计算脉冲在非线性耦合器中演化的Matlab 程序 |*+f N8 sm ~{fg % This Matlab script file solves the coupled nonlinear Schrodinger equations of
XH?} 0D( % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
"V;5Lp b % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
:DlgNR`bq % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
3 0fsVwE2 o"a~ %fid=fopen('e21.dat','w');
y(!Y N7_A N = 128; % Number of Fourier modes (Time domain sampling points)
|%@.@c M1 =3000; % Total number of space steps
'9Hah J =100; % Steps between output of space
Gw/imXL T =10; % length of time windows:T*T0
"#a_--"k9 T0=0.1; % input pulse width
5D32d1A MN1=0; % initial value for the space output location
Rt [zZv dt = T/N; % time step
JQhw >H9& n = [-N/2:1:N/2-1]'; % Index
]H4T80wm& t = n.*dt;
5zqlK-$ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
KAucSd` u20=u10.*0.0; % input to waveguide 2
>(}
I 7 u1=u10; u2=u20;
El}."}l& U1 = u1;
l#W9J.q( U2 = u2; % Compute initial condition; save it in U
2$g3AB fV ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
JIl<4 %A w=2*pi*n./T;
_djr>C=H" g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
4 \.1phe$a L=4; % length of evoluation to compare with S. Trillo's paper
eco i4f dz=L/M1; % space step, make sure nonlinear<0.05
pt rQ~m- for m1 = 1:1:M1 % Start space evolution
19u'{/Y" u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
rl0sN5n u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
<9]9; ca1 = fftshift(fft(u1)); % Take Fourier transform
q ^e4 ca2 = fftshift(fft(u2));
y3]7^+k c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
vT#$`M< c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
gRk%ObJGqm u2 = ifft(fftshift(c2)); % Return to physical space
l 4 zl|6% u1 = ifft(fftshift(c1));
1q])"l"< if rem(m1,J) == 0 % Save output every J steps.
=lzRx%tm U1 = [U1 u1]; % put solutions in U array
ZZ<uiN$ U2=[U2 u2];
b#:Pl`n6u MN1=[MN1 m1];
rHir>
p z1=dz*MN1'; % output location
]ZQ3|ZJ?< end
b>B.3E\Pc end
\M
H\! hg=abs(U1').*abs(U1'); % for data write to excel
S+mZ.aFS0z ha=[z1 hg]; % for data write to excel
jb!R t1=[0 t'];
FZW )C'j hh=[t1' ha']; % for data write to excel file
F
;o ^. %dlmwrite('aa',hh,'\t'); % save data in the excel format
&B</ ^: figure(1)
TsPx"+>7` waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
{R2gz]v4 figure(2)
1<y|, waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
yA8e"$ { *"I4 非线性超快脉冲耦合的数值方法的Matlab程序 Hl,.6 >F? z$VA]tI( 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。
VOk EDH 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
X*'tJN $ om`x"x&6 I. [2 -~yf \"]vSx> % This Matlab script file solves the nonlinear Schrodinger equations
c~@ Z % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
YceX) % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
tSr.0'CE % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
6;02_C]\o l ( EDe C=1;
"k)}qI{ M1=120, % integer for amplitude
~ nQv
yM!$ M3=5000; % integer for length of coupler
gEVN;G'B<= N = 512; % Number of Fourier modes (Time domain sampling points)
}tvLe3O dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
}klET T =40; % length of time:T*T0.
i@=0fHiZQ dt = T/N; % time step
y"Fp4$qb n = [-N/2:1:N/2-1]'; % Index
i'GBj, : t = n.*dt;
EJM6TI" ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7QXA*.'
F w=2*pi*n./T;
p;["> [" g1=-i*ww./2;
'[E|3K 5d g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
7oPLO(0L g3=-i*ww./2;
K3uNR w P1=0;
P}] xz Vy P2=0;
1:7 uS . P3=1;
3ErW3Ac Ou P=0;
.AIlv^:|U for m1=1:M1
,_STt) p=0.032*m1; %input amplitude
'W!N1W@ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
?-4 0bb s1=s10;
Pc+8CuN? s20=0.*s10; %input in waveguide 2
k 8C[fRev s30=0.*s10; %input in waveguide 3
Ck71N3~W s2=s20;
f`zH#{u s3=s30;
FtaO@5pS54 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
5 XK}8\ %energy in waveguide 1
' }G! D p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
8VbH Z9Q %energy in waveguide 2
:xn/9y+s p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
< r6e23 %energy in waveguide 3
z h5$$*\
for m3 = 1:1:M3 % Start space evolution
85>WK+= s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
(zW;&A s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
8<,b5 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
/%E l0X sca1 = fftshift(fft(s1)); % Take Fourier transform
F\' ^DtB sca2 = fftshift(fft(s2));
$$U Mc-Pq sca3 = fftshift(fft(s3));
~hubh!d= sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
z:R clDm sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
wz!a;]agg sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
0* G 5Vd s3 = ifft(fftshift(sc3));
}LXS!Ff: s2 = ifft(fftshift(sc2)); % Return to physical space
aNZJs<3;'D s1 = ifft(fftshift(sc1));
yZ
{H end
~ i`@ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
cY%[UK $l p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
-JL p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
]_cBd)3P} P1=[P1 p1/p10];
'ZyHp=RN) P2=[P2 p2/p10];
JfJU OaL P3=[P3 p3/p10];
4)'8fi P=[P p*p];
G8c 8`~t end
s[ {L.9Y figure(1)
DU_38tz plot(P,P1, P,P2, P,P3);
p&B
c<+3e @]*b$6tt 转自：
http://blog.163.com/opto_wang/
