计算脉冲在非线性耦合器中演化的Matlab 程序 n \G Ry' 8 <#U9] % This Matlab script file solves the coupled nonlinear Schrodinger equations of
(Xx n\*S % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
pBJAaCGm % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
K % g;NW % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-8Ti*: E
l&h;N %fid=fopen('e21.dat','w');
e$/B_o7( N = 128; % Number of Fourier modes (Time domain sampling points)
15H6:_+=0 M1 =3000; % Total number of space steps
Y: QD J =100; % Steps between output of space
mxG ]kqi T =10; % length of time windows:T*T0
+C {p%`< T0=0.1; % input pulse width
UVu DQ MN1=0; % initial value for the space output location
d]v+mVAyE dt = T/N; % time step
r0dDHj~F n = [-N/2:1:N/2-1]'; % Index
<,%:
t = n.*dt;
?pGkk=,KB u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
& *,:1=p u20=u10.*0.0; % input to waveguide 2
o4^Fo p u1=u10; u2=u20;
U bz"rCjq U1 = u1;
% 1U`@0 U2 = u2; % Compute initial condition; save it in U
'3(l-nPiG^ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
) M<vAUF w=2*pi*n./T;
U]4pA#*{| g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
rP=sG;d L=4; % length of evoluation to compare with S. Trillo's paper
JiS5um=(. dz=L/M1; % space step, make sure nonlinear<0.05
Cpl;vQ for m1 = 1:1:M1 % Start space evolution
p9ZXbAJ{ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
N=1JhjVk" u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
3 /6/G}s ca1 = fftshift(fft(u1)); % Take Fourier transform
mj,fp2D;% ca2 = fftshift(fft(u2));
3K0 tC= c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
}-<zWI {p c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
IO$z%r7 u2 = ifft(fftshift(c2)); % Return to physical space
#
'|'r+ u1 = ifft(fftshift(c1));
hsLzj\)6 if rem(m1,J) == 0 % Save output every J steps.
!b| ' Vp^U U1 = [U1 u1]; % put solutions in U array
H}0dd" U2=[U2 u2];
jFG0`n}I MN1=[MN1 m1];
[bQj,PZ& z1=dz*MN1'; % output location
f^Bc end
E _ucab-Fi end
;GHvPQc_ hg=abs(U1').*abs(U1'); % for data write to excel
r4 dOK] 0 ha=[z1 hg]; % for data write to excel
g=)J ~1&p t1=[0 t'];
H^%.=kf hh=[t1' ha']; % for data write to excel file
[THG4582oB %dlmwrite('aa',hh,'\t'); % save data in the excel format
$6>?; figure(1)
T)CzK<LbR waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
vq'c@yw; figure(2)
Bs tk{&ew waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
V,7%1TZ: ctmQWrk|B 非线性超快脉冲耦合的数值方法的Matlab程序 -\$`i c$"1 E">T* ao 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。
bMoAD.} 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
M~
h8Crz ;DRTQn`m !cEG}(|h |I8Mk.Z=FA % This Matlab script file solves the nonlinear Schrodinger equations
=(r*
5vd % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
N1Ee zC'^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
pa
.K-e)Mu % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"k W!{n -f(/B9} C=1;
g<*jlM1r M1=120, % integer for amplitude
%kI}
[6J_ M3=5000; % integer for length of coupler
oUDVy_k N = 512; % Number of Fourier modes (Time domain sampling points)
@)YY\l# dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
^+70<#Xc T =40; % length of time:T*T0.
")#<y@Rv dt = T/N; % time step
*tQk;'/A] n = [-N/2:1:N/2-1]'; % Index
p
QE)p
t = n.*dt;
E;\M1(\u ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7()?C}Ni- w=2*pi*n./T;
j#A%q"]8 g1=-i*ww./2;
m7]hJ ,0 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
>%b\yl%0 g3=-i*ww./2;
> O9 sk P1=0;
]L_w$ev' P2=0;
&wH:aD P3=1;
Xg<[fwW P=0;
VA Q)Hc] for m1=1:M1
&&8'0 .M{ p=0.032*m1; %input amplitude
!-]C;9 Zd s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
3 -Bl s1=s10;
m S=r(3# s20=0.*s10; %input in waveguide 2
- Xupq/[, s30=0.*s10; %input in waveguide 3
!R{R?? s2=s20;
* b(wVvz s3=s30;
6Y*;{\Rd p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
[ W,|kDK %energy in waveguide 1
o3Ot.9L p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
)6oGF>o> %energy in waveguide 2
pgc3j P! p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
a=}*mF[ug %energy in waveguide 3
~4 #B'Gy[ for m3 = 1:1:M3 % Start space evolution
lvSdY(8 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
* dE^-dm# s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
ZXiRw)rM s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
0~A#>R' sca1 = fftshift(fft(s1)); % Take Fourier transform
3fS}:!sQ sca2 = fftshift(fft(s2));
xN->cA$A sca3 = fftshift(fft(s3));
<-C!;Ce{ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
B&KL2&Z~Pq sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
S \C*iGeqJ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
eQN .sl5 s3 = ifft(fftshift(sc3));
+ Ghi} v s2 = ifft(fftshift(sc2)); % Return to physical space
/MTf0^9 s1 = ifft(fftshift(sc1));
P e7e ?7 9 end
J\co1kO9/ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
]?l {j p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
t%0?N<9YkU p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
:- +4:S P1=[P1 p1/p10];
`aSM 8C\ P2=[P2 p2/p10];
X T>('qy P3=[P3 p3/p10];
ZW4aY}~)$ P=[P p*p];
4iX-( ir, end
dSK 0h(8 figure(1)
f?UzD#50D plot(P,P1, P,P2, P,P3);
Di(9]: + 440FhD Mj 转自：
http://blog.163.com/opto_wang/
