计算脉冲在非线性耦合器中演化的Matlab 程序 n ]< >$ 2l.qINyz % This Matlab script file solves the coupled nonlinear Schrodinger equations of
~/R bYvyA % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
mNDd>4%H_ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
C8bB OC( % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
J;#7dRW{ H]<@\g*l@P %fid=fopen('e21.dat','w');
N_Q\+x}zq N = 128; % Number of Fourier modes (Time domain sampling points)
c>)_ I M1 =3000; % Total number of space steps
}}q_QD_ J =100; % Steps between output of space
B4kJ 7Pdny T =10; % length of time windows:T*T0
DRy,n)U& T0=0.1; % input pulse width
hTS?+l MN1=0; % initial value for the space output location
8;q2W
F{AX dt = T/N; % time step
Gi 7p`F. n = [-N/2:1:N/2-1]'; % Index
RKtU@MX49 t = n.*dt;
vNIQ1x5Za u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
b!gvvg< u20=u10.*0.0; % input to waveguide 2
+m]Kj3-z@ u1=u10; u2=u20;
qP4v H] U1 = u1;
=&-+ {txs U2 = u2; % Compute initial condition; save it in U
NA-)7i*>J ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
3OvQ,^[J4 w=2*pi*n./T;
IM 8lA g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
aS)Gj?Odf L=4; % length of evoluation to compare with S. Trillo's paper
-8pQI dz=L/M1; % space step, make sure nonlinear<0.05
Ns#R`WG) for m1 = 1:1:M1 % Start space evolution
Dqg~g|(Q< u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
K)_DaTmi) u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
/{sFrEMP\ ca1 = fftshift(fft(u1)); % Take Fourier transform
96]!*} ca2 = fftshift(fft(u2));
#Ks2a):8 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
kW.it5Z# c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
N[j*Q 8X_ u2 = ifft(fftshift(c2)); % Return to physical space
dHJ#xmE!pP u1 = ifft(fftshift(c1));
|x/00XhS if rem(m1,J) == 0 % Save output every J steps.
R A^-Pa.O U1 = [U1 u1]; % put solutions in U array
^wTod\y U2=[U2 u2];
w^ N3Ma MN1=[MN1 m1];
SXF~>|h5< z1=dz*MN1'; % output location
Ce-D ^9kC end
%D
$+Z( end
/j(3 ~%]o4 hg=abs(U1').*abs(U1'); % for data write to excel
p0b MgP ha=[z1 hg]; % for data write to excel
us$=) m~v+ t1=[0 t'];
( sN;B) hh=[t1' ha']; % for data write to excel file
{wy#HYhv %dlmwrite('aa',hh,'\t'); % save data in the excel format
8D5v'[j- figure(1)
_ YPu waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
rFl6xM;F figure(2)
`zj byY waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
}Gi4`Es #a|.cm>6 非线性超快脉冲耦合的数值方法的Matlab程序 d%w#a3( 4pG!m&4]ze 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。
p6|RV(?8 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
o@ j)clf
YIZ+BVa C[IY9s:Pf ]aqg{XdGt % This Matlab script file solves the nonlinear Schrodinger equations
f>kW\uC % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
t
IO 'ky % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
G }ccf% % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Y>i5ubR~ wN^$8m5\T^ C=1;
{- Y.C*E M1=120, % integer for amplitude
m l\2%07 M3=5000; % integer for length of coupler
Aat-938FP6 N = 512; % Number of Fourier modes (Time domain sampling points)
ie9,y e" dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
pon0!\ZT= T =40; % length of time:T*T0.
X$(Dem dt = T/N; % time step
:0'2 m@x~ n = [-N/2:1:N/2-1]'; % Index
iciw 54;4 t = n.*dt;
nQ}$jOU & ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
qOi"3_ w=2*pi*n./T;
REc+ @;B g1=-i*ww./2;
lk`, s g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
LktH*ePO g3=-i*ww./2;
V3t;V-Lkt P1=0;
8P[aX3T7G P2=0;
@b5zHXF83E P3=1;
j]5mzz~ P=0;
O=2SDuBZ for m1=1:M1
at5>h p=0.032*m1; %input amplitude
m\xlSNW'q s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
9zs!rlzQ s1=s10;
8 O% ?t s20=0.*s10; %input in waveguide 2
X^c 2 s30=0.*s10; %input in waveguide 3
1SO!a R#g s2=s20;
# @~H pqqR s3=s30;
c3]X#Qa#m$ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Eu)(@,]w e %energy in waveguide 1
QnN cGH p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
>J ,y1jzJ %energy in waveguide 2
v[J"/:] p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
SE;Yb' %energy in waveguide 3
|| 0n%"h>i for m3 = 1:1:M3 % Start space evolution
`Eq~W@';Q0 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
?Ja&LNI9S s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
5kbbeO|0G s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
;eQOBGX9 sca1 = fftshift(fft(s1)); % Take Fourier transform
G}8Zkz@+ sca2 = fftshift(fft(s2));
dw"{inMf sca3 = fftshift(fft(s3));
.{ +Ob i sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
;I@@PUnR sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
~+OAAkJ9 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
ZA {T0: s3 = ifft(fftshift(sc3));
\Jy/
a- s2 = ifft(fftshift(sc2)); % Return to physical space
=QQTHL{3 s1 = ifft(fftshift(sc1));
Lw_s'QNWR end
j$ h>CZ Z p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
v62O+{ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
oTLA&dy@ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
'PK ;Fg\ P1=[P1 p1/p10];
T \ 3a T P2=[P2 p2/p10];
jS<(O o P3=[P3 p3/p10];
@e OD+h' P=[P p*p];
p^>_VE[S end
pN?geF~t| figure(1)
9qcA+gz:| plot(P,P1, P,P2, P,P3);
?CU6RC n '2X6 >6`w 转自：
http://blog.163.com/opto_wang/
