计算脉冲在非线性耦合器中演化的Matlab 程序 N#] ypl y }
'@R$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
TvM~y \s % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
"tZe>> I % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
m'U0'}Ld}; % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+t.b` U`- IBGrt^$M %fid=fopen('e21.dat','w');
cK@wsA^4 N = 128; % Number of Fourier modes (Time domain sampling points)
54,er$$V M1 =3000; % Total number of space steps
xk5 ]^yDp J =100; % Steps between output of space
bD^o wa T =10; % length of time windows:T*T0
}vuARZ> T0=0.1; % input pulse width
Y2TtY ; MN1=0; % initial value for the space output location
:0/ 7, i dt = T/N; % time step
qK+5 NF| n = [-N/2:1:N/2-1]'; % Index
b>W %t t = n.*dt;
sKWfX Cd u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
i%/+5gq u20=u10.*0.0; % input to waveguide 2
/ FII07V u1=u10; u2=u20;
FmW(CGs U1 = u1;
[^)g%|W U2 = u2; % Compute initial condition; save it in U
(:_$5&i7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
NbobliC= w=2*pi*n./T;
v19-./H^
j g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
3Vwh|1? L=4; % length of evoluation to compare with S. Trillo's paper
(Z*!#}z` dz=L/M1; % space step, make sure nonlinear<0.05
#E?4E1 bnB for m1 = 1:1:M1 % Start space evolution
s iaG'%@*r u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
' QG?nu u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
`uFdwO'DD ca1 = fftshift(fft(u1)); % Take Fourier transform
<%d>v-=B ca2 = fftshift(fft(u2));
HQ g^
h c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
^~dWU> c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
[
3Gf2_ u2 = ifft(fftshift(c2)); % Return to physical space
b
6p|q_e u1 = ifft(fftshift(c1));
ig!+2g if rem(m1,J) == 0 % Save output every J steps.
g-A-kqo9 U1 = [U1 u1]; % put solutions in U array
0f/<7R U2=[U2 u2];
KXy6 Eno MN1=[MN1 m1];
*hx z1=dz*MN1'; % output location
<} .$l end
D- c4EV end
]lbuy7xj63 hg=abs(U1').*abs(U1'); % for data write to excel
8y L Y ha=[z1 hg]; % for data write to excel
Z r8*et t1=[0 t'];
F847pyOJnf hh=[t1' ha']; % for data write to excel file
&&+H+{_Q %dlmwrite('aa',hh,'\t'); % save data in the excel format
s*[bFJwN figure(1)
53 D ]3 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
x4 yR8n( figure(2)
\<' ?8ri# waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
*g%yRU{N >j/w@Fj 非线性超快脉冲耦合的数值方法的Matlab程序 paK2 xX8E o4X{L`m 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。
'NmRR]Q9 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
6'/ #+,d' khe}*y NOv a'qk gJXaPJA{ % This Matlab script file solves the nonlinear Schrodinger equations
DI>s-7 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
29Ki uP % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;`&kZi60Hz % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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k /` py4 h(04u C=1;
WcAkCH!L M1=120, % integer for amplitude
b;n[mk
M3=5000; % integer for length of coupler
xp t:BB o N = 512; % Number of Fourier modes (Time domain sampling points)
Cr Lrw T dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
HtFD lvdy] T =40; % length of time:T*T0.
DVA:Cmh\ dt = T/N; % time step
;+%rw 2Z,B n = [-N/2:1:N/2-1]'; % Index
icgfB-1|i t = n.*dt;
O-^Ma- } ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
z_HdISy0 w=2*pi*n./T;
HfVZ~P P g1=-i*ww./2;
CTb%(<r g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
L,\Iasv g3=-i*ww./2;
q m}@!z^ P1=0;
A"]YM'. P2=0;
&Jj<h: * P3=1;
@C$]//; P=0;
>7| VR:U?B for m1=1:M1
-f .,tM= p=0.032*m1; %input amplitude
7dWS s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
K0~rN.C!0 s1=s10;
Hs8>anVo[ s20=0.*s10; %input in waveguide 2
j%kncGS s30=0.*s10; %input in waveguide 3
Nb\4 /;# s2=s20;
8tL~FiHb" s3=s30;
By |4 m p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
]gOy(\B %energy in waveguide 1
aN?zmkPpov p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
'L'R9&o<X %energy in waveguide 2
<I? Zk80 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
]Z e1s02( %energy in waveguide 3
zCZf%ATq for m3 = 1:1:M3 % Start space evolution
$FV NCFN% s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
I9Xuok!0>= s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
vsPu*[% s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
@ JMiO^ sca1 = fftshift(fft(s1)); % Take Fourier transform
lA]8&+,ZM sca2 = fftshift(fft(s2));
{) XTk &" sca3 = fftshift(fft(s3));
?s01@f# sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
afV T~Sf{ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
';CNGv - sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
K+eM s3 = ifft(fftshift(sc3));
L *wYx| s2 = ifft(fftshift(sc2)); % Return to physical space
t Q)qCk07 s1 = ifft(fftshift(sc1));
ftb\0,- end
pi(m7Ci" p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
|Cv!, ]9:r p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
@d'j zs p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
p K*TE5] P1=[P1 p1/p10];
r!v\"6:OM P2=[P2 p2/p10];
(PL UFT P3=[P3 p3/p10];
6K^ #?Bn; P=[P p*p];
wk^B"+Uhy end
#a#F,ZT figure(1)
w )f#V s plot(P,P1, P,P2, P,P3);
Jy)/%p~ sJZ iI}Xc 转自：
http://blog.163.com/opto_wang/
