计算脉冲在非线性耦合器中演化的Matlab 程序 j0j!oj)7I xjSz Q| k- % This Matlab script file solves the coupled nonlinear Schrodinger equations of
~ g-( % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
]Y-Y.&b7t % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
& Zn`2% % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Alo L+eN@ alB' l %fid=fopen('e21.dat','w');
e(N},s:_ N = 128; % Number of Fourier modes (Time domain sampling points)
`N&*+!O% M1 =3000; % Total number of space steps
wdAKU +tM J =100; % Steps between output of space
(w{T[ ~6 T =10; % length of time windows:T*T0
E
.28G2& T0=0.1; % input pulse width
,Tu.cg MN1=0; % initial value for the space output location
;c>"gW8 dt = T/N; % time step
k s\q^ten n = [-N/2:1:N/2-1]'; % Index
3y+~l
H : t = n.*dt;
x=IZ0@p u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
tjwn Fq I u20=u10.*0.0; % input to waveguide 2
?wv^X`Q*~ u1=u10; u2=u20;
wV i TMlq U1 = u1;
z HvE_ - U2 = u2; % Compute initial condition; save it in U
<ch}]-_ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
*oeXmY w=2*pi*n./T;
t0jE\6r g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
LT
Pr8^ L=4; % length of evoluation to compare with S. Trillo's paper
m [^ )Q9o} dz=L/M1; % space step, make sure nonlinear<0.05
Zs{7km for m1 = 1:1:M1 % Start space evolution
BC/5 bA u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Il9xNVos# u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
FZn1$_Svr ca1 = fftshift(fft(u1)); % Take Fourier transform
&6C]| 13; ca2 = fftshift(fft(u2));
vPGUE`!D+ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
>zDQt7+g; c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
(oR~%2K u2 = ifft(fftshift(c2)); % Return to physical space
OdZ/ \_Z u1 = ifft(fftshift(c1));
c+E \e] { if rem(m1,J) == 0 % Save output every J steps.
YPGzI]\ U1 = [U1 u1]; % put solutions in U array
l?2 U2=[U2 u2];
QNINn>2 MN1=[MN1 m1];
P8}IDQ9 z1=dz*MN1'; % output location
dQ 7iieT end
2oEuqHL end
K}cA%Y hg=abs(U1').*abs(U1'); % for data write to excel
$u.rO7 ) ha=[z1 hg]; % for data write to excel
.%{B=_7 t1=[0 t'];
[ i, [ ^ hh=[t1' ha']; % for data write to excel file
Ahl&2f\ %dlmwrite('aa',hh,'\t'); % save data in the excel format
3o[(pfcU figure(1)
R[v0T/ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
=oIt.`rf figure(2)
=DfI^$Lr: waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
MKvmzLh$) {q`8+ $Z; 非线性超快脉冲耦合的数值方法的Matlab程序 bR) P-9rs #7 Q9^rG 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。
2,q*8=?{6P 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
2F`#df AC(qx:/6 D{Nd2G Be]z @E1x % This Matlab script file solves the nonlinear Schrodinger equations
;$6L_C4B % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
}dzVwP= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
w-ald?` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
. tLRY NZv 8# C=1;
A r~/KRK M1=120, % integer for amplitude
P$Vh{]4i{ M3=5000; % integer for length of coupler
APF`b N = 512; % Number of Fourier modes (Time domain sampling points)
y>0 @. dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
DvQV_D T =40; % length of time:T*T0.
MYvz%7 dt = T/N; % time step
^i#0aq2} n = [-N/2:1:N/2-1]'; % Index
/klo),|& t = n.*dt;
zA6C{L G3 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
0ZDm[# 7z w=2*pi*n./T;
0J'Cx&Rg g1=-i*ww./2;
kVM*[<k g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
9&=%shOc+x g3=-i*ww./2;
g]HWaFjc5 P1=0;
USN'-Ah P2=0;
\mGb|a F8 P3=1;
.wd7^wI^S P=0;
ty~Sf-Pri for m1=1:M1
_ps4-<ugC p=0.032*m1; %input amplitude
";(m,i f- s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
A\ rY~$Vr s1=s10;
flqr["czwK s20=0.*s10; %input in waveguide 2
V.u^;gr3 s30=0.*s10; %input in waveguide 3
89D`!`Ah] s2=s20;
!gLJB p s3=s30;
Q+K]:c p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
,e1c,} %energy in waveguide 1
P;25 F p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
hr.mzQd %energy in waveguide 2
I:=!, 4S; p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
p%>!1_'( %energy in waveguide 3
"~=}& for m3 = 1:1:M3 % Start space evolution
U= n s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
8q9 ^ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
cp8w
_TPU s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
/rD9) sca1 = fftshift(fft(s1)); % Take Fourier transform
4%nK0FAj sca2 = fftshift(fft(s2));
7YTO{E6]d\ sca3 = fftshift(fft(s3));
E5P .x^ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
t"%~r3{ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
-M] /Xv] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
jzDPn<WQ s3 = ifft(fftshift(sc3));
! ?i9fYu s2 = ifft(fftshift(sc2)); % Return to physical space
~8k`~t! s1 = ifft(fftshift(sc1));
5ip ZdQ ^ end
7 8xiT p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
mL }Wan p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
',FVT4OMw p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
P!9-!+F" P1=[P1 p1/p10];
`ZC -lAY P2=[P2 p2/p10];
e
jk?If 07 P3=[P3 p3/p10];
C ;ha2UV0H P=[P p*p];
}o
G MF~ end
p |;#frj figure(1)
p,8:(|( plot(P,P1, P,P2, P,P3);
mrE> o ! i0x[w>\- 转自：
http://blog.163.com/opto_wang/
