计算脉冲在非线性耦合器中演化的Matlab 程序 "97sH_
, Kd}%%L % This Matlab script file solves the coupled nonlinear Schrodinger equations of
be6`Sv"H % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
GWx?RIKF % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
LWo )x % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
D<Z\6)|%I MNfc1I_# %fid=fopen('e21.dat','w');
Mt4 `~`6 N = 128; % Number of Fourier modes (Time domain sampling points)
#;2kN
& M1 =3000; % Total number of space steps
6_EfOD9 J =100; % Steps between output of space
IFSIQ
q T =10; % length of time windows:T*T0
gd)VL}k T0=0.1; % input pulse width
d.sn D)X MN1=0; % initial value for the space output location
N,)rrBD dt = T/N; % time step
y_IF{%i n = [-N/2:1:N/2-1]'; % Index
i;2V t = n.*dt;
4YMUkwh u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Ud-c+, xX u20=u10.*0.0; % input to waveguide 2
Swv
=gu u1=u10; u2=u20;
m,J9:S<5; U1 = u1;
voN, u>U U2 = u2; % Compute initial condition; save it in U
-z/>W+k ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Dk~
JH9# w=2*pi*n./T;
`yXH b g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
K>+c2;t; L=4; % length of evoluation to compare with S. Trillo's paper
N8wA">u dz=L/M1; % space step, make sure nonlinear<0.05
o<S(ODOfi for m1 = 1:1:M1 % Start space evolution
Xp^71A? > u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Mc|UD*Z u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
:JxuaM8 ca1 = fftshift(fft(u1)); % Take Fourier transform
A*{V%7hs& ca2 = fftshift(fft(u2));
7*&q"
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
;;17 #T2 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
]T<RC\o u2 = ifft(fftshift(c2)); % Return to physical space
4!+ IsT u1 = ifft(fftshift(c1));
&-.2P! t if rem(m1,J) == 0 % Save output every J steps.
S#D6mg$Z, U1 = [U1 u1]; % put solutions in U array
jivGkIj!8 U2=[U2 u2];
y#{> tC MN1=[MN1 m1];
yzCamm4~0 z1=dz*MN1'; % output location
5DeAH ; end
"CQ:<$|$ end
p\|*ff0 hg=abs(U1').*abs(U1'); % for data write to excel
&C E){j C ha=[z1 hg]; % for data write to excel
bq}o#d5p-_ t1=[0 t'];
tw]Q5:6 hh=[t1' ha']; % for data write to excel file
fH
5/ %dlmwrite('aa',hh,'\t'); % save data in the excel format
_ AVP1 figure(1)
Pu]Pp `SP waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
H|!|fo-Tx figure(2)
o7@81QA!e waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
y}lqF8s ?F%,d{^ 非线性超快脉冲耦合的数值方法的Matlab程序 "M :0l Uy >^KO5N-:4 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。
tsTCZ);( 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
~d6zpQf7> $]]|#}J .37Jrh0Iv *1b)Va8v* % This Matlab script file solves the nonlinear Schrodinger equations
(f t$ R? % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
[[0u|`T/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
w'D =K_h % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
fnO>v/&B |`6*~ciUV C=1;
Ut^ {4_EC M1=120, % integer for amplitude
9r hl2E M3=5000; % integer for length of coupler
KdtQJ:_`k N = 512; % Number of Fourier modes (Time domain sampling points)
-]~vE fq+T dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
D~JrO]mi T =40; % length of time:T*T0.
m&8'O\$ dt = T/N; % time step
EJ `"npU
n = [-N/2:1:N/2-1]'; % Index
/aD3E"Op t = n.*dt;
L YyOcb[x ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
OuF%!~V w=2*pi*n./T;
s8 0$ g1=-i*ww./2;
q*4=sf,> g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
dJD8c 2G g3=-i*ww./2;
x.~A vJ P1=0;
hE>%LcP P2=0;
\$[S=&E P3=1;
-mK;f$X P=0;
CQm (N for m1=1:M1
jpek=4E p=0.032*m1; %input amplitude
K.K=\
Y2 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
aqzIMOAf s1=s10;
u3ns-e s20=0.*s10; %input in waveguide 2
e 2l !L*[g s30=0.*s10; %input in waveguide 3
W #kOcw s2=s20;
V
t@] s3=s30;
S
7 *LV; p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
m_g2 Cep %energy in waveguide 1
tjTnFP/= p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
(7_}UT@ w- %energy in waveguide 2
NvqIYW p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
wXnlu E %energy in waveguide 3
$@ (+"
$ for m3 = 1:1:M3 % Start space evolution
i j+)U` s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Q9h;`G
7t s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
I[v6Y^{q s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ny{Yr>:2 sca1 = fftshift(fft(s1)); % Take Fourier transform
NhYc e> sca2 = fftshift(fft(s2));
.~t.B!rVSB sca3 = fftshift(fft(s3));
U sS"WflB sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
%RS8zN sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
a08`h.dyN sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
soXIPf s3 = ifft(fftshift(sc3));
VuWBWb?0Q s2 = ifft(fftshift(sc2)); % Return to physical space
<@z!kl s1 = ifft(fftshift(sc1));
^>ICycJ end
85 GU~ . p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Y ZyV p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Q=~ *oYR p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
q71 ~Y:7f P1=[P1 p1/p10];
3"HW{= P2=[P2 p2/p10];
wYAi-gdOi P3=[P3 p3/p10];
A, ;V|jv9 P=[P p*p];
7uW=f kxT end
LW '3m 5 figure(1)
mW&hUP Rx plot(P,P1, P,P2, P,P3);
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u \7U'p:h=U 转自：
http://blog.163.com/opto_wang/
