计算脉冲在非线性耦合器中演化的Matlab 程序 Yn+d!w<3: /Y_)dz^ @ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
w;=g$Bn % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
l'm\ *=3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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RmKN % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Z6\H4,k& q1_iV.G< %fid=fopen('e21.dat','w');
appWq}db N = 128; % Number of Fourier modes (Time domain sampling points)
M:/)| fk M1 =3000; % Total number of space steps
ih\=mB J =100; % Steps between output of space
gi #g)9HG T =10; % length of time windows:T*T0
DYej<T'?3 T0=0.1; % input pulse width
`"RT(` m MN1=0; % initial value for the space output location
"x~su?KiA dt = T/N; % time step
b2vCr F; n = [-N/2:1:N/2-1]'; % Index
~[ZRE @ t = n.*dt;
.tQeOZW' u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
glI4Jb_[ u20=u10.*0.0; % input to waveguide 2
=4_Er{AT u1=u10; u2=u20;
H$4 4,8,m U1 = u1;
W^8Ms dM U2 = u2; % Compute initial condition; save it in U
!L?diR ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
jn,_Ncd# w=2*pi*n./T;
W^" C|4G } g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
K}a3Bj, L=4; % length of evoluation to compare with S. Trillo's paper
AdGDs+at, dz=L/M1; % space step, make sure nonlinear<0.05
l)K8.(2 for m1 = 1:1:M1 % Start space evolution
Z#znA4;) u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
fMl uVND u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
+DwE~l ca1 = fftshift(fft(u1)); % Take Fourier transform
/k H
7I ca2 = fftshift(fft(u2));
1ww#]p`1 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
J2av t c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
5 !jU i9 u2 = ifft(fftshift(c2)); % Return to physical space
0hv}*NYd u1 = ifft(fftshift(c1));
a,`f`;\7N% if rem(m1,J) == 0 % Save output every J steps.
D\0 q lCAs U1 = [U1 u1]; % put solutions in U array
ZgI ?#e U2=[U2 u2];
?&_u$Nn MN1=[MN1 m1];
R^k)^!/ $f z1=dz*MN1'; % output location
Wz&[ cj end
9?38 /2kX4 end
&qMt07 hg=abs(U1').*abs(U1'); % for data write to excel
d]r?mnN W ha=[z1 hg]; % for data write to excel
.u3Z*+ t1=[0 t'];
y *7 {S{9 hh=[t1' ha']; % for data write to excel file
<Gw>}/-^ %dlmwrite('aa',hh,'\t'); % save data in the excel format
/L^pU-}Z0 figure(1)
0i4XS*vPv waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
'4e,
e|r figure(2)
H{U(Rt]K waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
kkU#0p? 7 5KgAY;| 非线性超快脉冲耦合的数值方法的Matlab程序 z{wZLqG q#_<J1) z 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
,* m{Q Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
mV++7DY PFI^+'; H84Zg/ ^ b-?d(- % This Matlab script file solves the nonlinear Schrodinger equations
}F4%5go % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
K)N'~jCG % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
B1 Y
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
:zp9L/eh rk8Ce a C=1;
9r=yfc!cS M1=120, % integer for amplitude
vB Vg/ M3=5000; % integer for length of coupler
Zt
;u8O N = 512; % Number of Fourier modes (Time domain sampling points)
z*e`2n#\ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
DDBf89$\ T =40; % length of time:T*T0.
XE($t2x,M dt = T/N; % time step
0WQ d#l n = [-N/2:1:N/2-1]'; % Index
}ki6(_ t = n.*dt;
K_Gq M9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
( q}{ ; w=2*pi*n./T;
zT+ "Z(oz, g1=-i*ww./2;
s)~Wcp'+M: g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
AB=Wj*f r g3=-i*ww./2;
-GODM128 ^ P1=0;
mt\pndTy7! P2=0;
WCy jp P3=1;
@ S)p{T5G P=0;
w~ O)DhC for m1=1:M1
bltZQI| p=0.032*m1; %input amplitude
XM~eocn s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
ge|Cv v s1=s10;
CF]#0*MI s20=0.*s10; %input in waveguide 2
FV\$M6
_ s30=0.*s10; %input in waveguide 3
) ^ 7- qy s2=s20;
3(3-#MD0 s3=s30;
F0KNkL>&g p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
8d[!"lL %energy in waveguide 1
}WnoI2 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
g `I$U%a_2 %energy in waveguide 2
KvmXRf*z p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
%`0*KMO3
%energy in waveguide 3
gr \vC for m3 = 1:1:M3 % Start space evolution
q DPl( WXb s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
qdxDR
2]U s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
suE#'0K s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
* TByAa{ sca1 = fftshift(fft(s1)); % Take Fourier transform
?P"j5 sca2 = fftshift(fft(s2));
1O+$" 5H sca3 = fftshift(fft(s3));
j$Vtd & sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
^w*&7.Z sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
N 4w&g- sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
)F m'i&F_ s3 = ifft(fftshift(sc3));
d=/a{lP\ s2 = ifft(fftshift(sc2)); % Return to physical space
yX1OJg[s, s1 = ifft(fftshift(sc1));
cB_ 3~=fV end
lin p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
qkD9xFp p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Ns6C xE9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
ALt^@|!d P1=[P1 p1/p10];
XL`i9kV? P2=[P2 p2/p10];
S#l)|c_~ P3=[P3 p3/p10];
AME<V-5 P=[P p*p];
b X4]/4% end
Idr|-s%l6' figure(1)
eb7~\|9l1i plot(P,P1, P,P2, P,P3);
0pA> w8 mh Y |L]# 转自：
http://blog.163.com/opto_wang/
