计算脉冲在非线性耦合器中演化的Matlab 程序 vjzG
H* & >!- 67 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
gA`QV''/: % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
T^F83Py< % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
z9!OzGtIR % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
CH #K0hi G`;\"9t 5h %fid=fopen('e21.dat','w');
]j !pK4 N = 128; % Number of Fourier modes (Time domain sampling points)
l3*GQ~m7 M1 =3000; % Total number of space steps
:`4F0 J =100; % Steps between output of space
~MP |L?my T =10; % length of time windows:T*T0
artn _ T0=0.1; % input pulse width
,!, tU7-H MN1=0; % initial value for the space output location
l,~`o$ _ dt = T/N; % time step
:+
mULUi n = [-N/2:1:N/2-1]'; % Index
bT6VxbNS t = n.*dt;
t(dVd% u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
V;W{pd-I u20=u10.*0.0; % input to waveguide 2
@ q`T#vd u1=u10; u2=u20;
<5^m`F5 U1 = u1;
`!spi=f U2 = u2; % Compute initial condition; save it in U
|Y8}*C\M.h ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
5F!Qn\{u{ w=2*pi*n./T;
w3 kkam" g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
R(*t 1R\ L=4; % length of evoluation to compare with S. Trillo's paper
[Y~~C J dz=L/M1; % space step, make sure nonlinear<0.05
4"H * hKp for m1 = 1:1:M1 % Start space evolution
m"-kkH{I u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
{bADMj1 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
PU[<s r#, ca1 = fftshift(fft(u1)); % Take Fourier transform
pF7N = mO ca2 = fftshift(fft(u2));
Aix6O=K6 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
= p2AK\ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
ir )~T0 u2 = ifft(fftshift(c2)); % Return to physical space
]ao%9:P; u1 = ifft(fftshift(c1));
+{ e2TY if rem(m1,J) == 0 % Save output every J steps.
NTM.Vj
-_h U1 = [U1 u1]; % put solutions in U array
` NvJ U2=[U2 u2];
H8qAj MN1=[MN1 m1];
@q" #.?>s z1=dz*MN1'; % output location
=WFG[~8 end
1NlpOVq:) end
#k)J);&ZA hg=abs(U1').*abs(U1'); % for data write to excel
c30 kb ha=[z1 hg]; % for data write to excel
@2A&eLw LH t1=[0 t'];
(T GG?V hh=[t1' ha']; % for data write to excel file
V elX+|w %dlmwrite('aa',hh,'\t'); % save data in the excel format
R jR figure(1)
2 mvp|< " waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
:?gk =JH: figure(2)
euh rEjwkH waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
`~W ?a ^w}BXVn 非线性超快脉冲耦合的数值方法的Matlab程序 { r8H5X a*@4W3;7 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。
n<7R6)j6 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
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A,|lDsvM $k3l[@;hE % This Matlab script file solves the nonlinear Schrodinger equations
RZKczZGZg % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
^pa -2Ao6 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
..ht)Gex % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
7;:Uv= KA0_uty/T C=1;
a
s?)6 M1=120, % integer for amplitude
DKf: 0E8 M3=5000; % integer for length of coupler
ZNbb8v N = 512; % Number of Fourier modes (Time domain sampling points)
iX'#~eK*< dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
1|\/2 T =40; % length of time:T*T0.
mOi 8W,2 dt = T/N; % time step
6~6*(s|]A n = [-N/2:1:N/2-1]'; % Index
1:iT#~n t = n.*dt;
o4pe>hn ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
wS1zd? w=2*pi*n./T;
ob.=QQQs
g1=-i*ww./2;
!+I!J
s" g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
!@-g9z g3=-i*ww./2;
$T80vEi+u P1=0;
T]Eg9Y:+v P2=0;
6>B_ojj: P3=1;
|d8x55dk P=0;
;7 Y4 v`m for m1=1:M1
R k).D 6 p=0.032*m1; %input amplitude
UDz#?ZWnd s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
| sio:QP s1=s10;
d$` N Apr s20=0.*s10; %input in waveguide 2
t<2B3&o1 s30=0.*s10; %input in waveguide 3
!G3d5d2)C s2=s20;
9W <I~ s3=s30;
}EZd=_kAq~ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Z6 `[ dAo %energy in waveguide 1
PKM8MYvo p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
564)ha/^( %energy in waveguide 2
1tQl^ >r16 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
IvyBK]{| %energy in waveguide 3
x:)8+Rn} for m3 = 1:1:M3 % Start space evolution
Xy(o0/7F9 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
zLiFk<G@Xi s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
n++L
=&Wd s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
dLMKfh/4Q sca1 = fftshift(fft(s1)); % Take Fourier transform
qEo a%O sca2 = fftshift(fft(s2));
@ukI t sca3 = fftshift(fft(s3));
3o=K?eOdg sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
.UuCTH;6` sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
IPhV|7 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
,1+)qv#|i s3 = ifft(fftshift(sc3));
o4"7i 9+g s2 = ifft(fftshift(sc2)); % Return to physical space
>f$>Odqe s1 = ifft(fftshift(sc1));
T~rPpi& end
C"P40VQoo p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
BM&.Tw|x p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
3i'L5f67 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
f|f9[h' P1=[P1 p1/p10];
*3A[C-1~. P2=[P2 p2/p10];
lklMdsIdj P3=[P3 p3/p10];
,5_Hen=PI P=[P p*p];
S=o1k end
=hO0 @w figure(1)
RTW4r9~' plot(P,P1, P,P2, P,P3);
&K_"5.7-56 $=iV)- 转自：
http://blog.163.com/opto_wang/
