计算脉冲在非线性耦合器中演化的Matlab 程序 (hZ:X)E > d }0qJoH4 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
1-;?0en&0 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
zDBD .5R; % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
a, K ky ^B % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
a Snp/g |DG@ht %fid=fopen('e21.dat','w');
0~E 6QhV: N = 128; % Number of Fourier modes (Time domain sampling points)
%|Hp Bs#' M1 =3000; % Total number of space steps
-] "T^w ib J =100; % Steps between output of space
n TnRGf\T T =10; % length of time windows:T*T0
j64 4V|z T0=0.1; % input pulse width
M?:\9DDd MN1=0; % initial value for the space output location
=d20Xa dt = T/N; % time step
6n w&$I n = [-N/2:1:N/2-1]'; % Index
Etnb 3<^[t t = n.*dt;
M2 3& <}Q8 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
N7.
@FK u20=u10.*0.0; % input to waveguide 2
CUhV$A#oo u1=u10; u2=u20;
]O{_O&w U1 = u1;
Q)6va}2ai U2 = u2; % Compute initial condition; save it in U
P \B3
y+) ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
# 3.)H9
w=2*pi*n./T;
E3\ZJjG g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
N=ifI V c L=4; % length of evoluation to compare with S. Trillo's paper
m4**>!I dz=L/M1; % space step, make sure nonlinear<0.05
LcUl c)YH5 for m1 = 1:1:M1 % Start space evolution
? eWJa u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
_`aR_ %Gx u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
X5E
' *W ca1 = fftshift(fft(u1)); % Take Fourier transform
(:} <xxl ca2 = fftshift(fft(u2));
A PHPN:v c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Y1r ,2 k c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
1mUTtYU u2 = ifft(fftshift(c2)); % Return to physical space
qC
j*> D u1 = ifft(fftshift(c1));
@l,{x |00 if rem(m1,J) == 0 % Save output every J steps.
dq 8+m(7k U1 = [U1 u1]; % put solutions in U array
@InJ_9E U2=[U2 u2];
bXl8v MN1=[MN1 m1];
mU]s7` %<> z1=dz*MN1'; % output location
kMS5h~D[ end
i[=C_+2 end
<d! 6[,W; hg=abs(U1').*abs(U1'); % for data write to excel
ZlM_ m
>,o ha=[z1 hg]; % for data write to excel
4I ,o&TK t1=[0 t'];
(t74a E pi hh=[t1' ha']; % for data write to excel file
uX0
Bp8P %dlmwrite('aa',hh,'\t'); % save data in the excel format
J k*QcEE= figure(1)
6UB 6;- waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
\dNhzd# figure(2)
h6FgS9H waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
:0df B&7 cs5ix"1A 非线性超快脉冲耦合的数值方法的Matlab程序 w
a.f![ (HSw% e 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。
uHrb: X!q 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
I =b'j5c b A+[{ nt`<y0ta ?H0m<jO8~ % This Matlab script file solves the nonlinear Schrodinger equations
| XLFV % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
T{;=#rG < % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
|$Xf;N37t % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[Pqn 3I[ }z{wQ\ C=1;
%# 4 +! M1=120, % integer for amplitude
4(sttd_ M3=5000; % integer for length of coupler
+
o{*r# N = 512; % Number of Fourier modes (Time domain sampling points)
a^/K?lAB8 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
MBv/ T =40; % length of time:T*T0.
5%qH 7[dx dt = T/N; % time step
p\ok_*b n = [-N/2:1:N/2-1]'; % Index
J P_kQ t = n.*dt;
M/)B" q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
f~v"zT w=2*pi*n./T;
TRCI\ g1=-i*ww./2;
j #es2; g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
777rE[\@b g3=-i*ww./2;
X=#It&m%s P1=0;
x {vIT- f P2=0;
.hgH 9$\ P3=1;
omT(3)TP P=0;
mOSCkp{<e for m1=1:M1
\086O9 p=0.032*m1; %input amplitude
iGQ n/Xdo s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
K
/8qB~J* s1=s10;
y\z*p&I s20=0.*s10; %input in waveguide 2
>OTl2F}4 ! s30=0.*s10; %input in waveguide 3
Q.>/*8R; s2=s20;
+|M{I= 8 s3=s30;
k) Zn> p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
ktWZB QY %energy in waveguide 1
p*!q} %U p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
,=x
RoXYB} %energy in waveguide 2
K~$ 35c3M p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
M .t@@wq %energy in waveguide 3
5C* ?1&
! for m3 = 1:1:M3 % Start space evolution
`TkbF9N+ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
A O^]>/7ed s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
>0 7shNX s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
"C& J wm? sca1 = fftshift(fft(s1)); % Take Fourier transform
+L n M\n sca2 = fftshift(fft(s2));
M-vC>u3Y sca3 = fftshift(fft(s3));
dUZ $wbV%h sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
p ^](3Vi( sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
@N]5& 4NL sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
q< b"M$ s3 = ifft(fftshift(sc3));
!4_!J (q% s2 = ifft(fftshift(sc2)); % Return to physical space
*qbRP"#[$ s1 = ifft(fftshift(sc1));
3m3
EXz end
QT7_x`#J~o p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
(%Ng'~J\| p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
e7h\(`J0lj p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
w}"!l G P1=[P1 p1/p10];
/^~p~HKtx P2=[P2 p2/p10];
p AMo
XJ` P3=[P3 p3/p10];
U>bP}[&S P=[P p*p];
jm4)gmC end
\I:UC
% figure(1)
OX`?<@6 plot(P,P1, P,P2, P,P3);
IC\E , m +J% 6bn)U 转自：
http://blog.163.com/opto_wang/
