计算脉冲在非线性耦合器中演化的Matlab 程序 !EB[Lut m tl^![Z % This Matlab script file solves the coupled nonlinear Schrodinger equations of
.a7!*I#g % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
abkt&981K+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
HD153M, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
g @qrVQ v _
cm^Fi5 %fid=fopen('e21.dat','w');
!uSG 1j" y N = 128; % Number of Fourier modes (Time domain sampling points)
;lc/FV[/ M1 =3000; % Total number of space steps
Q[ MWzsx J =100; % Steps between output of space
;ji[ "b T =10; % length of time windows:T*T0
S94S[j0D T0=0.1; % input pulse width
1XJLGMW, MN1=0; % initial value for the space output location
DgODTxi X dt = T/N; % time step
I6rB_~]h n = [-N/2:1:N/2-1]'; % Index
WFG`-8_e[I t = n.*dt;
KYR64[1 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
YK )e u20=u10.*0.0; % input to waveguide 2
r0,XR u1=u10; u2=u20;
=p>IP"HJ U1 = u1;
1 i/&t[ U2 = u2; % Compute initial condition; save it in U
V~fPp"F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
wAF<_NG# w=2*pi*n./T;
]h?p3T$h g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
uc]`^,`2/ L=4; % length of evoluation to compare with S. Trillo's paper
f8S! FGiNc dz=L/M1; % space step, make sure nonlinear<0.05
[(m+Ejzi% for m1 = 1:1:M1 % Start space evolution
Z!2%{HQ=q u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
|: ,i u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
4^_'LiX3[ ca1 = fftshift(fft(u1)); % Take Fourier transform
x`Jh NAO> ca2 = fftshift(fft(u2));
^]X\boWlI c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
$u%7]]Y^\ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
# TPS? +( u2 = ifft(fftshift(c2)); % Return to physical space
>o ) v u1 = ifft(fftshift(c1));
D] +]Br8 if rem(m1,J) == 0 % Save output every J steps.
~ TYpq;rq U1 = [U1 u1]; % put solutions in U array
xP-\)d-.aN U2=[U2 u2];
Mq 52B_ MN1=[MN1 m1];
&*# Obv z1=dz*MN1'; % output location
+{L=cWA" end
'J_`CS end
bP VQ- hg=abs(U1').*abs(U1'); % for data write to excel
5F$~ZDu ha=[z1 hg]; % for data write to excel
>!W H%J t1=[0 t'];
OQiyAyX hh=[t1' ha']; % for data write to excel file
): 7mK03J %dlmwrite('aa',hh,'\t'); % save data in the excel format
x &*2R#Ai figure(1)
x}; sti R waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
h?P-
:E figure(2)
W] I+Rlv)U waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ndHUQ$/( {'z( 非线性超快脉冲耦合的数值方法的Matlab程序 q!AcM d\ JS^!XB' ! 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。
2Z +:^5 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
Ni>!b6 Z`[ ~_a$5Y MJ<jF(_= c]68$;Z7 % This Matlab script file solves the nonlinear Schrodinger equations
X=jHH=</ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
T&^b~T(y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
WB 5M ![ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
dy3fZ( =q^ I R~szUY6 C=1;
/a }`
y M1=120, % integer for amplitude
E7 P '} M3=5000; % integer for length of coupler
n!&F%|o^^ N = 512; % Number of Fourier modes (Time domain sampling points)
Z $Fm73 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
'$5Q daj T =40; % length of time:T*T0.
Vp1Ff dt = T/N; % time step
Ud)2Mq1#M n = [-N/2:1:N/2-1]'; % Index
c7A]\1 ~ t = n.*dt;
6cX Z3;a ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ZoR6f\2M w=2*pi*n./T;
D[dI_|59a g1=-i*ww./2;
m1Xc3=Y g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
l7#2
e ORm g3=-i*ww./2;
jIck! P1=0;
MG vp6/Pd P2=0;
v(;n|=O P3=1;
`\yQn7 Oq P=0;
RMlx[n sq for m1=1:M1
.* &F p=0.032*m1; %input amplitude
|O{kv}Y Z s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
3|BB#; s1=s10;
(BGflb s20=0.*s10; %input in waveguide 2
*g "X hk s30=0.*s10; %input in waveguide 3
soh9Oedml- s2=s20;
cUr5x8<W). s3=s30;
Lum5Va%0 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
#6@4c5{2=4 %energy in waveguide 1
4o<'
fY p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
W1ql[ DqE{ %energy in waveguide 2
t'[`"pp= p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Y%^qt]u.8 %energy in waveguide 3
w%$J<Z^-? for m3 = 1:1:M3 % Start space evolution
S3^(L s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Bo0f`EC I s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
ZhFlR*EQ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
> ,x``- sca1 = fftshift(fft(s1)); % Take Fourier transform
\?vn0;R4 sca2 = fftshift(fft(s2));
f@0Km^a Uc sca3 = fftshift(fft(s3));
5=Il2 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
XA\wZV
|{ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Bh;N:{&^Eu sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
C);I[H4Yfw s3 = ifft(fftshift(sc3));
{J-Ojw|Y b s2 = ifft(fftshift(sc2)); % Return to physical space
i93^E~q] s1 = ifft(fftshift(sc1));
EZ[e
a< end
KebC$g@W p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
f1q0*)fk p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
_|7bpt 9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
0+NGFX \p P1=[P1 p1/p10];
cUTG!
P\R P2=[P2 p2/p10];
{T 3~js P3=[P3 p3/p10];
{dwlW`{ P=[P p*p];
.9q`Tf end
B? 9"Ztb figure(1)
) H+ p6< plot(P,P1, P,P2, P,P3);
V`}u:t7 r 3*N0oc^m 转自：
http://blog.163.com/opto_wang/
