计算脉冲在非线性耦合器中演化的Matlab 程序 #H5*]"w6I 'jmcS0f
- % This Matlab script file solves the coupled nonlinear Schrodinger equations of
v< ;, x % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
/>+JK5 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Z., Pl % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`ORDN|s6 VsUEp _I %fid=fopen('e21.dat','w');
M@csB. ' N = 128; % Number of Fourier modes (Time domain sampling points)
!fz`O>-mZ M1 =3000; % Total number of space steps
lt(,/ J =100; % Steps between output of space
Lu-owP7nB T =10; % length of time windows:T*T0
V1j&>-]]9* T0=0.1; % input pulse width
|nocz]yU$ MN1=0; % initial value for the space output location
^S , "i V dt = T/N; % time step
\@I.K+hj$ n = [-N/2:1:N/2-1]'; % Index
}S%a] t = n.*dt;
6
*Q5.g u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
eW\_9E)cY u20=u10.*0.0; % input to waveguide 2
O|a v( F9 u1=u10; u2=u20;
+Mg^u-(A U1 = u1;
x6F \|nb U2 = u2; % Compute initial condition; save it in U
z RsA[F# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-6)ywq^{z w=2*pi*n./T;
G::6?+S g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
9E
(>mN L=4; % length of evoluation to compare with S. Trillo's paper
u4Vc:n dz=L/M1; % space step, make sure nonlinear<0.05
PqvwM2}4 for m1 = 1:1:M1 % Start space evolution
9:@os0^O u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
?u8+F u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
_+^3<MT ca1 = fftshift(fft(u1)); % Take Fourier transform
n>iPA D ca2 = fftshift(fft(u2));
+R*4`F:QJQ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
V&GFGds c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
* ~fN^{B'! u2 = ifft(fftshift(c2)); % Return to physical space
Up/1c:<J u1 = ifft(fftshift(c1));
k&^Megcb if rem(m1,J) == 0 % Save output every J steps.
-3KB:K< U1 = [U1 u1]; % put solutions in U array
q^12Rj;H U2=[U2 u2];
.# M 5L MN1=[MN1 m1];
h8S%Q|- z1=dz*MN1'; % output location
So! 1l7b end
E$Ge#
M@dM end
SuuWrt}5 hg=abs(U1').*abs(U1'); % for data write to excel
-=g`7^qa> ha=[z1 hg]; % for data write to excel
Jl5<9x t1=[0 t'];
rJNf&x%6 hh=[t1' ha']; % for data write to excel file
c#G(7. 0MU %dlmwrite('aa',hh,'\t'); % save data in the excel format
l~f +h?cF figure(1)
vTB*J,6. waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
9|#h )* figure(2)
EBebyQcon waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
d2(eX \56Z ]Q,RV EtKp 非线性超快脉冲耦合的数值方法的Matlab程序 cHR }`U$ a(}j n| 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。
d$Mj5wN:q Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Y,)9{T ";>D0h^D V=S`%1dLN r#{lpF,3Ib % This Matlab script file solves the nonlinear Schrodinger equations
/CZOO)n % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
dxASU|Yo9 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
[;X YT % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+)7NWR\ s&fU|Jk8 C=1;
Q'\j m=k M1=120, % integer for amplitude
!`aodz*PO M3=5000; % integer for length of coupler
`|PxEif+J N = 512; % Number of Fourier modes (Time domain sampling points)
4wNxn
lP dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Wx XVL" T =40; % length of time:T*T0.
mCq*@1Lp9 dt = T/N; % time step
6 a$% n = [-N/2:1:N/2-1]'; % Index
+_`F@^R_ t = n.*dt;
2QBtwlQ?[ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
tG#F7%+E w=2*pi*n./T;
tv;3~Y0i g1=-i*ww./2;
)p !dql K g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
7l:H~"9r g3=-i*ww./2;
ow`\7qr P1=0;
^Jkj /n' P2=0;
9xu&n%L= P3=1;
E+3~w?1 P=0;
GZ4{< QG for m1=1:M1
?2G^6>O ` p=0.032*m1; %input amplitude
rre;HJGEL s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
1 9)78kV{ s1=s10;
C8{CKrVE s20=0.*s10; %input in waveguide 2
C6, B qlio s30=0.*s10; %input in waveguide 3
;M JM~\L0 s2=s20;
K}$PI W s3=s30;
%%DK?{jo` p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
~S=hxKI %energy in waveguide 1
Sa<R8X' J p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
LLU>c]a %energy in waveguide 2
LpF6e9V\Wp p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
p ]a IMF_ %energy in waveguide 3
''WX for m3 = 1:1:M3 % Start space evolution
? j OpW1 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Y#N 'bvE|% s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
`[n e <F?e s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
v =W%|iZ sca1 = fftshift(fft(s1)); % Take Fourier transform
~MQN& sca2 = fftshift(fft(s2));
}M9'N%PU sca3 = fftshift(fft(s3));
I~mw\K{.3M sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
%?
iE3j!q sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
:Z+(H +lyZ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
e%f8|3<6 s3 = ifft(fftshift(sc3));
iu :e> r s2 = ifft(fftshift(sc2)); % Return to physical space
+~[19'GH s1 = ifft(fftshift(sc1));
CiMN J end
eq/s8]uM p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
}u|0 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
3Y r p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
x t-;7 P1=[P1 p1/p10];
+
6}FUi!"e P2=[P2 p2/p10];
Fm2t:,= P3=[P3 p3/p10];
koie P=[P p*p];
,Y&kW'2 end
ZERd#7@m+ figure(1)
Dbtw>:= plot(P,P1, P,P2, P,P3);
lca.(3u ]9x30UXLwD 转自：
http://blog.163.com/opto_wang/
