计算脉冲在非线性耦合器中演化的Matlab 程序 bw P=f.
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% This Matlab script file solves the coupled nonlinear Schrodinger equations of v1OVrk>s>
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of >3uNh:|>/
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Qo#]Lo> \g
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 BIWe Hx
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%fid=fopen('e21.dat','w'); |UXSUP
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N = 128; % Number of Fourier modes (Time domain sampling points) [I
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M1 =3000; % Total number of space steps WywS1viD
J =100; % Steps between output of space 9eMle?pF
T =10; % length of time windows:T*T0 %10ONe}
T0=0.1; % input pulse width h3?>jE=H
MN1=0; % initial value for the space output location (s3k2Z
dt = T/N; % time step GTdoUSUq
n = [-N/2:1:N/2-1]'; % Index HOP*QX8C%
t = n.*dt; )^ah, ;(
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 B)JMughq_
u20=u10.*0.0; % input to waveguide 2 5kiW@{m
u1=u10; u2=u20; $tmdE)"&
U1 = u1; vE:*{G;Y
U2 = u2; % Compute initial condition; save it in U uHg q"e
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. 9J3fiA_
w=2*pi*n./T; >yC=@Uq+
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T d_!Z /M,
L=4; % length of evoluation to compare with S. Trillo's paper W+ S~__K
dz=L/M1; % space step, make sure nonlinear<0.05 G4cgY|71
for m1 = 1:1:M1 % Start space evolution i>Q!5
u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS ;'7(gAE
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; `B)@
ca1 = fftshift(fft(u1)); % Take Fourier transform aK_5@8+ZD
ca2 = fftshift(fft(u2)); YYe G9yR
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation m/=nz.
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift :$k*y%Z*N&
u2 = ifft(fftshift(c2)); % Return to physical space oYqHl1cs
u1 = ifft(fftshift(c1)); CP7dn/
if rem(m1,J) == 0 % Save output every J steps. ]fM|cN8(zM
U1 = [U1 u1]; % put solutions in U array E4X6f
U2=[U2 u2]; "-Q+!byh
MN1=[MN1 m1]; AF'<
z1=dz*MN1'; % output location q1}!O kr"2
end Q~,Mzt"}W
end f^F;`;z
hg=abs(U1').*abs(U1'); % for data write to excel ALMsF2H
ha=[z1 hg]; % for data write to excel |+nmOi,z
t1=[0 t']; [}L~zn6>?a
hh=[t1' ha']; % for data write to excel file &QHJ%c
%dlmwrite('aa',hh,'\t'); % save data in the excel format I C
figure(1) gm9*z.S\'
waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn Uy?jVPL
figure(2) meX2Y;
waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn QG5WsuT
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非线性超快脉冲耦合的数值方法的Matlab程序 e*:K79y
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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。 (]]hSkE
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 $.`o
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% This Matlab script file solves the nonlinear Schrodinger equations TLwxP"
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of &;@L]
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% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +z;*r8d<X
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 :iE b^F}
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C=1; UoT`/.
M1=120, % integer for amplitude :HY$x
M3=5000; % integer for length of coupler :&BPKqKp
N = 512; % Number of Fourier modes (Time domain sampling points) v=llg ^
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. t1 3V>9to
T =40; % length of time:T*T0. 1:-'euA"
dt = T/N; % time step s$M(-"mg
n = [-N/2:1:N/2-1]'; % Index !ho^:}m
t = n.*dt; ] ?DU8
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. B>2R-pa4~
w=2*pi*n./T; '< Zm>L&
g1=-i*ww./2; noWF0+%
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; _b&|0j:Ud
g3=-i*ww./2; <C`bf$ak
P1=0; !rnjmc
P2=0; hP6f
P3=1; ]1
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P=0; # h;
for m1=1:M1 2`=jKt
p=0.032*m1; %input amplitude rq%]CsRY5
s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 !Tnjha*
s1=s10; wps/{h,
s20=0.*s10; %input in waveguide 2 }_+XN"}C
s30=0.*s10; %input in waveguide 3 5 ^{~xOM5
s2=s20; =$'>VPQ
s3=s30; @O#!W]6NT6
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); B!RfPk1B<*
%energy in waveguide 1 e;.,x 5+
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); l(>6Yq
%energy in waveguide 2 ](r}`u%}y
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); ~5HkDtI)
%energy in waveguide 3 JQQyl: =
for m3 = 1:1:M3 % Start space evolution 6"-$WUlg
s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS xFu ,e
s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ?|M-0{
s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; _}R$h=YD
sca1 = fftshift(fft(s1)); % Take Fourier transform N3G9o`k
sca2 = fftshift(fft(s2)); _U~R
sca3 = fftshift(fft(s3)); H{}&|;0
sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift A?YYR%o%'
sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Clf$EX;~
sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); vXKL<