计算脉冲在非线性耦合器中演化的Matlab 程序 y} R{A6X) kzMCI)>" % This Matlab script file solves the coupled nonlinear Schrodinger equations of
T4F}MVK % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
%e+hM $Q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
-"UK NB! % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
!LVWggk1 pJ ;J>7Gt %fid=fopen('e21.dat','w');
'(7]jug N = 128; % Number of Fourier modes (Time domain sampling points)
|[)t4A"} M1 =3000; % Total number of space steps
cO.U*UTmX J =100; % Steps between output of space
;@Alr?y T =10; % length of time windows:T*T0
lc,{0$
1< T0=0.1; % input pulse width
Kzb&aOw MN1=0; % initial value for the space output location
dw5.vXL` dt = T/N; % time step
qH: `
O%, n = [-N/2:1:N/2-1]'; % Index
N4}j,{# t = n.*dt;
.DMeW i u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
s7A{<>: u20=u10.*0.0; % input to waveguide 2
be |k"s|6) u1=u10; u2=u20;
MS)# S& U1 = u1;
! k)}p_e U2 = u2; % Compute initial condition; save it in U
BuCU_/H ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
rbHrG<+7zO w=2*pi*n./T;
vRpMZ)e g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
I3uaEv7OZc L=4; % length of evoluation to compare with S. Trillo's paper
%M2.h;9]*\ dz=L/M1; % space step, make sure nonlinear<0.05
mnzamp for m1 = 1:1:M1 % Start space evolution
lbZ,?wm u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
"CapP`: u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
^/47 *vcN5 ca1 = fftshift(fft(u1)); % Take Fourier transform
vv U;55- ca2 = fftshift(fft(u2));
"WdGY*r c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
( \{9W c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
B$1e AwT9 u2 = ifft(fftshift(c2)); % Return to physical space
o3 P`y:& u1 = ifft(fftshift(c1));
d kHcG&) if rem(m1,J) == 0 % Save output every J steps.
>9'G>~P~I= U1 = [U1 u1]; % put solutions in U array
]tA39JK-i U2=[U2 u2];
o7i/~JkTP MN1=[MN1 m1];
%*wJODtB| z1=dz*MN1'; % output location
qAUqlSP5 end
@C k6s end
GNS5v-" H hg=abs(U1').*abs(U1'); % for data write to excel
}L^Yoq] ha=[z1 hg]; % for data write to excel
qL 091P\F t1=[0 t'];
0}2Uj>!i hh=[t1' ha']; % for data write to excel file
j#S>8:
G %dlmwrite('aa',hh,'\t'); % save data in the excel format
c9/w-u~j figure(1)
^n!{ vHz
waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Q^$IlzG7i figure(2)
@C62%fU {5 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
R"Nvnpm C '4u+r aq 非线性超快脉冲耦合的数值方法的Matlab程序 TOdH "aHY] E{ 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。
H0Qpc<Z4/ 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
5V!L~# Z#BwJHh %H75u 6 B(w k $2 % This Matlab script file solves the nonlinear Schrodinger equations
kbJ/7 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
C(Ujx=G+3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@ +h2R % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
QDYS}{A:V QMea2 q|3$ C=1;
8+{WH/}y8 M1=120, % integer for amplitude
^)<>5.%1'' M3=5000; % integer for length of coupler
[X0Wfb}{ N = 512; % Number of Fourier modes (Time domain sampling points)
]`0(^)U & dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
B;XFPQ#b T =40; % length of time:T*T0.
(C*G)Aj7 dt = T/N; % time step
BoYWx^VHx^ n = [-N/2:1:N/2-1]'; % Index
V|zzj[c t = n.*dt;
+Gq h ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
H$au02dpU w=2*pi*n./T;
&>\E
>mJ g1=-i*ww./2;
5|f[evQj<S g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
1,=U^W.G g3=-i*ww./2;
aF2 eGh P1=0;
sJg-FVe2 P2=0;
y?GRxoCD"e P3=1;
^Crl~~Gk` P=0;
/s.sW l for m1=1:M1
dFD0l?0 N p=0.032*m1; %input amplitude
hPF9y@lh s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
$]|fjB#D s1=s10;
km,}7^?F0r s20=0.*s10; %input in waveguide 2
~j}di^<{ s30=0.*s10; %input in waveguide 3
^$f} s,09 s2=s20;
jC qs^`- s3=s30;
[_*% p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
J @C8;] %energy in waveguide 1
XFeHkU`C p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
s`GwRH<# %energy in waveguide 2
@;2,TY>Di p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
J7W ]St r %energy in waveguide 3
L3iY Z>] for m3 = 1:1:M3 % Start space evolution
GV#"2{t
j s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
\_}Y4 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
z1wy@1 o' s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
YbB8D- sca1 = fftshift(fft(s1)); % Take Fourier transform
b/cc\d < sca2 = fftshift(fft(s2));
~f0B u:A) sca3 = fftshift(fft(s3));
[U@#whE O sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
0][PL%3Z sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
m-S 4"!bl sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
wG6>.` : s3 = ifft(fftshift(sc3));
QyQ&xgS s2 = ifft(fftshift(sc2)); % Return to physical space
x~C%Hp*# s1 = ifft(fftshift(sc1));
\72(d end
jR`q y< p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
} md[hi J p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
0G ^73Z p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
J YA$_T P1=[P1 p1/p10];
-:b0fKn P2=[P2 p2/p10];
| YmQO#'' P3=[P3 p3/p10];
(@ @t,\iF P=[P p*p];
<o,]f E[ end
C-' n4AY^ figure(1)
QxG:NN;jW plot(P,P1, P,P2, P,P3);
H4 p N+ ~6L\9B ) 转自：
http://blog.163.com/opto_wang/
