计算脉冲在非线性耦合器中演化的Matlab 程序 a,r
B7aD l@ (:Q!Sk % This Matlab script file solves the coupled nonlinear Schrodinger equations of
1aCpeD4|) % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
w w #kc!' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
V Ew| N) % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
W|y;Kxy f8`dJ5i %fid=fopen('e21.dat','w');
WjCxTBI N = 128; % Number of Fourier modes (Time domain sampling points)
EdkIT|c{ M1 =3000; % Total number of space steps
;47z.i&T J =100; % Steps between output of space
3dSC`K T =10; % length of time windows:T*T0
Svr UXf T0=0.1; % input pulse width
c*\;!dbP MN1=0; % initial value for the space output location
x*= 1C,C dt = T/N; % time step
+C[g>c}d n = [-N/2:1:N/2-1]'; % Index
w~ON861 t = n.*dt;
m^=El7+ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
'4Fwh]Ee u20=u10.*0.0; % input to waveguide 2
,>8w|951' u1=u10; u2=u20;
1X&jlD? U1 = u1;
_A] )q U2 = u2; % Compute initial condition; save it in U
&/WE{W ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1j:aGj>{ w=2*pi*n./T;
Vxu V`P lf g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
P.QF9% L=4; % length of evoluation to compare with S. Trillo's paper
-6~ .;M 5 dz=L/M1; % space step, make sure nonlinear<0.05
NzTF2ve( for m1 = 1:1:M1 % Start space evolution
Ip:54 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
V; CPn u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
C/'w ca1 = fftshift(fft(u1)); % Take Fourier transform
Kf*Dy:e ca2 = fftshift(fft(u2));
bLAHVi<. c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
bI8uw|c c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
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u2 = ifft(fftshift(c2)); % Return to physical space
_53~D= u1 = ifft(fftshift(c1));
:O$bsw:3w< if rem(m1,J) == 0 % Save output every J steps.
Wpi3 5JrC U1 = [U1 u1]; % put solutions in U array
|_>^vW1f U2=[U2 u2];
U+@U/s%8 MN1=[MN1 m1];
y&-QLX L z1=dz*MN1'; % output location
"WUS?Q end
zsJermF,O end
_B&Lyg !J hg=abs(U1').*abs(U1'); % for data write to excel
]JV'z< ha=[z1 hg]; % for data write to excel
nSC2wTH!1 t1=[0 t'];
" aCAA#$J hh=[t1' ha']; % for data write to excel file
H;l _; c` %dlmwrite('aa',hh,'\t'); % save data in the excel format
d Rnf figure(1)
q$mc{F($D waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
stBe ^C figure(2)
fe,6YXUf waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
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2wHbhW [ 非线性超快脉冲耦合的数值方法的Matlab程序 ;}"Eqq : {svo!pN: 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。
)<:TpMdUk 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
Y`Io}h G$ G0Qw&
mqF I hYR4?e ZcQu9XDIt % This Matlab script file solves the nonlinear Schrodinger equations
<7`zc7c]# % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
$i5J} % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
$
V P1(C % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
>[,eK= I4 {x QI C=1;
`+"(GaZ M1=120, % integer for amplitude
X["xC3 i M3=5000; % integer for length of coupler
#c>GjUJ.w N = 512; % Number of Fourier modes (Time domain sampling points)
$?G@ijk , dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
ng"=vmu T =40; % length of time:T*T0.
hN
&?x5aC> dt = T/N; % time step
}:
HG)V n = [-N/2:1:N/2-1]'; % Index
kzDN(_<1 t = n.*dt;
)J}v.8 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Oo}h :3? w=2*pi*n./T;
O 'mcN* g1=-i*ww./2;
bYnq,JRA g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
J-5>+E,nZ g3=-i*ww./2;
K+F"V W*? P1=0;
C; N6",s! P2=0;
dD=$$(
je P3=1;
L ,dh$F P=0;
.4)oZ for m1=1:M1
{;c'@U p=0.032*m1; %input amplitude
0lg$zi x( s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
~\jP+ [>M' s1=s10;
VP~2F
E s20=0.*s10; %input in waveguide 2
6FA+q YSV s30=0.*s10; %input in waveguide 3
>|E]??v s2=s20;
Q L WnP- s3=s30;
a (~Y:v p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
f
+{=##'0 %energy in waveguide 1
D}98ZKi p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Q=`yPK>{$N %energy in waveguide 2
H@=oVyn/ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
ctZ,qg*N %energy in waveguide 3
/I=|; FGq for m3 = 1:1:M3 % Start space evolution
Zj2 si s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
* 9^8NY] s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
si]VM_w6 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
@MES.g sca1 = fftshift(fft(s1)); % Take Fourier transform
`
k T\V' sca2 = fftshift(fft(s2));
#1DEZ4]jjY sca3 = fftshift(fft(s3));
tDX& ~1s sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
zjQ746<&)i sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
&Q883A
J sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
](w)e
p~;3 s3 = ifft(fftshift(sc3));
)S g6B;CJ s2 = ifft(fftshift(sc2)); % Return to physical space
nF <K84 s1 = ifft(fftshift(sc1));
hv|a8=U!R end
u}[ a p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
]#)(D-i p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
$r/ $aq=K p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
u 2 s P1=[P1 p1/p10];
Zv;nY7B P2=[P2 p2/p10];
4v\HaOk P3=[P3 p3/p10];
l{{,D57J P=[P p*p];
.SD-6GVD end
>GGM76vB=, figure(1)
A@}5'LzL plot(P,P1, P,P2, P,P3);
'"B $oBs%.Jp 转自：
http://blog.163.com/opto_wang/
