计算脉冲在非线性耦合器中演化的Matlab 程序 `[:f ;2(@ !D6@ \ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
GQ[\R&]q< % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
O^IpfS\/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
a ]ftE\99 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
YHAy+S S&QZ "4jq %fid=fopen('e21.dat','w');
xUe LX`73 N = 128; % Number of Fourier modes (Time domain sampling points)
+q =/}| M1 =3000; % Total number of space steps
3 -Ti'xM J =100; % Steps between output of space
U~T/f-CT T =10; % length of time windows:T*T0
w-\GrxlbX T0=0.1; % input pulse width
icnp^2P MN1=0; % initial value for the space output location
a"ht\v}1 dt = T/N; % time step
2} T" |56 n = [-N/2:1:N/2-1]'; % Index
R_ Z
H+@O t = n.*dt;
D vK}UAj= u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
ND I|; u20=u10.*0.0; % input to waveguide 2
.IG(Y!cB u1=u10; u2=u20;
g@S"!9[;U U1 = u1;
py,z7_Nuh U2 = u2; % Compute initial condition; save it in U
J M!o(zbt ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9 s>JdAw? w=2*pi*n./T;
p~M^' k=d g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
p'_* >%4~ L=4; % length of evoluation to compare with S. Trillo's paper
B GUP-_& dz=L/M1; % space step, make sure nonlinear<0.05
O-mP{ for m1 = 1:1:M1 % Start space evolution
W Aob"`8] u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
,c7 8O8| u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
XRaq\a`=: ca1 = fftshift(fft(u1)); % Take Fourier transform
;zp0,[r ca2 = fftshift(fft(u2));
,H.q%!{h_ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
h "q`gj c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
>-]Y%O;} u2 = ifft(fftshift(c2)); % Return to physical space
*,z_ _S$Q) u1 = ifft(fftshift(c1));
^Dd$8$?[ if rem(m1,J) == 0 % Save output every J steps.
oU{m\r U1 = [U1 u1]; % put solutions in U array
/tV)8pEj U2=[U2 u2];
yyBy|7QgO MN1=[MN1 m1];
:}j{ NM# z1=dz*MN1'; % output location
wLNO\JP' end
Q;`#ujxL end
4GaF: / hg=abs(U1').*abs(U1'); % for data write to excel
/(XtNtO* ha=[z1 hg]; % for data write to excel
ZG< <6y*. t1=[0 t'];
uZg Kex;c hh=[t1' ha']; % for data write to excel file
\/'u (|G %dlmwrite('aa',hh,'\t'); % save data in the excel format
mO]>(^c figure(1)
J6|5*|*^ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
&|55:Y87 figure(2)
Rsq b<+7 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
}cMb0`oA _kgw+NA&-H 非线性超快脉冲耦合的数值方法的Matlab程序 XG*Luc-v 8g&uCv/Uk 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。
.3!=]= 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
@e+QGd;} p]IF=~b vB KBMnSd mmEr2\L % This Matlab script file solves the nonlinear Schrodinger equations
@/XA* 9]l % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Svy bP&i| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
jsc1 B % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
I=|b 3- le X&py C=1;
yp_:] R E M1=120, % integer for amplitude
i,Yv M3=5000; % integer for length of coupler
IIs'm!"Y> N = 512; % Number of Fourier modes (Time domain sampling points)
(* BQd1Z dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
05.^MU?^U T =40; % length of time:T*T0.
&+d>xy\^/ dt = T/N; % time step
'$;S?6$eW n = [-N/2:1:N/2-1]'; % Index
"{j4?3f) t = n.*dt;
9U ZKL @KC ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8( 7DW
|\ w=2*pi*n./T;
F3i+t+Jt g1=-i*ww./2;
9 }jF]P*Q g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Y6 &w0~?! g3=-i*ww./2;
; Sq_DP1W P1=0;
J9zSBsp_ P2=0;
O| ) [j@7 P3=1;
C /\ )-^ P=0;
- ] \UFR for m1=1:M1
z* "zXL C p=0.032*m1; %input amplitude
fOtL6/? s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
u-$(TyDEl| s1=s10;
V*2uW2\} s20=0.*s10; %input in waveguide 2
a4Fe MCvV9 s30=0.*s10; %input in waveguide 3
:B6hYx s2=s20;
db'Jl^ s3=s30;
xJ:15eDC p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
,dLh`t<\ %energy in waveguide 1
nK)U.SZ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
%l( qyH)* %energy in waveguide 2
c-(,%0G 0 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
*?VbN}g2 %energy in waveguide 3
!MOVv\@O for m3 = 1:1:M3 % Start space evolution
3Gubq4r s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
nm_]2z O s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
,|<2wn#q s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
2Xys;Dwx sca1 = fftshift(fft(s1)); % Take Fourier transform
pQKR sca2 = fftshift(fft(s2));
6*J`2U9Q sca3 = fftshift(fft(s3));
1>r7s* sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
s{4|eYR sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
imv [xBA(d sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
, `ST Va- s3 = ifft(fftshift(sc3));
n*D-01v YP s2 = ifft(fftshift(sc2)); % Return to physical space
/'ccFm2 s1 = ifft(fftshift(sc1));
7F!_gj p end
TL-sxED,,D p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
y0k*i S
e p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
CkKr@. dV p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
tpwMy:<Ex P1=[P1 p1/p10];
K[!OfP P2=[P2 p2/p10];
* 7 u~` P3=[P3 p3/p10];
Ne!F
p P=[P p*p];
s<Px au+A end
3(0k!o0 " figure(1)
[p^N ].K$ plot(P,P1, P,P2, P,P3);
iZ} w>1 D~E1hr&Vd> 转自：
http://blog.163.com/opto_wang/
