计算脉冲在非线性耦合器中演化的Matlab 程序 A> (EM}\, 9_Z_5w;h % This Matlab script file solves the coupled nonlinear Schrodinger equations of
C[;7i!Dv % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
.'2"83f % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
M3dUGM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
i?)bF!J u{dkUG1ia %fid=fopen('e21.dat','w');
6vzvH N = 128; % Number of Fourier modes (Time domain sampling points)
^{NN- M1 =3000; % Total number of space steps
WMFn #.aY5 J =100; % Steps between output of space
=w:H9uj6F T =10; % length of time windows:T*T0
R/6
v#9m7 T0=0.1; % input pulse width
d[E= HN MN1=0; % initial value for the space output location
,V&E"D{u dt = T/N; % time step
y;O
6q206 n = [-N/2:1:N/2-1]'; % Index
h-o;vC9fC t = n.*dt;
Qb;]4[3 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
]*0t?'go' u20=u10.*0.0; % input to waveguide 2
+RK/u u1=u10; u2=u20;
TBHd)BhI. U1 = u1;
@#9x Ss# U2 = u2; % Compute initial condition; save it in U
~u?rjkSFoh ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
K5(T7S w=2*pi*n./T;
-7 EwZRS@9 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
472 'P L=4; % length of evoluation to compare with S. Trillo's paper
D^{jXNDNO dz=L/M1; % space step, make sure nonlinear<0.05
h[ C XH" for m1 = 1:1:M1 % Start space evolution
!=+;9Ry$z u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
!
e?=g%( u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
'n?"f |G ca1 = fftshift(fft(u1)); % Take Fourier transform
F-$NoE L ca2 = fftshift(fft(u2));
p%OVl[^jp c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
%,d+ jBM c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
d 5h x%M u2 = ifft(fftshift(c2)); % Return to physical space
l8l J & u1 = ifft(fftshift(c1));
9YBlMf`KEf if rem(m1,J) == 0 % Save output every J steps.
cL"Ral-qB U1 = [U1 u1]; % put solutions in U array
paxZlA
o U2=[U2 u2];
_ CzAv % MN1=[MN1 m1];
CKDg3p'; z1=dz*MN1'; % output location
va.Ve# N end
qtP*O#1q end
LBcqFvj{& hg=abs(U1').*abs(U1'); % for data write to excel
rj<-sfs ha=[z1 hg]; % for data write to excel
4X eO^# t1=[0 t'];
E/E|*6R hh=[t1' ha']; % for data write to excel file
Wx8;+!2Q/ %dlmwrite('aa',hh,'\t'); % save data in the excel format
Qk^ } figure(1)
pU u')y waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
FwQGxGZ figure(2)
;47 =x1j i waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
YIYuqtnSJ 6p 14BruV 非线性超快脉冲耦合的数值方法的Matlab程序 n|PW^kOE/ b_@bS<wsF} 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。
Lf8{']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
H#b u3*' fl*49-d @$wfE\ _L z}p*";)A % This Matlab script file solves the nonlinear Schrodinger equations
"(:8 $F b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
{_4zm& % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
TG.\C8;vFh % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0LP>3"Sm L_>LxF43 C=1;
cP0(Q+i7 M1=120, % integer for amplitude
J!zL)u| M3=5000; % integer for length of coupler
<Oj'0NK- N = 512; % Number of Fourier modes (Time domain sampling points)
r;fcBepO dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
?gXdi<2Qn T =40; % length of time:T*T0.
4{ "
v dt = T/N; % time step
o^ BX:\} n = [-N/2:1:N/2-1]'; % Index
PC)V".W 1 t = n.*dt;
3d_g@x#9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
SLu d}|f;o w=2*pi*n./T;
lq2 7^K g1=-i*ww./2;
@Lm (bW g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
?/KkN3Y_j[ g3=-i*ww./2;
JZD&u6tB P1=0;
d,t'e? P2=0;
v <?k$ e5 P3=1;
zc>LwX}< P=0;
g^:7mG6C for m1=1:M1
75']fFO@! p=0.032*m1; %input amplitude
W1UqvaR s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
"ScY'< s1=s10;
W-vEh s20=0.*s10; %input in waveguide 2
et6@);F s30=0.*s10; %input in waveguide 3
x4@IK|CE s2=s20;
0"`|f0 }c s3=s30;
`I5So-^&z p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
*&W1|Qkg_ %energy in waveguide 1
iIg99c7/&9 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
!p4FK]B/u %energy in waveguide 2
g0RfvR p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
O,7*dniH %energy in waveguide 3
&4Y@-;REt for m3 = 1:1:M3 % Start space evolution
kL% o9=R1 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Je~<2EsQ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
~ponYc.Y s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Yo2n [ sca1 = fftshift(fft(s1)); % Take Fourier transform
lQer|?# sca2 = fftshift(fft(s2));
6X GqZ!2 sca3 = fftshift(fft(s3));
u[coWaPsZ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
,SoqVboRl sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
(t-JGye> sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
J<7nOB}OD s3 = ifft(fftshift(sc3));
M'ZA(LVp s2 = ifft(fftshift(sc2)); % Return to physical space
5> =Ia@I
s1 = ifft(fftshift(sc1));
x^6sjfA W end
#pp6 ycy p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
[moz{Y p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
q,_ 1?A) p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
U~{sJwB P1=[P1 p1/p10];
tj e P2=[P2 p2/p10];
}G[Qm2k P3=[P3 p3/p10];
OYNPZRu P=[P p*p];
JUC62s#_z end
+8q]O%B
figure(1)
`n~bDG> plot(P,P1, P,P2, P,P3);
LXcH<) Fu#mMn0c 转自：
http://blog.163.com/opto_wang/
