计算脉冲在非线性耦合器中演化的Matlab 程序 (bXCc -wY6da*.W % This Matlab script file solves the coupled nonlinear Schrodinger equations of
ct/I85c@P % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Tu x~4W % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
j@9A!5<CCk % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<{'':/tXI HzW ZQ6o %fid=fopen('e21.dat','w');
==$Ox6. N = 128; % Number of Fourier modes (Time domain sampling points)
%bddR;c M1 =3000; % Total number of space steps
KxY|:-"Tt J =100; % Steps between output of space
fz:F*zT1 T =10; % length of time windows:T*T0
ek.L(n,J| T0=0.1; % input pulse width
r8@:Ko= a MN1=0; % initial value for the space output location
2(UT;PSI dt = T/N; % time step
:qI myaGQ n = [-N/2:1:N/2-1]'; % Index
}O_6wi t = n.*dt;
m(9E{; u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
keX0br7u_ u20=u10.*0.0; % input to waveguide 2
ak<?Eu9rV u1=u10; u2=u20;
'?#e$<uS- U1 = u1;
K~[/n<ks U2 = u2; % Compute initial condition; save it in U
SMnbI .0 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Hd4&"oeY w=2*pi*n./T;
4H{L>e g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
o8bV z2E L=4; % length of evoluation to compare with S. Trillo's paper
+W-sb 5) dz=L/M1; % space step, make sure nonlinear<0.05
B~ z&
"` for m1 = 1:1:M1 % Start space evolution
X^"95I c u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
:I1bGa&I u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
r0_3 `; H ca1 = fftshift(fft(u1)); % Take Fourier transform
o6'`W 2P ca2 = fftshift(fft(u2));
&bTadd%0 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
ZQ@^(64 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
F+9|D u2 = ifft(fftshift(c2)); % Return to physical space
$lUZm\R|k u1 = ifft(fftshift(c1));
,VbP$1 t if rem(m1,J) == 0 % Save output every J steps.
Pf]L`haGN U1 = [U1 u1]; % put solutions in U array
KWM.b"WnXr U2=[U2 u2];
eml(F MN1=[MN1 m1];
`$Q
$l z1=dz*MN1'; % output location
nAg|m,gA end
8 DyE
end
M7UVL&_z% hg=abs(U1').*abs(U1'); % for data write to excel
, >e)8 ha=[z1 hg]; % for data write to excel
S__+S7]Nr t1=[0 t'];
*|MPYxJ< hh=[t1' ha']; % for data write to excel file
=U2`]50 %dlmwrite('aa',hh,'\t'); % save data in the excel format
vfmKY iLp figure(1)
v cq L waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
PJO +@+"{@ figure(2)
v;irk<5 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
c!E+&5|n R /iB 非线性超快脉冲耦合的数值方法的Matlab程序 =f?| f *S`&
X Pj 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
>|mmJ4T Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
J$@3,=L6V <{:$ ]3 Ig*!0(v5$ [Nsv]Yz % This Matlab script file solves the nonlinear Schrodinger equations
#*XuU8q? % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
]#K Z
W)M % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
J!~?}Fq/z % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
pv;}Sv$
]- D<C ZhYJ C=1;
(hs[B4nV M1=120, % integer for amplitude
(?;Fnq M3=5000; % integer for length of coupler
T ^% $ N = 512; % Number of Fourier modes (Time domain sampling points)
9 Iy>oV dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
|'Z6M];8t T =40; % length of time:T*T0.
e\tcP dt = T/N; % time step
44]/rP_m n = [-N/2:1:N/2-1]'; % Index
u 6$fF= t = n.*dt;
<Hig,(=`. ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9!}&&]Q` w=2*pi*n./T;
V1,O7m+F2 g1=-i*ww./2;
zH eqV g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
{H=DeQ g3=-i*ww./2;
Sc`W'q^X P1=0;
1s "6 P2=0;
#'_i6 P3=1;
] |@RWzA P=0;
"~> # ;x{ for m1=1:M1
'OK)[\ p=0.032*m1; %input amplitude
v= RQ"iv8 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
#0zMPh /U} s1=s10;
a}c .] zm] s20=0.*s10; %input in waveguide 2
? L|m:A` s30=0.*s10; %input in waveguide 3
LSs!U
3" s2=s20;
7 &DhEI ^ s3=s30;
Rbm"Qz p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
)u7y.o %energy in waveguide 1
$2~I-[ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
t6W$t %energy in waveguide 2
:RBp p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
p;,Cvw{.;% %energy in waveguide 3
2zZ" }Zr# for m3 = 1:1:M3 % Start space evolution
]_G!(`Udh s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
"d^h Y}Xx s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
3){ /u$iH. s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
/\q1,}M sca1 = fftshift(fft(s1)); % Take Fourier transform
]X ,f sca2 = fftshift(fft(s2));
{ =pRU_-^ sca3 = fftshift(fft(s3));
xxL D8?@e7 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
w)2X0ev" sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
(&np r96f sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
s G!SSRL@ s3 = ifft(fftshift(sc3));
xlg 6cO s2 = ifft(fftshift(sc2)); % Return to physical space
Y_ b;1R N s1 = ifft(fftshift(sc1));
E Z15 end
]>M{Q n* p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
fRS)YE@a: p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
XT~!dq5 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
F @~zVu3' P1=[P1 p1/p10];
38ChS.( P2=[P2 p2/p10];
yj13>"n h P3=[P3 p3/p10];
2y s'q ! P=[P p*p];
(U#4j 6Q end
;5urIYd figure(1)
v!{mpF plot(P,P1, P,P2, P,P3);
35|F?Jx.r U
bUl ] 转自：
http://blog.163.com/opto_wang/
