计算脉冲在非线性耦合器中演化的Matlab 程序 "Om=N@? I/a/ )No % This Matlab script file solves the coupled nonlinear Schrodinger equations of
nH`Q#ZFz]? % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
"]"|"0#i % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
:e_V7t ) o % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_kj wFq IEXt: %fid=fopen('e21.dat','w');
Hw7;;HK
7 N = 128; % Number of Fourier modes (Time domain sampling points)
(MR_^t M1 =3000; % Total number of space steps
>64P6P;S J =100; % Steps between output of space
xfpa]Z T =10; % length of time windows:T*T0
_oHNkKQ T0=0.1; % input pulse width
G`n_YH084 MN1=0; % initial value for the space output location
.} q&5v dt = T/N; % time step
W yB3ls ~ n = [-N/2:1:N/2-1]'; % Index
R$ q;
! t = n.*dt;
C"!gZ8*\!9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
N):t OD@B u20=u10.*0.0; % input to waveguide 2
N.\-
8?> u1=u10; u2=u20;
&X|#R1\ U1 = u1;
-n=^U U2 = u2; % Compute initial condition; save it in U
z`!Xh U ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
nSW=LjrO~< w=2*pi*n./T;
<g1 hxfKx5 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
%+j8["VEC L=4; % length of evoluation to compare with S. Trillo's paper
,eTUhK dz=L/M1; % space step, make sure nonlinear<0.05
'^No)n\` for m1 = 1:1:M1 % Start space evolution
X;i~ <Tq u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
_I)U%? V+ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
L\@I*QP ca1 = fftshift(fft(u1)); % Take Fourier transform
eM$s v 9? ca2 = fftshift(fft(u2));
+ Af"f' ) c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
W8ouO+wK c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
W+PJZn u2 = ifft(fftshift(c2)); % Return to physical space
U^Q:Y}^ u1 = ifft(fftshift(c1));
o=50>$5jlS if rem(m1,J) == 0 % Save output every J steps.
_C mO d-y U1 = [U1 u1]; % put solutions in U array
2nSSF x r U2=[U2 u2];
H,DM1Z9rz MN1=[MN1 m1];
(#Wu# F1; z1=dz*MN1'; % output location
ZZHDp&lh} end
pi
Z[Y
5OE end
Bwa'`+bC hg=abs(U1').*abs(U1'); % for data write to excel
Hkwl>R$ ha=[z1 hg]; % for data write to excel
YL]Z<%aKt t1=[0 t'];
mS~o?q-n hh=[t1' ha']; % for data write to excel file
MUTj-1 H6) %dlmwrite('aa',hh,'\t'); % save data in the excel format
K('hC)1 figure(1)
yf[~Yl>Ogw waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
*M:B\ D figure(2)
.}O[dR waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
L1 cI`9 +89*)pk 非线性超快脉冲耦合的数值方法的Matlab程序 AS
=?@2 q t .7? 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。
-( 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
9aze>nxh. .NYbi@bk(< ) n2 re?S ~/98Id}v % This Matlab script file solves the nonlinear Schrodinger equations
l|kSsP:GO % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
5*Y^\N % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;1%-8f:lW % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
U)E(`{p] f@Zszt C=1;
aX5
z&r:{ M1=120, % integer for amplitude
y#U+c*LB M3=5000; % integer for length of coupler
] lrWgm N = 512; % Number of Fourier modes (Time domain sampling points)
4lKq{X5< dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
0:9.;x9_ T =40; % length of time:T*T0.
(oEC6F dt = T/N; % time step
m 8aITd8 n = [-N/2:1:N/2-1]'; % Index
3Nq N \5B: t = n.*dt;
3HcQ(+Z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1Cgso` w=2*pi*n./T;
#,":vr g1=-i*ww./2;
?u "
4@ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
>zXsNeGQR g3=-i*ww./2;
y CVI\y \B P1=0;
| }(`kW P2=0;
23RN}LUi P3=1;
J&.{7Y F P=0;
5h Q E4/hH for m1=1:M1
-o $QS, p=0.032*m1; %input amplitude
M$/|)U' W s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
ki?S~' a s1=s10;
{q `jDDM s20=0.*s10; %input in waveguide 2
??M"6k s30=0.*s10; %input in waveguide 3
>[*8I\ *@n s2=s20;
Z0Vl+ s3=s30;
{^\+iK4bS p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
"1 L$| %energy in waveguide 1
W-?()dX{ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
1~Oe=`{& %energy in waveguide 2
q*_/to p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
U%q7Ai7 %energy in waveguide 3
pe] A5\4c for m3 = 1:1:M3 % Start space evolution
C71qPb|$R s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
!cO]< CWPq s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
4^WpS/#4 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
.Le?T&_ sca1 = fftshift(fft(s1)); % Take Fourier transform
5|o6v1bM sca2 = fftshift(fft(s2));
+a^nlW9g sca3 = fftshift(fft(s3));
El.hu%#n*G sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
6{n!Cb[e sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
yku5SEJ\ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
WvBc#s- s3 = ifft(fftshift(sc3));
ew#B [[ s2 = ifft(fftshift(sc2)); % Return to physical space
JtEo'As :[ s1 = ifft(fftshift(sc1));
Jk7|{W\OA end
= \'}g? p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
IsZHe lg p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
y9q8i(E0 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
>qS9PX P1=[P1 p1/p10];
YwDb PX P2=[P2 p2/p10];
U+:m4a P3=[P3 p3/p10];
*K|W
/'_& P=[P p*p];
(tIo: j end
&cxRD figure(1)
gW>uR3Ca4 plot(P,P1, P,P2, P,P3);
p "n$!ilbm ,z;cbsV-{ 转自：
http://blog.163.com/opto_wang/
