计算脉冲在非线性耦合器中演化的Matlab 程序 ( qONeLf% I%*Z j,> % This Matlab script file solves the coupled nonlinear Schrodinger equations of
kV%y%l(6 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
L`@&0Zk % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
s"F,=]HQ!G % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
EMH}VigR { 3P!b|V> %fid=fopen('e21.dat','w');
vKLG9ovlY N = 128; % Number of Fourier modes (Time domain sampling points)
62'0 )Cy^ M1 =3000; % Total number of space steps
Ec/+ 9H6g J =100; % Steps between output of space
.%h_W\M<l T =10; % length of time windows:T*T0
#^w 1!xXD T0=0.1; % input pulse width
}(O
kl1 MN1=0; % initial value for the space output location
]= D dt = T/N; % time step
ATewdq[C n = [-N/2:1:N/2-1]'; % Index
E0Xu9IW/A t = n.*dt;
yf>,oNIAg u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
o%Q'<0d u20=u10.*0.0; % input to waveguide 2
S%|'
/cFo u1=u10; u2=u20;
N Pq2C8: U1 = u1;
uV\#J{'* U2 = u2; % Compute initial condition; save it in U
{lw
ec"{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Ek\Zi#f< w=2*pi*n./T;
dQ o$^? g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
|EU08b]P29 L=4; % length of evoluation to compare with S. Trillo's paper
fP*C*4#X dz=L/M1; % space step, make sure nonlinear<0.05
O4 URr for m1 = 1:1:M1 % Start space evolution
N.J:Qn`( u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
j}Mpc;XOc u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Qd=/ e pkm ca1 = fftshift(fft(u1)); % Take Fourier transform
:9>n Y ca2 = fftshift(fft(u2));
v3]M;Y\ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
E_*T0&P.P c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
1O{67Pf u2 = ifft(fftshift(c2)); % Return to physical space
9$t@Gm n u1 = ifft(fftshift(c1));
}Q*ec/^{f if rem(m1,J) == 0 % Save output every J steps.
!2,.C+, U1 = [U1 u1]; % put solutions in U array
o f<OOh%3 U2=[U2 u2];
`Q[$R &\ MN1=[MN1 m1];
4K,&Q/Vdd7 z1=dz*MN1'; % output location
A]slssE+ end
g:V6 B/M& end
Va:jMN hg=abs(U1').*abs(U1'); % for data write to excel
|1$X`|S ha=[z1 hg]; % for data write to excel
} :A kpm t1=[0 t'];
7wiu%zfa:= hh=[t1' ha']; % for data write to excel file
eLWzd_ln %dlmwrite('aa',hh,'\t'); % save data in the excel format
,s<d"]< figure(1)
tt OsL')| waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Z r*ytbt figure(2)
>m46tfoM waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
83 |/sWrvh w}0PtzOe 非线性超快脉冲耦合的数值方法的Matlab程序 0_) \ e i;7jJ(#V 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。
_TiF}b!hi 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
dv: &N z5 zm,Jw WbF\=;$= 7 nfR5W~%*: % This Matlab script file solves the nonlinear Schrodinger equations
{M5IJt"{4b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
r>OE[C69 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
vOU -bF% u % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
?J
AzN nfU}ECun4 C=1;
37DvI& M1=120, % integer for amplitude
/vU31_eZt M3=5000; % integer for length of coupler
$1F9TfA N = 512; % Number of Fourier modes (Time domain sampling points)
[\y>Gv% dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
rA7S1)Kq T =40; % length of time:T*T0.
NjLd-v"2 dt = T/N; % time step
qx NV~aK n = [-N/2:1:N/2-1]'; % Index
bjZ?WZr t = n.*dt;
RdjUw#\33b ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
[VH t#JuN, w=2*pi*n./T;
`,z{7 0 g1=-i*ww./2;
5, 3h'\ "! g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Uk#1PcPd g3=-i*ww./2;
b(F`$N@7C P1=0;
[Pl$=[+ P2=0;
`K.yE0^i P3=1;
Tbw8#[6AX P=0;
\ U_DTI for m1=1:M1
~drNlt9jf p=0.032*m1; %input amplitude
H3b`)k
sFr s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
~V5jjx* s1=s10;
j
yE+?4w; s20=0.*s10; %input in waveguide 2
v2^CBKZ+ s30=0.*s10; %input in waveguide 3
>ZT3gp?E s2=s20;
TOs|f8a y s3=s30;
~EymD * p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Cq=c'(cX %energy in waveguide 1
kBkhuKd)V p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
n/-I7Q!;u %energy in waveguide 2
TqC"lO>:Q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
E ^G= %energy in waveguide 3
;%&@^;@k% for m3 = 1:1:M3 % Start space evolution
f#?R!pR s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
DuaOi1Gw s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
+Aq}BjD# s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
; NEHbLH#F sca1 = fftshift(fft(s1)); % Take Fourier transform
2zAS
\Y sca2 = fftshift(fft(s2));
QH eUpJ/^ sca3 = fftshift(fft(s3));
kE1u -EA sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
_ ~r>C sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
4f+Ke*^[RA sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
pAYuOk9n s3 = ifft(fftshift(sc3));
6N ^FJCs s2 = ifft(fftshift(sc2)); % Return to physical space
4 ^
A\w s1 = ifft(fftshift(sc1));
6mZF sB end
y}8j_r p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
L))(g][; p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
S ;
>_9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
e |!i1e! P1=[P1 p1/p10];
Yd9y8Tq J P2=[P2 p2/p10];
[>fE{ ~Y P3=[P3 p3/p10];
5u8 YHv P=[P p*p];
rTcH~s
D` end
S Exd- =G figure(1)
}\B6d\ k plot(P,P1, P,P2, P,P3);
q;U[f6JjE }Q*8QV 转自：
http://blog.163.com/opto_wang/
