计算脉冲在非线性耦合器中演化的Matlab 程序 -z$2pXT ^ TF-Ty % This Matlab script file solves the coupled nonlinear Schrodinger equations of
uE`| 0 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
lkg*AAR?' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
_i@eOqoC % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
zN)\2 8 {]Gh 0+ %fid=fopen('e21.dat','w');
f\U&M,L\ ' N = 128; % Number of Fourier modes (Time domain sampling points)
;;hyjFGq% M1 =3000; % Total number of space steps
}k0-?_Z=1 J =100; % Steps between output of space
eSNSnh]' T =10; % length of time windows:T*T0
6H,=S`V]EK T0=0.1; % input pulse width
0 DVZRB MN1=0; % initial value for the space output location
3,L3C9V' dt = T/N; % time step
.]s( c !{y n = [-N/2:1:N/2-1]'; % Index
1 3 `0d t = n.*dt;
S5u#g`I] u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
{V% O4/ u20=u10.*0.0; % input to waveguide 2
)z235}P
u1=u10; u2=u20;
OrEuQ-,i@ U1 = u1;
RrdtU7i3 U2 = u2; % Compute initial condition; save it in U
g+ 1=5g ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
TT ZxkK w=2*pi*n./T;
7Ljj#!`lUp g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
'R d*X6dv L=4; % length of evoluation to compare with S. Trillo's paper
# 3 yw
dz=L/M1; % space step, make sure nonlinear<0.05
Vy^yV|`v for m1 = 1:1:M1 % Start space evolution
L\wpS1L( u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
9Jy2T/l u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
!_-sTZ ca1 = fftshift(fft(u1)); % Take Fourier transform
I,4- ca2 = fftshift(fft(u2));
R =9~*9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
~J>gVg%66 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
?t0zs q u2 = ifft(fftshift(c2)); % Return to physical space
~@uY?jr u1 = ifft(fftshift(c1));
! H|82:`t+ if rem(m1,J) == 0 % Save output every J steps.
#>m ,
Cm U1 = [U1 u1]; % put solutions in U array
gr`Ar; U2=[U2 u2];
vo6[2.HS MN1=[MN1 m1];
yaRcBT? z1=dz*MN1'; % output location
c\)&yGE end
p=_XMh`; end
ezr\ T hg=abs(U1').*abs(U1'); % for data write to excel
mDF"&.(j ha=[z1 hg]; % for data write to excel
mk%"G =w t1=[0 t'];
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hh=[t1' ha']; % for data write to excel file
A`
o?+2s_ %dlmwrite('aa',hh,'\t'); % save data in the excel format
3_\{[_ W figure(1)
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nt? waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
vf' cx :m figure(2)
p 37zz4 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
oa &z/`@ 0i*'N ch#i 非线性超快脉冲耦合的数值方法的Matlab程序 +eBMn(7Cgv kUg+I_j6* 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。
HLSfoQ&)v 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
6/mkJj+" @UpC{M--Wr yD[zzEuQ xv$)u<V e % This Matlab script file solves the nonlinear Schrodinger equations
Z[k#AgC) % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
lbB.*oQ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;;YcuzQI3 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
lP@) fys5-1@-p C=1;
P^8^1-b M1=120, % integer for amplitude
Z\|u9DO M3=5000; % integer for length of coupler
WXLe,7y N = 512; % Number of Fourier modes (Time domain sampling points)
uS,p|}Q& dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
fwi};)K T =40; % length of time:T*T0.
A-a17}fta dt = T/N; % time step
~IlF*Zz#}6 n = [-N/2:1:N/2-1]'; % Index
Hz]4A S t = n.*dt;
Dh &:- ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
KbwTj*k[ w=2*pi*n./T;
$bZu^ d, g1=-i*ww./2;
qukjS#>+ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
kRN|TDx( g3=-i*ww./2;
X(GmiH /E P1=0;
1m>^{u P2=0;
CJ9cCtA P3=1;
b|sc'eP#? P=0;
aJ :A%+1 for m1=1:M1
(VYR!(17 p=0.032*m1; %input amplitude
Qj
6gg s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
u/gm10<OWa s1=s10;
3z,v#2 s20=0.*s10; %input in waveguide 2
N>d|A]zH s30=0.*s10; %input in waveguide 3
,8c
dXt
s2=s20;
8%o~ 4u3 s3=s30;
Gr5` 1`8| p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
T[0V%Br{d+ %energy in waveguide 1
5N oe/6 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
/x %energy in waveguide 2
LkJ$aW/ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
-6rf( ER %energy in waveguide 3
!}> eo2$r^ for m3 = 1:1:M3 % Start space evolution
8yE!7$Mj s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
mi7sBA9L8 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
owE<7TGPI? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
G*i.a*9<) sca1 = fftshift(fft(s1)); % Take Fourier transform
5oz >1 sca2 = fftshift(fft(s2));
44|deE3Z sca3 = fftshift(fft(s3));
Z0e-W:&;kF sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
HUj+ - sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
$brKl 8P sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
i {gDW+N s3 = ifft(fftshift(sc3));
.Qd}.E G s2 = ifft(fftshift(sc2)); % Return to physical space
7{n\y l? s1 = ifft(fftshift(sc1));
luW
<V> end
( "_Q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
L)q`D2|' p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
xME(B@j p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
3PsxOb+ P1=[P1 p1/p10];
jEUx
q%BH P2=[P2 p2/p10];
fO*)LPen.z P3=[P3 p3/p10];
y0,Ft/D P=[P p*p];
+x(YG(5\w end
u\`/Nhn figure(1)
5B%w]n plot(P,P1, P,P2, P,P3);
xb%/sz(4 j7f5|^/x3 转自：
http://blog.163.com/opto_wang/
