计算脉冲在非线性耦合器中演化的Matlab 程序 YF>t {| N`Bt|#R % This Matlab script file solves the coupled nonlinear Schrodinger equations of
UWn}0:6t % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
v[a#>!; s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;mi0Q. % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Xq>e]#gR z}bnw2d] %fid=fopen('e21.dat','w');
z{#F9'\ & N = 128; % Number of Fourier modes (Time domain sampling points)
>>$IHz4Z" M1 =3000; % Total number of space steps
b=|&0B$E J =100; % Steps between output of space
:LBe{ Jbw T =10; % length of time windows:T*T0
cZ!s/^o?f T0=0.1; % input pulse width
0dcXgP MN1=0; % initial value for the space output location
km c9P& dt = T/N; % time step
o~-X7)] n = [-N/2:1:N/2-1]'; % Index
TLSy+x_gX t = n.*dt;
;2@sn+@ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
@i{JqHU" u20=u10.*0.0; % input to waveguide 2
9)l_(*F u1=u10; u2=u20;
.@6]_h; U1 = u1;
MW`a>' 0t? U2 = u2; % Compute initial condition; save it in U
|Lhz^5/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
]R4)FH|>< w=2*pi*n./T;
Yi p9K[ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
amBz75N{ L=4; % length of evoluation to compare with S. Trillo's paper
#h3+T*5} 6 dz=L/M1; % space step, make sure nonlinear<0.05
3-mw-;. for m1 = 1:1:M1 % Start space evolution
phc1AN=[E u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
l#~Fe D u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
44W3U~1 ca1 = fftshift(fft(u1)); % Take Fourier transform
%C3cdy_c ca2 = fftshift(fft(u2));
*}_/:\v c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
y2 +a2 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
:>X7(&j8 u2 = ifft(fftshift(c2)); % Return to physical space
h+74W0
$ u1 = ifft(fftshift(c1));
4 iLU "~ if rem(m1,J) == 0 % Save output every J steps.
Mt YP3: U1 = [U1 u1]; % put solutions in U array
*b)b#p U2=[U2 u2];
q~^:S~q MN1=[MN1 m1];
%UQ{'JW?K z1=dz*MN1'; % output location
uWWv`bI>x end
(t]>=p%4g end
.u*].As= hg=abs(U1').*abs(U1'); % for data write to excel
zl:D|h77 ha=[z1 hg]; % for data write to excel
$1 ?X%8V t1=[0 t'];
<=inogf hh=[t1' ha']; % for data write to excel file
o(` `7A@7a %dlmwrite('aa',hh,'\t'); % save data in the excel format
@}?D<O8#"# figure(1)
V^ {!d} waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
{6n \532@ figure(2)
`e9uSF:9C waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
bvgD;:Aj .]e6TFsrO 非线性超快脉冲耦合的数值方法的Matlab程序 w3w*"M vf yv a 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
A pjqSz" Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0l6iv[qu5w SN U
bY6 cP2R2 4th yy } 0_ % This Matlab script file solves the nonlinear Schrodinger equations
o3yqG#dA % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
`_' Dj> % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
d8kwW!m+ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]= NYvv>H c_q+_$t C=1;
IA^)`l 7H M1=120, % integer for amplitude
.O#lab`:2 M3=5000; % integer for length of coupler
z{g<y^Im+E N = 512; % Number of Fourier modes (Time domain sampling points)
]R{"=H' dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
,&?q}M T =40; % length of time:T*T0.
W`'|&7~ dt = T/N; % time step
iy82QNe n = [-N/2:1:N/2-1]'; % Index
mG~y8nUtp t = n.*dt;
XC1lo 4| ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
.:ZXtU w=2*pi*n./T;
ar Ll8G[ g1=-i*ww./2;
8~ )[d!' g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
y+scJ+ < g3=-i*ww./2;
IJc#)J.2A P1=0;
s ~$4bN>LD P2=0;
j$ |C/E5? P3=1;
0o| ,& K P=0;
)Zf}V0!?+ for m1=1:M1
B ^(rU R p=0.032*m1; %input amplitude
Kg`x9._2 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
IVzA>Vd s1=s10;
jN} 7Bb X s20=0.*s10; %input in waveguide 2
87(^P3;@ s30=0.*s10; %input in waveguide 3
HCIF9{o1j> s2=s20;
- fx88 s3=s30;
]XG n2U\ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
4D8y b|o %energy in waveguide 1
DsW`V~ T p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
PBs<8xBx^ %energy in waveguide 2
c;rp@_ULG? p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
*@arn Eu %energy in waveguide 3
`VF l|o#H for m3 = 1:1:M3 % Start space evolution
f5GR#3-h( s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
z{3% Hq s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
<Ihed | s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
]az}
n(B, sca1 = fftshift(fft(s1)); % Take Fourier transform
kw^D p[8X sca2 = fftshift(fft(s2));
/-YlC (kL sca3 = fftshift(fft(s3));
<o aBh)=7 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
N"x\YHp sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
) .-(-6=R sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
TnBG MI,g' s3 = ifft(fftshift(sc3));
FV6he [, s2 = ifft(fftshift(sc2)); % Return to physical space
cevV<Wy+ s1 = ifft(fftshift(sc1));
@
U8}sH ^ end
e N< pU%7 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Vtzm Y p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
30(m-D$K>9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
1x dESorX( P1=[P1 p1/p10];
~R?dDL P2=[P2 p2/p10];
<,X +`m& P3=[P3 p3/p10];
v*'iWHCl, P=[P p*p];
Ul713Bjz end
~2A$R'x b figure(1)
8@W/43K8- plot(P,P1, P,P2, P,P3);
FP'u)eU&3 3@ F+ E\k 转自：
http://blog.163.com/opto_wang/
