计算脉冲在非线性耦合器中演化的Matlab 程序 Lc!%
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% This Matlab script file solves the coupled nonlinear Schrodinger equations of $UAmUQg)}_
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of %SL'X`j
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear iXt >!f*
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 W~J@v@..4
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%fid=fopen('e21.dat','w'); E4aCL#}D
N = 128; % Number of Fourier modes (Time domain sampling points) Q"KD O-t
M1 =3000; % Total number of space steps PK@hf[YHe
J =100; % Steps between output of space L<encPJt
T =10; % length of time windows:T*T0 F'DO46
T0=0.1; % input pulse width 0!YB.=\{_q
MN1=0; % initial value for the space output location xJ)hGPrAl
dt = T/N; % time step C3^QNhv
n = [-N/2:1:N/2-1]'; % Index A"8`5qa
t = n.*dt; #8G(r9
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 ~{hcJ:bI
u20=u10.*0.0; % input to waveguide 2 /pZ]:.A
u1=u10; u2=u20; b/:&iG;
U1 = u1; ^b=9{.5
U2 = u2; % Compute initial condition; save it in U 1H{M0e
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. Z> jk\[
w=2*pi*n./T; ,rT62w*e
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T M/XxiF
L=4; % length of evoluation to compare with S. Trillo's paper vq|o}6Et
dz=L/M1; % space step, make sure nonlinear<0.05 lL.3$Rp;
for m1 = 1:1:M1 % Start space evolution 5_@ u Be~
u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS *Y'@|xf*
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; I6d4<#Q@L
ca1 = fftshift(fft(u1)); % Take Fourier transform #E%0 o
ca2 = fftshift(fft(u2)); A`x_M!m
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation fX=o,=-f
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift [hE0 9W
u2 = ifft(fftshift(c2)); % Return to physical space pZ?7'+u$L
u1 = ifft(fftshift(c1)); [m3[plwe
if rem(m1,J) == 0 % Save output every J steps. 4vi P lO
U1 = [U1 u1]; % put solutions in U array 5|>FM&
U2=[U2 u2]; (he cvJ
MN1=[MN1 m1]; j3`#v3
z1=dz*MN1'; % output location Nf(Np1?;c
end dGf:0xE"
end WVUa:_5{
hg=abs(U1').*abs(U1'); % for data write to excel Y;ytm
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ha=[z1 hg]; % for data write to excel ,;LxFS5\
t1=[0 t']; B -XM(Cj
hh=[t1' ha']; % for data write to excel file bkfwsYZx
%dlmwrite('aa',hh,'\t'); % save data in the excel format
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figure(1) ;fLYO6
waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn i`-,=RJ
figure(2) #p@8m_g
waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn "L'0"
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非线性超快脉冲耦合的数值方法的Matlab程序 UruD&=AMK
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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。 n\8;4]n
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 =SJwCT0;
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% This Matlab script file solves the nonlinear Schrodinger equations 9aYDi)
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of tHlKo0S$0
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear bvY'=
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 : tKa1vL
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C=1; <xOv0B
M1=120, % integer for amplitude thWQU"z4
M3=5000; % integer for length of coupler ;Ml??B]C
N = 512; % Number of Fourier modes (Time domain sampling points) >_3+s~
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. $F V!HD
T =40; % length of time:T*T0.
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dt = T/N; % time step kkfwICBI
n = [-N/2:1:N/2-1]'; % Index Z|&Y1k-h
t = n.*dt; 9Yih%d,
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ;4DqtR"7Y
w=2*pi*n./T; "YLH]9"=
g1=-i*ww./2; Xq"@Z
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; =Kdd+g!
g3=-i*ww./2; H]v"_!(\
P1=0; tEEeek(!
P2=0; o(iv=(o
P3=1; |~Q`DdkX
P=0; lLD-QO}/
for m1=1:M1 VT.BHZ
p=0.032*m1; %input amplitude <