计算脉冲在非线性耦合器中演化的Matlab 程序 o7gY j\ D.[h`Hkc % This Matlab script file solves the coupled nonlinear Schrodinger equations of
/Pbytu);ds % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
BE0Ov{' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
(-}:'5 |Yj % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
K#"J8h; x `!Z0 ; qk %fid=fopen('e21.dat','w');
EF>vu+YK N = 128; % Number of Fourier modes (Time domain sampling points)
i2+r#Hw#5R M1 =3000; % Total number of space steps
\eF _Xk[ J =100; % Steps between output of space
#}PQ !gZ T =10; % length of time windows:T*T0
A&?8 r c T0=0.1; % input pulse width
5taR[ukM MN1=0; % initial value for the space output location
R"wBDWs dt = T/N; % time step
uOQ!av2"Rf n = [-N/2:1:N/2-1]'; % Index
*|gY7Av* t = n.*dt;
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9|1 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
|~K 5 ] u20=u10.*0.0; % input to waveguide 2
Z Zs@P#] u1=u10; u2=u20;
5VS};&f U1 = u1;
/M : 7 U2 = u2; % Compute initial condition; save it in U
^cU mLzM ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
M2kvj'WWq w=2*pi*n./T;
, 59G6o g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
k!Ym<RD%N L=4; % length of evoluation to compare with S. Trillo's paper
| 2Vhj<6 dz=L/M1; % space step, make sure nonlinear<0.05
cp:U@Nh( for m1 = 1:1:M1 % Start space evolution
.B+Bl/ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
%K`th&331 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
}s7@0#j@a ca1 = fftshift(fft(u1)); % Take Fourier transform
XnwVK ca2 = fftshift(fft(u2));
adcH3 rV c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
+TZVx(Z&A c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
@~z4GTF 9i u2 = ifft(fftshift(c2)); % Return to physical space
~hZr1hT6L u1 = ifft(fftshift(c1));
*b}/fG)XZ if rem(m1,J) == 0 % Save output every J steps.
3 < A ? U1 = [U1 u1]; % put solutions in U array
"u.'JE;j U2=[U2 u2];
sSL V R^ MN1=[MN1 m1];
!V'~<& z1=dz*MN1'; % output location
h]Y,gya[yk end
q90
~)n? end
bMA0#e2 hg=abs(U1').*abs(U1'); % for data write to excel
&wX568o ha=[z1 hg]; % for data write to excel
~W2Od2p ! t1=[0 t'];
s||c#+j"8 hh=[t1' ha']; % for data write to excel file
.rw a=IW %dlmwrite('aa',hh,'\t'); % save data in the excel format
{'-^CoR figure(1)
S`Xx('!/| waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
b$eN]L figure(2)
~eyZH8& waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Ak dx1h, c(kYCVc 非线性超快脉冲耦合的数值方法的Matlab程序 {/|tVc63 OcE,E6LD 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。
U>i}C _7g 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
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E ! J'E ?Z 0 :anR/ FvJkb!5*e_ % This Matlab script file solves the nonlinear Schrodinger equations
)GKY#O09x9 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
JLbmh1' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
NY
GWA4 L % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]Pl Ly:( 7<*,O&![ | C=1;
^H!45ph?Jc M1=120, % integer for amplitude
K8Jsh F Ie M3=5000; % integer for length of coupler
g5 ;Ig N = 512; % Number of Fourier modes (Time domain sampling points)
Z et80|q dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
":_~(?1+ T =40; % length of time:T*T0.
_]zH4o<p dt = T/N; % time step
ydTd .` n = [-N/2:1:N/2-1]'; % Index
7.*Mmx ~]= t = n.*dt;
d3 ]<'B:nb ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Ftdx+\O_i& w=2*pi*n./T;
2xBYJoF( g1=-i*ww./2;
Ck:+F+7_v g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
aM4-quaG] g3=-i*ww./2;
,YBe|3 P1=0;
FOAXm4" P2=0;
%l3f . P3=1;
/?1^&a P=0;
_/J`v`}G for m1=1:M1
Ltk-1zhI p=0.032*m1; %input amplitude
6@ ;sOiN+ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
vO)]~AiB s1=s10;
! mZWd' s20=0.*s10; %input in waveguide 2
tZY 6{,K%4 s30=0.*s10; %input in waveguide 3
fizL_`uMqb s2=s20;
T|2v1Vj s3=s30;
RB 9ZaL\ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
K 8W99:v %energy in waveguide 1
2v<O} p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
6!C>J#T %energy in waveguide 2
%us# p|Ya p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
0 _N.s5~N %energy in waveguide 3
-'
=?Hs. for m3 = 1:1:M3 % Start space evolution
q8}he~a s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
h!7Lvh`o s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
tC5>K9Ed s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
zJ_y"bt sca1 = fftshift(fft(s1)); % Take Fourier transform
')TS'p,n sca2 = fftshift(fft(s2));
s`|KT&r sca3 = fftshift(fft(s3));
q<K/q"0-l sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
=z4J[8bb sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
)|GYxG;8C sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
rY M@ e s3 = ifft(fftshift(sc3));
M }$Td_g s2 = ifft(fftshift(sc2)); % Return to physical space
,F n-SrB: s1 = ifft(fftshift(sc1));
"|BSGV!8 end
buDz]ec
b p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
\ x|8 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Q)=2 %X p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
TPYh<p# P1=[P1 p1/p10];
U_RWqKL P2=[P2 p2/p10];
p*U!94Pb P3=[P3 p3/p10];
^I{/j 'b& P=[P p*p];
72vp6/;) end
/I:&P Pff figure(1)
[{:
l? plot(P,P1, P,P2, P,P3);
-@XOe&q Lf`<4 P 转自：
http://blog.163.com/opto_wang/
