计算脉冲在非线性耦合器中演化的Matlab 程序 8wmQ4){ U=QA e % This Matlab script file solves the coupled nonlinear Schrodinger equations of
WFDCPQ@ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
,Xtj;@~- % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
AY88h$a % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
:tbd,Uo c1#+Vse %fid=fopen('e21.dat','w');
$ >r5>6 N = 128; % Number of Fourier modes (Time domain sampling points)
V|: qow:F M1 =3000; % Total number of space steps
U\bC0q J =100; % Steps between output of space
vaB!R 0 T =10; % length of time windows:T*T0
D/: 3R ZF T0=0.1; % input pulse width
`eD1|Go9 MN1=0; % initial value for the space output location
5v|EAjB6o dt = T/N; % time step
gDC2
>nV n = [-N/2:1:N/2-1]'; % Index
;;Tq$#vd t = n.*dt;
vyU!+ml c u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Yt{&rPv, u20=u10.*0.0; % input to waveguide 2
1Es qQz*$u u1=u10; u2=u20;
n&d/?aJ7a\ U1 = u1;
/b%Q[
Ck_ U2 = u2; % Compute initial condition; save it in U
$[z<oN_Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
YgimJsm w=2*pi*n./T;
:1_mfX g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
(Ilsk{aB;A L=4; % length of evoluation to compare with S. Trillo's paper
vp L Mhf` dz=L/M1; % space step, make sure nonlinear<0.05
>rf5)Y~f for m1 = 1:1:M1 % Start space evolution
(p,}'I#i* u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
8 Z 8Y[p u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
|^K jz{ ca1 = fftshift(fft(u1)); % Take Fourier transform
C}Qt "-% ca2 = fftshift(fft(u2));
>|
m.?{^ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
ab4LTF| c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
V^rW?Do u2 = ifft(fftshift(c2)); % Return to physical space
: Ss3ck*= u1 = ifft(fftshift(c1));
d G0 VBE if rem(m1,J) == 0 % Save output every J steps.
1exfCm U1 = [U1 u1]; % put solutions in U array
CDCC1B G" U2=[U2 u2];
ti9}*8 MN1=[MN1 m1];
P
{H{UKs# z1=dz*MN1'; % output location
vr4S9`, end
] .5O X84 end
'9q6 aM/& hg=abs(U1').*abs(U1'); % for data write to excel
m UgRm] ha=[z1 hg]; % for data write to excel
z_l. V /G) t1=[0 t'];
k
,fTW^ ? hh=[t1' ha']; % for data write to excel file
HJ@ 5 B" %dlmwrite('aa',hh,'\t'); % save data in the excel format
vGN3 YcH figure(1)
% wL, v.} waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Xw^X&Pp figure(2)
ik\S88| waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Pfan7fq+ 1JeJxzv>C 非线性超快脉冲耦合的数值方法的Matlab程序 3dm'xe tM it,w^VU_] 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。
o0`q#>7!_b 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
jVYH;B%%z @]?R 2bI #U@| J}a a D | Yo % This Matlab script file solves the nonlinear Schrodinger equations
YoAg % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Ub)M*Cq0(o % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
p( ?3
V % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
/b{HG7i\ M&[b.t* C=1;
woau'7}XOu M1=120, % integer for amplitude
* nCx[ M3=5000; % integer for length of coupler
c<tmj{$
N = 512; % Number of Fourier modes (Time domain sampling points)
q[c Etp28h dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
v}P!HczmMP T =40; % length of time:T*T0.
$?f]ZyZr. dt = T/N; % time step
A.U'Q| n = [-N/2:1:N/2-1]'; % Index
%U?)?iZdL t = n.*dt;
@ ?a4i ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
CQ> ]jQ,2 w=2*pi*n./T;
O<X
)p`,` g1=-i*ww./2;
Jck"Ks g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
3;Hd2 ;G g3=-i*ww./2;
]^ 'ZiyJX P1=0;
>{XScxaB` P2=0;
J]\^QMX P3=1;
o4 ~kX P=0;
/qXzOd for m1=1:M1
,8VXA +'_ p=0.032*m1; %input amplitude
+-ewE-:|L s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
e5OVq
, s1=s10;
FL &dv s20=0.*s10; %input in waveguide 2
P`
]ps?l s30=0.*s10; %input in waveguide 3
=|V" #3$f s2=s20;
OjATSmZ@@ s3=s30;
+WL D p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
4J}3,+ %energy in waveguide 1
Tf[dZ( +\ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
b1 )\Zi %energy in waveguide 2
[*HiI = p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
OG}KqG!n %energy in waveguide 3
0WXV c for m3 = 1:1:M3 % Start space evolution
[q"NU&SX s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
~`[8"YUL s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
.vaJ Avg s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
T#r=<YH[C sca1 = fftshift(fft(s1)); % Take Fourier transform
2 4X=5Aj sca2 = fftshift(fft(s2));
K ?YEoz'y[ sca3 = fftshift(fft(s3));
+{*)}[w{x sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Pz1G<eh#{g sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
3?^NN|xg sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
JV%nH! Fs s3 = ifft(fftshift(sc3));
@,Jb7V< s2 = ifft(fftshift(sc2)); % Return to physical space
iAHZ0Du s1 = ifft(fftshift(sc1));
uMpl#N p end
ArX]L$ D p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
H &fTh p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
L!vWRwZwC p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
|D+p$^L P1=[P1 p1/p10];
M:(&n@e P2=[P2 p2/p10];
CjV7q y P3=[P3 p3/p10];
D-D # ` P=[P p*p];
X+*<B(E end
#G~wE*VR$ figure(1)
tWX7dspx/ plot(P,P1, P,P2, P,P3);
i'iO H|s 6VFirLd 转自：
http://blog.163.com/opto_wang/
