计算脉冲在非线性耦合器中演化的Matlab 程序 /4y o ` =O~_Q- % This Matlab script file solves the coupled nonlinear Schrodinger equations of
y\/1/WjBn % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
_qF+tm % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
dB{Q" ! % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
p'Y^ X CT&|QH{ %fid=fopen('e21.dat','w');
0 j^Kgx N = 128; % Number of Fourier modes (Time domain sampling points)
4j-Xi M1 =3000; % Total number of space steps
-{("mR&] J =100; % Steps between output of space
ko!)s T =10; % length of time windows:T*T0
)~X2
&^orW T0=0.1; % input pulse width
? w$kue MN1=0; % initial value for the space output location
v_yw@ dt = T/N; % time step
irZ])a n = [-N/2:1:N/2-1]'; % Index
D ;RiGW4 t = n.*dt;
R8K& R\
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+V2F#fI/ u20=u10.*0.0; % input to waveguide 2
A@`}c,G u1=u10; u2=u20;
VM ZMG$C U1 = u1;
t^&Cx h U2 = u2; % Compute initial condition; save it in U
:: ` HQ@^ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
!n`fTK<$ w=2*pi*n./T;
M*0]ai|; g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
p#-Z4- ` L=4; % length of evoluation to compare with S. Trillo's paper
-uS!\ dz=L/M1; % space step, make sure nonlinear<0.05
Zj( AJ* r for m1 = 1:1:M1 % Start space evolution
x5pdS: u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
j/DzCc p7 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
;[ZEDF5H ca1 = fftshift(fft(u1)); % Take Fourier transform
MxKS4k ca2 = fftshift(fft(u2));
{FI&^39
F$ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
`>o{P/ HN c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
KR} ?H#% u2 = ifft(fftshift(c2)); % Return to physical space
KS+'|q<?w u1 = ifft(fftshift(c1));
3<Lx&p~%T if rem(m1,J) == 0 % Save output every J steps.
poE0{HOU U1 = [U1 u1]; % put solutions in U array
& l<.X U2=[U2 u2];
_;"il%l=1 MN1=[MN1 m1];
i$Ul(? z1=dz*MN1'; % output location
,~U>'&M; end
./Xz}< ($8 end
Ov@gh
kr hg=abs(U1').*abs(U1'); % for data write to excel
KYm0@O>; ha=[z1 hg]; % for data write to excel
2DA]i5
t1=[0 t'];
t 9lPb_70 hh=[t1' ha']; % for data write to excel file
U gat1Pz %dlmwrite('aa',hh,'\t'); % save data in the excel format
\
#F figure(1)
HZE#A b*L waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
^^sE: figure(2)
G[ PtkPSJ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
@?s Rj&w z(O Nv#}p 非线性超快脉冲耦合的数值方法的Matlab程序 = jN.1} .^` {1% 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
`v!urE/gg% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
yZY \MB/ :U|1 xgB P\tB~SZ* bIDj[-CDG % This Matlab script file solves the nonlinear Schrodinger equations
Q-okt RK % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
k=$TGq QY? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;?Tbnn Wn % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
h8q[1"a: BKC iIf kZ C=1;
s[>,X#7 y M1=120, % integer for amplitude
6yG^p]zZ M3=5000; % integer for length of coupler
8
/]S^'> N = 512; % Number of Fourier modes (Time domain sampling points)
+HpA:]#Y dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
5{WE~8$ T =40; % length of time:T*T0.
gx/,)> E. dt = T/N; % time step
QE+g
j 8 n = [-N/2:1:N/2-1]'; % Index
NG=-NxEcN t = n.*dt;
J[|y:N ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
x;.Jw 6g w=2*pi*n./T;
d'gfQlDny g1=-i*ww./2;
WDYeOtc g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
?=msH=N<l g3=-i*ww./2;
! I:% 0D P1=0;
X,%
0/6*] P2=0;
W+c<2? d: P3=1;
_yx>TE2e P=0;
( $MlX BI for m1=1:M1
oCv.Ln1;Z p=0.032*m1; %input amplitude
R%WCH?B<} s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
3pROf#M s1=s10;
%IA\pSE s20=0.*s10; %input in waveguide 2
8 FK/~,I s30=0.*s10; %input in waveguide 3
7aRi 5 s2=s20;
_.Nbt(mz s3=s30;
x _}:D *aI p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
6Pnjm w.HV %energy in waveguide 1
gs[uD5oo < p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
;8&3 dm] %energy in waveguide 2
2zA4vZkbcw p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
?! :ha;n %energy in waveguide 3
^)S;xb9 for m3 = 1:1:M3 % Start space evolution
`?rSlR@+[I s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
B]wk+8SMY. s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
qr^ 3R&z!} s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
CsR$c,8X. sca1 = fftshift(fft(s1)); % Take Fourier transform
~W '{p sca2 = fftshift(fft(s2));
f}ji?p sca3 = fftshift(fft(s3));
re?,Wext\ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
=o(5_S.u; sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
XEp{VC@= sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
!Pvf;rNI1T s3 = ifft(fftshift(sc3));
0S_~ \t s2 = ifft(fftshift(sc2)); % Return to physical space
%XDc,AR[ s1 = ifft(fftshift(sc1));
8W(*~}ydYY end
~H_/zK 6e p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
TER =*"! p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
[ ({nj` p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
7>0o& P1=[P1 p1/p10];
J1|\Q:-7p P2=[P2 p2/p10];
\ZFGw&yN P3=[P3 p3/p10];
k,6f
&#x P=[P p*p];
%nZo4hnr$r end
H5B:; g@ figure(1)
.G XBc plot(P,P1, P,P2, P,P3);
wk D^r(hiH iN\4gQ! 转自：
http://blog.163.com/opto_wang/
