*T0.
h3@v+Z<} dt = T/N; % time step
m9 }P9 ? n = [-N/2:1:N/2-1]'; % Index
w"& n? L t = n.*dt;
J!7MZL b ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
m<2M4u w=2*pi*n./T;
!_Z&a g1=-i*ww./2;
5.J.RE"M g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
vEz"xz1j!] g3=-i*ww./2;
2T[9f;jM' P1=0;
t5IEQ2 P2=0;
SOvF[,+ P3=1;
4|#WFLo@ P=0;
QnX(V[ for m1=1:M1
i<g-+ Qs p=0.032*m1; %input amplitude
CQDkFQq-dq s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
t9IW/Q s1=s10;
|)/aGZ+ s20=0.*s10; %input in waveguide 2
=rX>1 s30=0.*s10; %input in waveguide 3
yyy|Pw4:Z s2=s20;
KRK CD4 s3=s30;
3%=~) 7cF p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
`,*5wBC %energy in waveguide 1
P J[ `| p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
)IZ~G\Ra' %energy in waveguide 2
}| 5Pr(I p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
b9dLt6d %energy in waveguide 3
^@NU}S):yN for m3 = 1:1:M3 % Start space evolution
V,N%;iB} s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
! #2{hQRu s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Y% 5eZ=z s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
4)o sca1 = fftshift(fft(s1)); % Take Fourier transform
0h7r&t%YsV sca2 = fftshift(fft(s2));
SGlNKA},A sca3 = fftshift(fft(s3));
vd4ytC sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
l_%6 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
0>Z _*U~6 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
fXQNHZ|4 s3 = ifft(fftshift(sc3));
nwCrZW s2 = ifft(fftshift(sc2)); % Return to physical space
sZF6h=67D s1 = ifft(fftshift(sc1));
3=]sLn0L end
W X6&oy> p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
/%A*aGyIc p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
UN<]N76! p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
' F#KM1s P1=[P1 p1/p10];
$l &(%\pp P2=[P2 p2/p10];
2x0<&Xy#P P3=[P3 p3/p10];
XAL1|] S P=[P p*p];
-4_$ln w$ end
WU=59gB+jL figure(1)
3 WIk plot(P,P1, P,P2, P,P3);
G {%L B}2 0F><P?5 转自：
http://blog.163.com/opto_wang/
