计算脉冲在非线性耦合器中演化的Matlab 程序 -@7?N6~qZx t@X{qm:%Z % This Matlab script file solves the coupled nonlinear Schrodinger equations of
g'X{ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
K;8{qQ* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
79&=MTM
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]S0=&x@, uNKf!\Y %fid=fopen('e21.dat','w');
@LSfP N = 128; % Number of Fourier modes (Time domain sampling points)
"+XF'ZO M1 =3000; % Total number of space steps
oU l0w~Xn J =100; % Steps between output of space
g)dKXsy(F T =10; % length of time windows:T*T0
O0l1AX" T0=0.1; % input pulse width
q$7w?(Lk MN1=0; % initial value for the space output location
953GmNZ7 dt = T/N; % time step
!LR9}Xon n = [-N/2:1:N/2-1]'; % Index
>O]u4G! t = n.*dt;
*""iXi[ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
mX2X.ww(4 u20=u10.*0.0; % input to waveguide 2
V p$<@Y u1=u10; u2=u20;
}A}cq!I^ U1 = u1;
^O.` P U2 = u2; % Compute initial condition; save it in U
VwN=AFk
Oj ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
U|
T} 0 w=2*pi*n./T;
"]T1DG" g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Z-j?N{3& L=4; % length of evoluation to compare with S. Trillo's paper
-e\OF3 Td dz=L/M1; % space step, make sure nonlinear<0.05
' QSj- for m1 = 1:1:M1 % Start space evolution
~@#s<a,%; u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
GX+Gqj . u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
xLdkeuL[% ca1 = fftshift(fft(u1)); % Take Fourier transform
$~e55X'!+ ca2 = fftshift(fft(u2));
h[bC#( c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
g-pEt# c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
}wB!Bx2 u2 = ifft(fftshift(c2)); % Return to physical space
'2qbIYanh u1 = ifft(fftshift(c1));
r}:D g
fn if rem(m1,J) == 0 % Save output every J steps.
vs^) = U1 = [U1 u1]; % put solutions in U array
!k<k]^Z\ U2=[U2 u2];
ZU$Qw I8 MN1=[MN1 m1];
'/s/o]'sUd z1=dz*MN1'; % output location
|J"\~%8 end
e/uLBZ end
CZ!gu Y= hg=abs(U1').*abs(U1'); % for data write to excel
_WGWU7h ha=[z1 hg]; % for data write to excel
!q~f;&rg t1=[0 t'];
c8N pk< hh=[t1' ha']; % for data write to excel file
:IO"' b %dlmwrite('aa',hh,'\t'); % save data in the excel format
]n! oa figure(1)
\#v(f2j PF waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
+4n}H}9l figure(2)
$0cE iq?Hf waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
QYj*|p^x tl
9` 非线性超快脉冲耦合的数值方法的Matlab程序 %+((F +[ hWiHKR] 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
>uo=0=9= Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-k
}L W4 l1.eAs5U Z6zLL bZ#KfR % This Matlab script file solves the nonlinear Schrodinger equations
| .b&\ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
610u! _- % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
2uT@jfj:r % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
| 2G rOM&S pxI[/vS
N C=1;
M96Nt&P` M1=120, % integer for amplitude
24po}nrO M3=5000; % integer for length of coupler
P_P~c ~o N = 512; % Number of Fourier modes (Time domain sampling points)
= Qn8Y`U dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
r3Kx T =40; % length of time:T*T0.
)h]tKYx dt = T/N; % time step
sZwa#CQK q n = [-N/2:1:N/2-1]'; % Index
VVEJE$ t = n.*dt;
YkQ=rurE ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
)afH: w=2*pi*n./T;
S"fq E% g1=-i*ww./2;
E*yot[kj g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
_dc ,}C g3=-i*ww./2;
3t5W wrNh P1=0;
*l@T
9L[M' P2=0;
@.=2*e.z|b P3=1;
* c( J 4 P=0;
^Ge|tBMoKE for m1=1:M1
5>:p'zI p=0.032*m1; %input amplitude
P@<K&S+f s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
?'>[n m s1=s10;
Ko!a`I2M} s20=0.*s10; %input in waveguide 2
!95Q4WH-@ s30=0.*s10; %input in waveguide 3
#bb$Icmtk s2=s20;
'N&s$XB, s3=s30;
BA9;=orx p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Qqd +=mgc %energy in waveguide 1
}5d|y* p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
{;38& Izwz %energy in waveguide 2
Q@s G6 iz p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
m[w~h\FS %energy in waveguide 3
'h> l_A for m3 = 1:1:M3 % Start space evolution
[C3wjYi s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
}]pO R&o s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
L(/wsw~y*
s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
v){X&HbP sca1 = fftshift(fft(s1)); % Take Fourier transform
r3YfY \ sca2 = fftshift(fft(s2));
2bf#L?5g/ sca3 = fftshift(fft(s3));
m.U&O=] 5 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
`J}FSUn\ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
^Uldyv/ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
L @8[. s3 = ifft(fftshift(sc3));
.Pa6HA ! s2 = ifft(fftshift(sc2)); % Return to physical space
K14 {c1 s1 = ifft(fftshift(sc1));
%"3tGi : / end
i;#AW($+a p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
VKr
oikz@] p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
2!a~YT p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
tY?evsVgz P1=[P1 p1/p10];
{z# W- P2=[P2 p2/p10];
Z-i$KF P3=[P3 p3/p10];
>;X^+JH!) P=[P p*p];
Bs-MoT! end
U}W7[f lc figure(1)
8 =3$U+ plot(P,P1, P,P2, P,P3);
n(\VP!u5r (X Ql2C 转自：
http://blog.163.com/opto_wang/
