计算脉冲在非线性耦合器中演化的Matlab 程序 R9E6uz.j x~(y "^ph % This Matlab script file solves the coupled nonlinear Schrodinger equations of
@Y NGxg~*g % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
$O]^Xm3{ @ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
iE +6UK % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4g'}h`kh ] j1
vbk %fid=fopen('e21.dat','w');
TPqvp|~2 N = 128; % Number of Fourier modes (Time domain sampling points)
D?J# u;h~f M1 =3000; % Total number of space steps
!3?~#e{_ J =100; % Steps between output of space
p . aE T =10; % length of time windows:T*T0
Wa}"SqYr h T0=0.1; % input pulse width
>gGi l|I MN1=0; % initial value for the space output location
cS
4T\{B; dt = T/N; % time step
Av[Ud
*~ n = [-N/2:1:N/2-1]'; % Index
UC;= ) t = n.*dt;
}(cY| u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
w?/f Z x u20=u10.*0.0; % input to waveguide 2
$ %;jk u1=u10; u2=u20;
mQnL<0_<f U1 = u1;
t}c v2S U2 = u2; % Compute initial condition; save it in U
fT
x4vlI4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
VX&WlG`wa w=2*pi*n./T;
@ oA0{&G{ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
7>KQRLw L=4; % length of evoluation to compare with S. Trillo's paper
V:QdQ;c dz=L/M1; % space step, make sure nonlinear<0.05
W\a!Q]pV for m1 = 1:1:M1 % Start space evolution
n8Q*
_?Z/ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
AW62~* u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
:Ip~)n9t ca1 = fftshift(fft(u1)); % Take Fourier transform
T&! ZD 2I ca2 = fftshift(fft(u2));
`L;OY 4 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
M(NH9EE c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
2\ ,e u2 = ifft(fftshift(c2)); % Return to physical space
rF' <r~Lw u1 = ifft(fftshift(c1));
fvO;lA>` if rem(m1,J) == 0 % Save output every J steps.
` )]lUvR U1 = [U1 u1]; % put solutions in U array
m.T wgin U2=[U2 u2];
^Yqbj L MN1=[MN1 m1];
+!G4tA$g z1=dz*MN1'; % output location
D|"s E> end
&6Ns7w6*z end
S>(z\`1qm hg=abs(U1').*abs(U1'); % for data write to excel
5W|u5AIw ha=[z1 hg]; % for data write to excel
d~ 3GV(M t1=[0 t'];
%5` r-F hh=[t1' ha']; % for data write to excel file
Hl!1h% %dlmwrite('aa',hh,'\t'); % save data in the excel format
2S'AIuIew figure(1)
8KZ$ F>T]> waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
y>%W;r) figure(2)
]u~Os< waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
|c=d;+ E}Ljo 非线性超快脉冲耦合的数值方法的Matlab程序 7Onk!NH 8b{U
tT 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。
hl* MUD, 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
(2cGHYU3N< bd.j,4^ "Jf4N k"0%' Y % This Matlab script file solves the nonlinear Schrodinger equations
9x4wk*z % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
JXlTN[O % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
)Kxs@F % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
RFh U# ;B*L1'FF%t C=1;
\f6lT3"VN M1=120, % integer for amplitude
<\+Po<)3 j M3=5000; % integer for length of coupler
3e#x)H/dr N = 512; % Number of Fourier modes (Time domain sampling points)
zI1(F67d` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
/7.wQeL9 T =40; % length of time:T*T0.
sYl&Q. \q dt = T/N; % time step
3&O% & n = [-N/2:1:N/2-1]'; % Index
eB)UXOu1 t = n.*dt;
sV]i /B ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
~}epq6L> w=2*pi*n./T;
5%EaX ?0h+ g1=-i*ww./2;
[SKP |`I>I g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
^ b=5 6~[ g3=-i*ww./2;
[^h/(a` P1=0;
MacL3f P2=0;
Ma% E&.ed P3=1;
:8GlyN<E P=0;
e!TG< (S for m1=1:M1
|G[{{qZM5 p=0.032*m1; %input amplitude
Bidqf7v s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
@\#'oIc| s1=s10;
s$K@X ` s20=0.*s10; %input in waveguide 2
!a. 3OpQ s30=0.*s10; %input in waveguide 3
hz&^_ G6` s2=s20;
ZJ;wRd@ s3=s30;
n%7 A;l!{ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
,| $|kO/ %energy in waveguide 1
%Y#[% ~|( p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
BnY\FQ)K %energy in waveguide 2
MBnK&GS p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
|:!E HFr %energy in waveguide 3
Jr Y"J]/ for m3 = 1:1:M3 % Start space evolution
8Sd?b5|G~ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
gEcnn .(S s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
;mCGh~?G s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
8A`p sca1 = fftshift(fft(s1)); % Take Fourier transform
:
OS mr sca2 = fftshift(fft(s2));
; |E! |w sca3 = fftshift(fft(s3));
:< KSf#O sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
w*|= k~z sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
' [7C~r{% sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
u * #-7 s3 = ifft(fftshift(sc3));
w a-_O< s2 = ifft(fftshift(sc2)); % Return to physical space
HYa$EE2 s1 = ifft(fftshift(sc1));
Pf^Ly 97 end
75Q XkJu p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
8u7K$Q p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
,"v)vTt p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
KT]J,b P1=[P1 p1/p10];
'@3a,pl P2=[P2 p2/p10];
b |o`Q7Hj P3=[P3 p3/p10];
-(%ar%~Zd P=[P p*p];
\4]zNV ~x end
>*<6 zQf figure(1)
r1^m#!=B plot(P,P1, P,P2, P,P3);
\ N-|
iq ai<MsQQ:= 转自：
http://blog.163.com/opto_wang/
