计算脉冲在非线性耦合器中演化的Matlab 程序 '(>N
gd[ 4f-C]N= % This Matlab script file solves the coupled nonlinear Schrodinger equations of
#Og_q$})f % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
sB!A: % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Q :|E % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
rvO+=Tk Bqgw %_ %fid=fopen('e21.dat','w');
cIkLdh N = 128; % Number of Fourier modes (Time domain sampling points)
UG$i5PV%i M1 =3000; % Total number of space steps
]F#kM21 1 J =100; % Steps between output of space
T^>cT"ux_ T =10; % length of time windows:T*T0
>s~`K^zS T0=0.1; % input pulse width
gE(03SX MN1=0; % initial value for the space output location
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76yz`D dt = T/N; % time step
$ OuA<- n = [-N/2:1:N/2-1]'; % Index
/n=/WGl t = n.*dt;
Z)0R$j`2 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
q[g^[~WM# u20=u10.*0.0; % input to waveguide 2
YJ`> &AJ u1=u10; u2=u20;
qQryv_QP U1 = u1;
2US8<sq+ U2 = u2; % Compute initial condition; save it in U
l6O(+*6Us ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<C(2( 3 w=2*pi*n./T;
r]{: { Z g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
;pq4El_ L=4; % length of evoluation to compare with S. Trillo's paper
S OJHw6 dz=L/M1; % space step, make sure nonlinear<0.05
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~ for m1 = 1:1:M1 % Start space evolution
:l{-UkbB u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
_uacpN/<| u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
vzPrG%Uu7g ca1 = fftshift(fft(u1)); % Take Fourier transform
%/p 5C ca2 = fftshift(fft(u2));
W'yICt(#G c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
ZN/" ) c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
BZsxf'eN' u2 = ifft(fftshift(c2)); % Return to physical space
'UCL? $ u1 = ifft(fftshift(c1));
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Y{_ if rem(m1,J) == 0 % Save output every J steps.
0jMrL\>C U1 = [U1 u1]; % put solutions in U array
K+H82$
# U2=[U2 u2];
:a2?K 5 MN1=[MN1 m1];
,0O!w>u_]J z1=dz*MN1'; % output location
kS>j!U(%d end
A,@"(3 end
&3M He$ hg=abs(U1').*abs(U1'); % for data write to excel
j\<S 6%p#R ha=[z1 hg]; % for data write to excel
z841g `:C t1=[0 t'];
R8_qZ;t:z hh=[t1' ha']; % for data write to excel file
q m_\#r %dlmwrite('aa',hh,'\t'); % save data in the excel format
.7q#{`K^= figure(1)
W%x#p s5% waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
`Jo}/c 5R figure(2)
-!" 8j"pA: waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
9i@*\Ada p V M;xxJ 非线性超快脉冲耦合的数值方法的Matlab程序 L'(^[vR( Oi RqqD 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。
G1BVI:A&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
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C xr@ uxBk7E%6 % This Matlab script file solves the nonlinear Schrodinger equations
e3.TGv7= % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
XT\;2etVL % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
H}X"yLog* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ZWv$K0agu xxYFW vi C=1;
ft5 Bk'ZJ M1=120, % integer for amplitude
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M3=5000; % integer for length of coupler
Ek:u[Uw\ N = 512; % Number of Fourier modes (Time domain sampling points)
#g q3 e dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
fw5AZvE6$ T =40; % length of time:T*T0.
gDH x+"? dt = T/N; % time step
??4QDa- n = [-N/2:1:N/2-1]'; % Index
iw%DQ }$ t = n.*dt;
CwAl -o ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
a^N/N5-Z w=2*pi*n./T;
G:UdU{ g1=-i*ww./2;
@<P [z[ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
GIp?}tM
g3=-i*ww./2;
IkupW|}rc P1=0;
m&2m' =( P2=0;
3WhJ,~o-y P3=1;
jU=)4nx P=0;
XHV+Y+VG for m1=1:M1
,v/C-b)I p=0.032*m1; %input amplitude
@Q'5/q+ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
3|C"F-'< s1=s10;
IQ\`n| s20=0.*s10; %input in waveguide 2
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l s30=0.*s10; %input in waveguide 3
j \SDw s2=s20;
yy 9 Bd> s3=s30;
`g #\ Ws p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
N24+P5 %energy in waveguide 1
i'' dY !2 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
4h|D [Cb] %energy in waveguide 2
3.>jagu p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
r`5;G4UI %energy in waveguide 3
s;A] GJ for m3 = 1:1:M3 % Start space evolution
@9^ kl$ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
`ul"D% s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
ym:JtI69 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
n_5g :`Y sca1 = fftshift(fft(s1)); % Take Fourier transform
PRs[:we~~ sca2 = fftshift(fft(s2));
; qvZ * sca3 = fftshift(fft(s3));
f+d{^- sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
371E S4 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
a-7nA sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Od"-w<' s3 = ifft(fftshift(sc3));
m^`X|xK- s2 = ifft(fftshift(sc2)); % Return to physical space
pt=[XhxC(> s1 = ifft(fftshift(sc1));
NKd):>d% end
RgEU TpX p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
uH`ds+Hp p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
kG%<5Q H p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
] TGJ|X P1=[P1 p1/p10];
}L@YLnc% P2=[P2 p2/p10];
bju0l[;= P3=[P3 p3/p10];
]RxNSr0e P=[P p*p];
,u $$w end
r,F'Jd5 figure(1)
l*h6 JgU plot(P,P1, P,P2, P,P3);
qoOHWh& IUzRE?Kzf 转自：
http://blog.163.com/opto_wang/
