计算脉冲在非线性耦合器中演化的Matlab 程序 =tU{7i*+ DI;DECQl$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
R1Ye<R!Q % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Iyo@r%I % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
u`(-
- % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
L}m8AAkP[ MC&\bf %fid=fopen('e21.dat','w');
Uje|`<X N = 128; % Number of Fourier modes (Time domain sampling points)
Zatf9yGD M1 =3000; % Total number of space steps
>q7BVF6V | J =100; % Steps between output of space
:pRpv hm T =10; % length of time windows:T*T0
Y4IGDY* T0=0.1; % input pulse width
A6oq.I0 MN1=0; % initial value for the space output location
}KD; 0t4 dt = T/N; % time step
b~BIz95 n = [-N/2:1:N/2-1]'; % Index
K 0hu:1l) t = n.*dt;
AfC>Q!-w u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
DKVT(#@T u20=u10.*0.0; % input to waveguide 2
>h+349 u1=u10; u2=u20;
f+.T^es U1 = u1;
OMk5{-8B U2 = u2; % Compute initial condition; save it in U
kw`WH)+F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
S^Au#1e
w=2*pi*n./T;
+wW@'X
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
B-d(@7,1 L=4; % length of evoluation to compare with S. Trillo's paper
RwVaZJe)l dz=L/M1; % space step, make sure nonlinear<0.05
*;|`E( for m1 = 1:1:M1 % Start space evolution
yFhB>i u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
_owjTo} u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
`c+/q2 M ca1 = fftshift(fft(u1)); % Take Fourier transform
umLb+GbI4 ca2 = fftshift(fft(u2));
%c)[
kAU! c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Yav2q3 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
h3gWOU u2 = ifft(fftshift(c2)); % Return to physical space
vKoP|z=m u1 = ifft(fftshift(c1));
#'4OYY. if rem(m1,J) == 0 % Save output every J steps.
_ q(Q U1 = [U1 u1]; % put solutions in U array
/=?ETth @ U2=[U2 u2];
Npn=cLC & MN1=[MN1 m1];
, %YBG1E[y z1=dz*MN1'; % output location
q8ImrC.'^ end
@ d"wAZzD? end
]S 7^ITn hg=abs(U1').*abs(U1'); % for data write to excel
k
n8N,,+
ha=[z1 hg]; % for data write to excel
I?Q+9Rmm`J t1=[0 t'];
^zEE6i hh=[t1' ha']; % for data write to excel file
Q)af|GW$ %dlmwrite('aa',hh,'\t'); % save data in the excel format
!G_ jGc=v figure(1)
oPKXZU(c waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
U/;]zdP.K figure(2)
amQz^^ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
%i)B*9k S'B6jJK2x 非线性超快脉冲耦合的数值方法的Matlab程序 hY<{t.ws x| eeRf| 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。
A>.2OC+ 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
@ tRMe6 4 d77r9 ,)~E>[=+ 6aOp[-Le % This Matlab script file solves the nonlinear Schrodinger equations
N]5m( @h
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
o oj iJ~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
bXM/2Z?6 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
=neL}Fav56 8cHE[I C=1;
u1K\@jlw M1=120, % integer for amplitude
p2x [p M3=5000; % integer for length of coupler
[FQ\I-GNC N = 512; % Number of Fourier modes (Time domain sampling points)
+pqM ^3t|y dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
=7
,Kf} 6 T =40; % length of time:T*T0.
;K: 8#XuV dt = T/N; % time step
> 8]j
n = [-N/2:1:N/2-1]'; % Index
`Iy4=nVb t = n.*dt;
u@%|k c ` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
;mAh Y w=2*pi*n./T;
]B9 ^3x[: g1=-i*ww./2;
b4,jN~ci g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
K'6[J"dB g3=-i*ww./2;
G% TL/Z40 P1=0;
GO5 ~!g P2=0;
m(sXk}e;1 P3=1;
JhR W[~ P=0;
,yLw$- for m1=1:M1
O2-M1sd$ p=0.032*m1; %input amplitude
)WR_
ug s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
EY>8O+ s1=s10;
9 -jO,l s20=0.*s10; %input in waveguide 2
e9u@`ZC07 s30=0.*s10; %input in waveguide 3
i gDyp0t s2=s20;
p* ;Qz s3=s30;
|;;!8VO3J p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
aW5~Be$
_ %energy in waveguide 1
m$ y]Lf p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
h5 @j`{ %energy in waveguide 2
ACBQ3 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
{w`:KR6o7 %energy in waveguide 3
#A <1aQ for m3 = 1:1:M3 % Start space evolution
J m e% s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
a5`eyL[f s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
4?]oV%aP) s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
QV,E #(\5 sca1 = fftshift(fft(s1)); % Take Fourier transform
zJ & b|L sca2 = fftshift(fft(s2));
^>r^3C)_- sca3 = fftshift(fft(s3));
r25Z`X Z sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
xDr V5bg sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
u39FN?<^ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
% ]Cjhs"v s3 = ifft(fftshift(sc3));
K%,$ V ,# s2 = ifft(fftshift(sc2)); % Return to physical space
/B HepD} s1 = ifft(fftshift(sc1));
~LE[,
I:q end
Z6=~1'< X p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
lg/sMF>z\f p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Rlc$; Z9K p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
K=kH%ZK P1=[P1 p1/p10];
{},;-%xE P2=[P2 p2/p10];
.1ddv4Hk P3=[P3 p3/p10];
B/YcSEY; P=[P p*p];
W L~`u end
DNth4 z figure(1)
By)3*<5 a_ plot(P,P1, P,P2, P,P3);
\5[-Ml <NQyP{p 转自：
http://blog.163.com/opto_wang/
