计算脉冲在非线性耦合器中演化的Matlab 程序 +'|nsIx, |:w)$i& * % This Matlab script file solves the coupled nonlinear Schrodinger equations of
$c {fPFe- % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
: X}n[K % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
vf5q8/a % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
B#DnU;=O#+ ${)oi:K@: %fid=fopen('e21.dat','w');
5 ) q_Aro N = 128; % Number of Fourier modes (Time domain sampling points)
xx@[ecW M1 =3000; % Total number of space steps
+ 7 0x0z2 J =100; % Steps between output of space
VUi> ]v/e T =10; % length of time windows:T*T0
eo*l^7 T0=0.1; % input pulse width
a]/KJn /B( MN1=0; % initial value for the space output location
B:Y F|k}T dt = T/N; % time step
e9R H [: n = [-N/2:1:N/2-1]'; % Index
jp;]dyU t = n.*dt;
B*(BsXQLY u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
b:5-0uxjs u20=u10.*0.0; % input to waveguide 2
u69UUkG u1=u10; u2=u20;
yJ/Y K U1 = u1;
jF@BWPtF= U2 = u2; % Compute initial condition; save it in U
< 1%}8t" ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
43 vF(<r&f w=2*pi*n./T;
XV}}A ^ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
%8H$6 2w] L=4; % length of evoluation to compare with S. Trillo's paper
9W0*|!tQ,+ dz=L/M1; % space step, make sure nonlinear<0.05
Lf)J O|o for m1 = 1:1:M1 % Start space evolution
M1]}yTCd u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
k;B [wEW@ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
;W T<] ca1 = fftshift(fft(u1)); % Take Fourier transform
C
:An ca2 = fftshift(fft(u2));
y/E:6 w c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
h'HI92; [ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
H:|.e)$i u2 = ifft(fftshift(c2)); % Return to physical space
0l3[?YtXc u1 = ifft(fftshift(c1));
%AN,cE* if rem(m1,J) == 0 % Save output every J steps.
OwT _W)$ U1 = [U1 u1]; % put solutions in U array
1>uAVPa U2=[U2 u2];
gnGh ) MN1=[MN1 m1];
H| _@9V z1=dz*MN1'; % output location
vV xw*\`<6 end
twu,yC ! end
x`c 7*q% hg=abs(U1').*abs(U1'); % for data write to excel
nU' qE ha=[z1 hg]; % for data write to excel
m _;fj~m t1=[0 t'];
0hhxTOp
hh=[t1' ha']; % for data write to excel file
-K lR":
%dlmwrite('aa',hh,'\t'); % save data in the excel format
{sf
,(.W figure(1)
-wrVEH8 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
R[14scV figure(2)
+;\w'dBi, waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
'}9 Nvr)+ RcO"k3J 非线性超快脉冲耦合的数值方法的Matlab程序 &XV9_{Hm (uDAdE5 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。
(3K3)0fy 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
N,Z*d oN[}i6^,e nw\C+1F o">~Ob R % This Matlab script file solves the nonlinear Schrodinger equations
' #yqw% % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
4Z>gK ( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
(6B ; % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
m I5J] hk \i/HHP[ % C=1;
4BUG\~eI3 M1=120, % integer for amplitude
}LC m_av M3=5000; % integer for length of coupler
!qp$Xtf+ N = 512; % Number of Fourier modes (Time domain sampling points)
9t U"+ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
:'B(DzUR T =40; % length of time:T*T0.
_7\`xU dt = T/N; % time step
_?:j Z1wZ n = [-N/2:1:N/2-1]'; % Index
P))BS t = n.*dt;
M 9-Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
'iF%mnJ w=2*pi*n./T;
Pc*lHo VL g1=-i*ww./2;
a7c`[ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
u4 IK7[= g3=-i*ww./2;
p @kRo#~l P1=0;
}2@Z{5sh) P2=0;
z
&X l P3=1;
f*<Vq:N=\ P=0;
-Uy)=]Zae for m1=1:M1
J}&U[ds p p=0.032*m1; %input amplitude
0uIY6e0E s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
)2RRa^=& s1=s10;
vRH^en s20=0.*s10; %input in waveguide 2
r&m49N,d s30=0.*s10; %input in waveguide 3
pJvPEKN s2=s20;
r@}`Sw]@ s3=s30;
ij!d-eM/b p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
_\KFMe= PV %energy in waveguide 1
` @
YV p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
gy%.+!4>v` %energy in waveguide 2
g kO^J{_@q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
2zqaR [C %energy in waveguide 3
>STth PO for m3 = 1:1:M3 % Start space evolution
`X5!s s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
)-_^vB s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
tu<<pR> s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
p~@,zetS sca1 = fftshift(fft(s1)); % Take Fourier transform
O_8 SlW0e sca2 = fftshift(fft(s2));
x)*Lu"> sca3 = fftshift(fft(s3));
aSvv(iV sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Nna.N U1 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
0t? o6 e sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
*0xL( s3 = ifft(fftshift(sc3));
: c~SH/qS s2 = ifft(fftshift(sc2)); % Return to physical space
5a izWz s1 = ifft(fftshift(sc1));
?VNtT/ end
sJ|pR=g)! p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
c 9f"5~ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
]B,tCBt p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
h40;Q<D P1=[P1 p1/p10];
Cu8mN B{H P2=[P2 p2/p10];
a$|U4Eqo P3=[P3 p3/p10];
p /-du^:2 P=[P p*p];
0TmEa59P end
n#g_)\ figure(1)
R>O_2`c plot(P,P1, P,P2, P,P3);
V?j,$LixY yuZLs H 转自：
http://blog.163.com/opto_wang/
