计算脉冲在非线性耦合器中演化的Matlab 程序 v*As:;D_ PVljb=8F % This Matlab script file solves the coupled nonlinear Schrodinger equations of
jr# *;go % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
q*a~9.i @ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0u( 0*Xl % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
b<"jmB{ eq&QWxiD* %fid=fopen('e21.dat','w');
K@Q%NK, N = 128; % Number of Fourier modes (Time domain sampling points)
cQBc6eAi M1 =3000; % Total number of space steps
yUxz,36wZ J =100; % Steps between output of space
ouFKqRs; T =10; % length of time windows:T*T0
o "A)t= T0=0.1; % input pulse width
<X& fs*x& MN1=0; % initial value for the space output location
2@ZRz%(Oa& dt = T/N; % time step
k:@N6K/$P^ n = [-N/2:1:N/2-1]'; % Index
6zNWDUf t = n.*dt;
O?A% u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
E
GZiWBr u20=u10.*0.0; % input to waveguide 2
gLZJQubz
6 u1=u10; u2=u20;
vo&h6'i>7 U1 = u1;
15' fU! U2 = u2; % Compute initial condition; save it in U
,Sy& ?t}` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
e0 Gs|c+6 w=2*pi*n./T;
!su773vo g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
OZ"76|H1` L=4; % length of evoluation to compare with S. Trillo's paper
BTG_c_ ?]e dz=L/M1; % space step, make sure nonlinear<0.05
m9&%A 0 for m1 = 1:1:M1 % Start space evolution
jWh) bsqI! u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Zp<#( OIu u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
-Xw S?* O ca1 = fftshift(fft(u1)); % Take Fourier transform
\6"=`H0} ca2 = fftshift(fft(u2));
oEFo7X`t c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
V U5</si+ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
J}#2Wy^{ u2 = ifft(fftshift(c2)); % Return to physical space
Iij$ce`nx u1 = ifft(fftshift(c1));
@ qx$b~% if rem(m1,J) == 0 % Save output every J steps.
X AtRA1. U1 = [U1 u1]; % put solutions in U array
&o1k_! 25 U2=[U2 u2];
d'3"A"9R7- MN1=[MN1 m1];
y+{)4ptg$< z1=dz*MN1'; % output location
Xrpvq(] end
G8/q&6f_ end
I,)\506 hg=abs(U1').*abs(U1'); % for data write to excel
y"U)&1 c% ha=[z1 hg]; % for data write to excel
ZBN,%P!P0 t1=[0 t'];
sdyNJh7Jr hh=[t1' ha']; % for data write to excel file
v* <rNZI %dlmwrite('aa',hh,'\t'); % save data in the excel format
`P*BW,P'T figure(1)
=20
+(< waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
734n1-F?I% figure(2)
y}|E) waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
T3 4Z#PFwe *n[B Bz 非线性超快脉冲耦合的数值方法的Matlab程序 AP1ZIc6 A:yql`&s 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。
-"H0Qafm 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
R(cg`8 eQ n[ KU+\fwYpnk Z 5)v % This Matlab script file solves the nonlinear Schrodinger equations
&}pF6eIar % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Km,o+9?1gF % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
u7Ix7`V % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"Ehh9 m1& ?d{O' &|: C=1;
nLv~)IQ}: M1=120, % integer for amplitude
u=vBjaN2_w M3=5000; % integer for length of coupler
#e,TS`"eD N = 512; % Number of Fourier modes (Time domain sampling points)
(~E-=+R[$& dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
p|dn &<kd T =40; % length of time:T*T0.
}&2,!;"">3 dt = T/N; % time step
b0f6p>~q^ n = [-N/2:1:N/2-1]'; % Index
_G'A]O/BZD t = n.*dt;
YG8)`X qC ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
niW"o -} w=2*pi*n./T;
<hTHY E= g1=-i*ww./2;
~kSO YvK$' g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
`NEi/jB g3=-i*ww./2;
H270)Cwn+ P1=0;
o)7Ot\:E P2=0;
^yq}> _ P3=1;
:M f8q!Q' P=0;
cs9h\]ZA for m1=1:M1
.cw)Y#;IG p=0.032*m1; %input amplitude
fqq4Qc)#U& s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
3
v.8 s1=s10;
/ #rH18 s20=0.*s10; %input in waveguide 2
ED" fi$ s30=0.*s10; %input in waveguide 3
p|mFF0SL s2=s20;
rXE0jTf:a s3=s30;
!c M<&3/ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
g0}jE%) %energy in waveguide 1
lcjOBu p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
7DoU7I\u %energy in waveguide 2
*n7=m=%) p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
X# ud5h %energy in waveguide 3
HuU $x ;~ for m3 = 1:1:M3 % Start space evolution
@o^$/AE? s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
k`|E&+og s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
x a< KF s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
c _M[>#` sca1 = fftshift(fft(s1)); % Take Fourier transform
Hs:zfvD sca2 = fftshift(fft(s2));
|O oczYf sca3 = fftshift(fft(s3));
x|dP-E41\ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
(FaYagD sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
?CC.xE sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
&ni#( s3 = ifft(fftshift(sc3));
tgi%#8ZDpz s2 = ifft(fftshift(sc2)); % Return to physical space
G
kG# +C0L s1 = ifft(fftshift(sc1));
Iz . h end
kD%MFT4 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
f5b|,JJ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
!X~NL+ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
v {u q P1=[P1 p1/p10];
j%-Ems*H P2=[P2 p2/p10];
pUF JQ* P3=[P3 p3/p10];
~O PBZ# P=[P p*p];
Y;huTZ end
/ Wjc\n$' figure(1)
{k-_+#W" plot(P,P1, P,P2, P,P3);
F~
\ONO5 fDplYn# 转自：
http://blog.163.com/opto_wang/
