计算脉冲在非线性耦合器中演化的Matlab 程序 ?Mp1~{8 9Z6C8Jv % This Matlab script file solves the coupled nonlinear Schrodinger equations of
R1-k3;v^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
/i)Hb`(S % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
I@l>w._. % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
T#O??3/%$1 SLhEc %fid=fopen('e21.dat','w');
g8'DoHJ* N = 128; % Number of Fourier modes (Time domain sampling points)
jFerYv&K~ M1 =3000; % Total number of space steps
m/`IGT5J J =100; % Steps between output of space
r
Db>&s3 T =10; % length of time windows:T*T0
(H?ZSeWx T0=0.1; % input pulse width
IB|]fzy MN1=0; % initial value for the space output location
OSzjK7: dt = T/N; % time step
_B,_4} n = [-N/2:1:N/2-1]'; % Index
E-1"+p t = n.*dt;
(}:C+p
'I u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
X;!D};;M u20=u10.*0.0; % input to waveguide 2
&D#+6M&LK{ u1=u10; u2=u20;
Z v0C@r U1 = u1;
dZGbC 9 U2 = u2; % Compute initial condition; save it in U
=w<v3 wWN4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/9Ilo\MdD w=2*pi*n./T;
k:#6^!b1 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Icp0A\L@ L=4; % length of evoluation to compare with S. Trillo's paper
y7<&vIEC dz=L/M1; % space step, make sure nonlinear<0.05
Pj7gGf6v for m1 = 1:1:M1 % Start space evolution
0p fnV% u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
v.W{x?5 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
["3df>!f ca1 = fftshift(fft(u1)); % Take Fourier transform
ad!(z[F'Y ca2 = fftshift(fft(u2));
w5]l1}rl c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
NE"jh_m- c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
oj}"H>tTp u2 = ifft(fftshift(c2)); % Return to physical space
wUi(3g|A u1 = ifft(fftshift(c1));
GLKO]y if rem(m1,J) == 0 % Save output every J steps.
rdj@u47 U1 = [U1 u1]; % put solutions in U array
bO49GEUT _ U2=[U2 u2];
#/j ={*- MN1=[MN1 m1];
7SI)1_%G z1=dz*MN1'; % output location
+zWrLf_Rc end
]2+g&ox4' end
>kdM:MK hg=abs(U1').*abs(U1'); % for data write to excel
R V!o4"\] ha=[z1 hg]; % for data write to excel
!W1eUY t1=[0 t'];
U q X1E hh=[t1' ha']; % for data write to excel file
SZVV40w %dlmwrite('aa',hh,'\t'); % save data in the excel format
xKp0r1} figure(1)
gZ(O)uzv waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
M@?"t_e1 figure(2)
0^]t"z5f0 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
015Owi a]1i/3/ 非线性超快脉冲耦合的数值方法的Matlab程序 ;mO,3dV 7unA"9=[4V 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。
qmmv7== 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
|*Ot/TvG 6b:DJ MWq$AK] ]Sta]}VQ % This Matlab script file solves the nonlinear Schrodinger equations
$(>f8)Uku( % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
PI7IBI % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
oA3d^%(c % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
X9'xn 0n; ,0T)Oc|HL/ C=1;
g'G8 3F M1=120, % integer for amplitude
'TEyP56 M3=5000; % integer for length of coupler
@;9()ad N = 512; % Number of Fourier modes (Time domain sampling points)
*1;23BiH- dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
0|2%# E T =40; % length of time:T*T0.
jA2ofC dt = T/N; % time step
ci7~KewJ* n = [-N/2:1:N/2-1]'; % Index
\ j]~>9 t = n.*dt;
w67xl ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
*4#on> w=2*pi*n./T;
3%NE/lw1 g1=-i*ww./2;
onzA7Gre g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
>5i ?JUZ g3=-i*ww./2;
}W
"(cYN_ P1=0;
*?Wtj P2=0;
hZ#\t P3=1;
GUCM4jVT^ P=0;
nx :)k-p_[ for m1=1:M1
A;%kl`~iyz p=0.032*m1; %input amplitude
-HT L5 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-q(:%; s1=s10;
luF#OP C s20=0.*s10; %input in waveguide 2
s<{GpWT8 s30=0.*s10; %input in waveguide 3
wU0K3qZL s2=s20;
s1@@o#r s3=s30;
2$ VTu+ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
f)tc 4iV %energy in waveguide 1
,'-?:`hP' p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
K|~AA"I; %energy in waveguide 2
g!`BXmW p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
!'PlDGD %energy in waveguide 3
~mcZUiP9 for m3 = 1:1:M3 % Start space evolution
]1Qi=2' s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
sVD([`Nmc s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
q+J0}y{#8) s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
' WnpwY sca1 = fftshift(fft(s1)); % Take Fourier transform
*C/KM;& sca2 = fftshift(fft(s2));
g!5#,kJM sca3 = fftshift(fft(s3));
ULbP_y>(Y sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
O &\<F T5 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
7`+UB>8 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
.ftUhg s3 = ifft(fftshift(sc3));
/^QFqM; s2 = ifft(fftshift(sc2)); % Return to physical space
\"bLE0~ s1 = ifft(fftshift(sc1));
eb7UoZw end
q]?+By-0 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
E$&;]a p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
s|p(KWo2U p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
I9:%@g]uYw P1=[P1 p1/p10];
lzI/\% P2=[P2 p2/p10];
L.Vq1RU\" P3=[P3 p3/p10];
.n=xbx:= P=[P p*p];
R_~F6O^EO end
Z0z) figure(1)
SOYDp;j plot(P,P1, P,P2, P,P3);
'iDu0LX *q[^Q'jnN 转自:
http://blog.163.com/opto_wang/