计算脉冲在非线性耦合器中演化的Matlab 程序 v Ni;)"&* _z p<en[ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
^^ q&VL % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
*%uz LW0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
2gWR2 H@ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
M)13'B. -TD\?Q %fid=fopen('e21.dat','w');
2V~E
<K - N = 128; % Number of Fourier modes (Time domain sampling points)
k(H&Af+ M1 =3000; % Total number of space steps
8Qi)E 1n J =100; % Steps between output of space
F:/x7]7??Z T =10; % length of time windows:T*T0
`%YMUBa I T0=0.1; % input pulse width
*eg0^ByeD MN1=0; % initial value for the space output location
st iF`l dt = T/N; % time step
loA/d n = [-N/2:1:N/2-1]'; % Index
tE %g )hL- t = n.*dt;
)at:Xm<s u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
&JX<)JEB=< u20=u10.*0.0; % input to waveguide 2
e EXNEgbn u1=u10; u2=u20;
|!FQQ(1b U1 = u1;
bo<P%$(D U2 = u2; % Compute initial condition; save it in U
,h=a+ja8 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
vom3 C9o w=2*pi*n./T;
4 ?Y7. :x g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
! aSj1
2J L=4; % length of evoluation to compare with S. Trillo's paper
:G>w MMv&z dz=L/M1; % space step, make sure nonlinear<0.05
'goKYl#1Q for m1 = 1:1:M1 % Start space evolution
yH( 'Vl u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
D>k(#vYKB u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
1j<uFhi > ca1 = fftshift(fft(u1)); % Take Fourier transform
D? #l8 ca2 = fftshift(fft(u2));
n*"r!&Dg c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
%GTFub0 F c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
' pgP QM< u2 = ifft(fftshift(c2)); % Return to physical space
='jT
5Mg u1 = ifft(fftshift(c1));
]AQ}_dRi= if rem(m1,J) == 0 % Save output every J steps.
JPn)Op6 U1 = [U1 u1]; % put solutions in U array
D\G .p |9= U2=[U2 u2];
PR5N:Bw
MN1=[MN1 m1];
,K[e?(RP z1=dz*MN1'; % output location
XB7*S*"! end
]y.V#,6e end
O*v&C Hd3 hg=abs(U1').*abs(U1'); % for data write to excel
k eC'/\e ha=[z1 hg]; % for data write to excel
-+{[.U<1jk t1=[0 t'];
"a].v 8l! hh=[t1' ha']; % for data write to excel file
Uj;JN}k %dlmwrite('aa',hh,'\t'); % save data in the excel format
:+6W%B figure(1)
=s!0EwDH3 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
wxqX4 2v figure(2)
0 aH&M4 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
^+Nd\t p @]q^O MLY 非线性超快脉冲耦合的数值方法的Matlab程序 8OZ asf 4/~x+tdc 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。
x?o#}:S 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
[ne51F5_ 4_5f4 %S 5@+?{Cl UB5H8&Rf! % This Matlab script file solves the nonlinear Schrodinger equations
W]/J]O6 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
w\s`8S % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
UH-873AK % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`$Rgn3 g
ptf*^s C=1;
! DOyOTR&3 M1=120, % integer for amplitude
J @:Q( M3=5000; % integer for length of coupler
KGM__Z O. N = 512; % Number of Fourier modes (Time domain sampling points)
d^A] ]Xg dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
BL 1KM2] T =40; % length of time:T*T0.
V5(_7b#z`` dt = T/N; % time step
`sqr>QD n = [-N/2:1:N/2-1]'; % Index
LH2B*8=^2 t = n.*dt;
iOg4(SPci ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
>fWGiFmlk w=2*pi*n./T;
5h/,*p6Nje g1=-i*ww./2;
J{b#X"i g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
w"?Q0bhV9y g3=-i*ww./2;
c +3`hVV P1=0;
ldUZ\z(* P2=0;
:41Y P3=1;
?)-6~p 4N P=0;
S?b&4\: for m1=1:M1
F}So=Jz9h p=0.032*m1; %input amplitude
c`;oV- f s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
: |s;2Y s1=s10;
)iw -l~y; s20=0.*s10; %input in waveguide 2
7JBs7L G s30=0.*s10; %input in waveguide 3
3XlQ 4 s2=s20;
Gw3+TvwU+Q s3=s30;
|1!fuB A p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
]%D!-[C%1 %energy in waveguide 1
Gt#r$.]W?o p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Q,5PscE6&k %energy in waveguide 2
>hNSEWMY` p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
<8 <P, %energy in waveguide 3
[T r7SU#x for m3 = 1:1:M3 % Start space evolution
8_!qoW@B s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Oh1U=V2~ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
qY8; k
# s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
P1[.[q/-e sca1 = fftshift(fft(s1)); % Take Fourier transform
2x<BU 3 sca2 = fftshift(fft(s2));
Xw9]WJc sca3 = fftshift(fft(s3));
u;$qJjS
N sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
_m?i$5 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
\@Cz 32wg sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
|.Vgk8oTl s3 = ifft(fftshift(sc3));
D Z*c.|W s2 = ifft(fftshift(sc2)); % Return to physical space
ThX3@o s1 = ifft(fftshift(sc1));
L;:PeYPL end
E|9`J00 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
>oq \`E p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
7fypUQ:y p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
]vf_ 4QW= P1=[P1 p1/p10];
DtBvfYO8)> P2=[P2 p2/p10];
!:\0}w$- P3=[P3 p3/p10];
q(~jP0pj% P=[P p*p];
-sv%A7i end
g0B-<> E figure(1)
0Md.3kY plot(P,P1, P,P2, P,P3);
C1 f$^N rE p\ld 转自：
http://blog.163.com/opto_wang/
