计算脉冲在非线性耦合器中演化的Matlab 程序 I A%ZCdA; r.q*S4IS.m % This Matlab script file solves the coupled nonlinear Schrodinger equations of
t zShds % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
;Rlf[](iL % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
(_%l[:o 6 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
x2,;ar\D J! Q #xs %fid=fopen('e21.dat','w');
0u;a*#V @ N = 128; % Number of Fourier modes (Time domain sampling points)
#iKPp0`K* M1 =3000; % Total number of space steps
})+iAxR J =100; % Steps between output of space
wz.. T =10; % length of time windows:T*T0
0q4P hxR`e T0=0.1; % input pulse width
.p =OAh< MN1=0; % initial value for the space output location
2`^6`` dt = T/N; % time step
P{L S +. n = [-N/2:1:N/2-1]'; % Index
+Wl]1
c/ t = n.*dt;
) &DsRA7v u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
8J#x B u20=u10.*0.0; % input to waveguide 2
p()q)P u1=u10; u2=u20;
* > /w,E] U1 = u1;
~:L5Ar< U2 = u2; % Compute initial condition; save it in U
@d5$OpL$% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ihJ!]#Fbm w=2*pi*n./T;
O> N/6Z g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
2TG2<wqvE L=4; % length of evoluation to compare with S. Trillo's paper
mGDy3R90 dz=L/M1; % space step, make sure nonlinear<0.05
Sp6==(:. for m1 = 1:1:M1 % Start space evolution
.]H/u
"d u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
<BIQc,)2} u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
kbL7Xjk ca1 = fftshift(fft(u1)); % Take Fourier transform
b<!' WpY- ca2 = fftshift(fft(u2));
\2!. c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
qnHjw Mi c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
sSf;j,7V u2 = ifft(fftshift(c2)); % Return to physical space
T6b~uE u1 = ifft(fftshift(c1));
lN&+<>a if rem(m1,J) == 0 % Save output every J steps.
,PoG=W
U1 = [U1 u1]; % put solutions in U array
|"PS e~ u U2=[U2 u2];
$EHF f $M MN1=[MN1 m1];
? H!jKX z1=dz*MN1'; % output location
s2( 7z9jR end
H |
C3{9 end
/0cm7[a ? hg=abs(U1').*abs(U1'); % for data write to excel
_M&n~ r ha=[z1 hg]; % for data write to excel
n*ROlCxV t1=[0 t'];
mU(v9Jpf7 hh=[t1' ha']; % for data write to excel file
z;?ztpa@ %dlmwrite('aa',hh,'\t'); % save data in the excel format
)3A+Ell` figure(1)
E2 FnC}#W waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
'%ByFZ zi figure(2)
<& 3[|Ca waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Y} xM&% r@zs4N0WP 非线性超快脉冲耦合的数值方法的Matlab程序 Zn0 a)VH%
uF|Up]Z G 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
Tay$::V 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
(f^/KB= t^Lb}A# $4 q sUBvq #6
ni~d&0 % This Matlab script file solves the nonlinear Schrodinger equations
O8A(OfX % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
&^K(9 " % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
#'},/Lm@ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
=>l X brJ Nmd{C(^o C=1;
@ ;@ ~ =w M1=120, % integer for amplitude
S(U9Dlyarg M3=5000; % integer for length of coupler
j'Jb+@W? N = 512; % Number of Fourier modes (Time domain sampling points)
YD@Z}NE
v" dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
`mW~ {)x T =40; % length of time:T*T0.
~NPhVlT dt = T/N; % time step
e v0>j4Q n = [-N/2:1:N/2-1]'; % Index
IA&V?{OE@I t = n.*dt;
qdy(C^(fa ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
$m~&| s w=2*pi*n./T;
T{^ P g1=-i*ww./2;
"wcw`TsK g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
',!jYh}Uxk g3=-i*ww./2;
pH.&C 5kA P1=0;
d>mT+{3 P2=0;
PNd'21N P3=1;
@)0 P=0;
Qe7=6< for m1=1:M1
-"S94<Y p=0.032*m1; %input amplitude
h)fsLzn]Tf s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
y$bY
8L s1=s10;
Q"U%]2@= s20=0.*s10; %input in waveguide 2
fVgN8b|&' s30=0.*s10; %input in waveguide 3
]cv|d c= s2=s20;
F-b]>3r s3=s30;
wkPj MmW+! p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
9_d# F'#F %energy in waveguide 1
f8SO:ihXL p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
]" e'z %energy in waveguide 2
cr<j<#(Z} p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
^&C/,,U %energy in waveguide 3
^n<YO=|u for m3 = 1:1:M3 % Start space evolution
ZA. S X|m s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
C se`MP s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
fMUh\u3 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
u=qaz7E sca1 = fftshift(fft(s1)); % Take Fourier transform
rr2 !H%: sca2 = fftshift(fft(s2));
6it
[i@*" sca3 = fftshift(fft(s3));
[<{r~YFjWW sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
NOwd'iU sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
9G2 rV k sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
q2J |koT s3 = ifft(fftshift(sc3));
Q0 Do B s2 = ifft(fftshift(sc2)); % Return to physical space
;,6C&|n]w s1 = ifft(fftshift(sc1));
Dn J `]r end
y\uBVa<B p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
8f[ztT0`g p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
G1w$lc p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
!w Q?+ :6 P1=[P1 p1/p10];
QEbf]U= P2=[P2 p2/p10];
7S
8X) P3=[P3 p3/p10];
]UEA"^ P=[P p*p];
gED|2%BXb end
-C(Yl= figure(1)
_EP]|DTfr plot(P,P1, P,P2, P,P3);
`JDZR:bMaT <XG]aYBR 转自：
http://blog.163.com/opto_wang/
