计算脉冲在非线性耦合器中演化的Matlab 程序 Xyz/CZPi c*R\fQd % This Matlab script file solves the coupled nonlinear Schrodinger equations of
# Rs5W % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
M djxTr^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
muK.x7zyl % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
!lZ }kz0
noB8*n0 %fid=fopen('e21.dat','w');
&oZU=CN N = 128; % Number of Fourier modes (Time domain sampling points)
h^,L ) E M1 =3000; % Total number of space steps
o7PS1qcya< J =100; % Steps between output of space
\ j.l1O T =10; % length of time windows:T*T0
>lJTS t5{ T0=0.1; % input pulse width
K0I.3| 6C MN1=0; % initial value for the space output location
f\R TO63|O dt = T/N; % time step
d mT ZEO n = [-N/2:1:N/2-1]'; % Index
?-0, x|ul t = n.*dt;
96; gzG@1! u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
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F) u20=u10.*0.0; % input to waveguide 2
@S5HMJ2= u1=u10; u2=u20;
#l9sQ-1Q U1 = u1;
Bw+ ?MdS U2 = u2; % Compute initial condition; save it in U
tU!Yg "4Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
4OAR ["f w=2*pi*n./T;
XW2ZQMos1 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
23'<R i L=4; % length of evoluation to compare with S. Trillo's paper
"|,KXv') dz=L/M1; % space step, make sure nonlinear<0.05
1BP/,d |+ for m1 = 1:1:M1 % Start space evolution
^ e $!19g u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
v7hw % 9(= u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
LU @1Gol ca1 = fftshift(fft(u1)); % Take Fourier transform
M*Q}^<E* ca2 = fftshift(fft(u2));
k#/cdK!K c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
1TGE>HG c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Vvfd?G" u2 = ifft(fftshift(c2)); % Return to physical space
#IDLfQ5g u1 = ifft(fftshift(c1));
gg#lI| if rem(m1,J) == 0 % Save output every J steps.
tt6GtYrC 1 U1 = [U1 u1]; % put solutions in U array
<{YzmN\Z U2=[U2 u2];
2BT+[ MN1=[MN1 m1];
]!jfrj z1=dz*MN1'; % output location
DqmKD U end
B"5x s end
sK/ymEfRv hg=abs(U1').*abs(U1'); % for data write to excel
V_n tS& 2o ha=[z1 hg]; % for data write to excel
cT&lkS t1=[0 t'];
YuJ{@"H hh=[t1' ha']; % for data write to excel file
1M55!b %dlmwrite('aa',hh,'\t'); % save data in the excel format
{F\P3-ub figure(1)
6p3cMJ'8y waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
,":_ CY4( figure(2)
*xj2Z,u waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
7A$mZPKh q['3M <q 非线性超快脉冲耦合的数值方法的Matlab程序 zF? 6" 6o(.zk`d 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。
<F-IF7>a 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
B| M@o^Tf Dk2Z l jJ 'NYG X%B$*y5 % This Matlab script file solves the nonlinear Schrodinger equations
?=-/5A4K % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
x'6i9]+r % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
bwszfPM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
W ?ghG W(-son~I C=1;
y~M 6 M1=120, % integer for amplitude
vkG%w ; M3=5000; % integer for length of coupler
^4Se=Hr
z2 N = 512; % Number of Fourier modes (Time domain sampling points)
$DnR[V}rR! dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
$? [pcgv T =40; % length of time:T*T0.
&arJe !K dt = T/N; % time step
,K PrUM} n = [-N/2:1:N/2-1]'; % Index
_t4(H))]vG t = n.*dt;
;l < amB ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
hD, |CQ w=2*pi*n./T;
PB BJ.!Pb g1=-i*ww./2;
e~R_ bBQ0 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
n%02,pC6, g3=-i*ww./2;
BXz g33 P1=0;
Y Ov hMi P2=0;
+<B"g{dLuX P3=1;
R 4DfqX P=0;
A\E ))b 9+ for m1=1:M1
;Cty"H, p=0.032*m1; %input amplitude
?UeV5<TewS s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
dAOJ:
@y s1=s10;
g2u\gR5 s20=0.*s10; %input in waveguide 2
OW! y7 s30=0.*s10; %input in waveguide 3
cqm:[0Xf5> s2=s20;
|X6R 2I s3=s30;
,WW=,P p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
K,*z8@ %energy in waveguide 1
e9QjRx p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
]Qp-$)N %energy in waveguide 2
]<Q& p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
EEx:Xk%5hX %energy in waveguide 3
2l:cP2 fa for m3 = 1:1:M3 % Start space evolution
[l<&eI&ln s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
K(Tej W# s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
p ^ OHLT s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
5rQu^6& sca1 = fftshift(fft(s1)); % Take Fourier transform
VT#`l0I } sca2 = fftshift(fft(s2));
xv%]g= Q sca3 = fftshift(fft(s3));
+u&3pK>f sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
gieso f sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
C!6D /S sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
{/48n83n s3 = ifft(fftshift(sc3));
@zLyG#kHY s2 = ifft(fftshift(sc2)); % Return to physical space
n5tsaU; s1 = ifft(fftshift(sc1));
~Ra8(KocD end
Fp]ErDan p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
?pa pk4w p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
oMoco tQ;$ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Y'+K U/H P1=[P1 p1/p10];
` /B+ P2=[P2 p2/p10];
-q? , P3=[P3 p3/p10];
HT m`_}G9 P=[P p*p];
| U $ "GI end
|PGT P#O< figure(1)
2gEF$?+q? plot(P,P1, P,P2, P,P3);
Tv~Ho&LS ?_T[ ]I' 转自：
http://blog.163.com/opto_wang/
