计算脉冲在非线性耦合器中演化的Matlab 程序 &r5&6p
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% This Matlab script file solves the coupled nonlinear Schrodinger equations of qr<-eJf
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of FVvv
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 8Izn'>"
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 4EaSg#
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%fid=fopen('e21.dat','w'); [~Z'xY
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N = 128; % Number of Fourier modes (Time domain sampling points) ,YAPCj
M1 =3000; % Total number of space steps 5kRwSOG%'
J =100; % Steps between output of space ]%WD} 4e
T =10; % length of time windows:T*T0 GDNh?R
T0=0.1; % input pulse width a
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MN1=0; % initial value for the space output location S1x.pLHj8
dt = T/N; % time step B~'VDOG$Z
n = [-N/2:1:N/2-1]'; % Index buxI-wv
t = n.*dt; <?=mLOo=
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 ^R8U-V8:
u20=u10.*0.0; % input to waveguide 2 O[5_9W
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u1=u10; u2=u20; pJ)+}vascR
U1 = u1; {YO%JTQ
U2 = u2; % Compute initial condition; save it in U uZ=UBir
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. jU3;jm.)
w=2*pi*n./T; XeIUdg4>R
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 6|"!sW`%N
L=4; % length of evoluation to compare with S. Trillo's paper b[&,%Sm+6
dz=L/M1; % space step, make sure nonlinear<0.05 U`8^N.Snrp
for m1 = 1:1:M1 % Start space evolution I]WeZ,E
u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS 7/U<\(V!g
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; JtrDZ;^@
ca1 = fftshift(fft(u1)); % Take Fourier transform "Wn?8vR
ca2 = fftshift(fft(u2)); zw%n!wc_\
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation +{=_|3(
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift aJa^~*N/Aa
u2 = ifft(fftshift(c2)); % Return to physical space Kt!IyIa;Ht
u1 = ifft(fftshift(c1)); HHu7{,
if rem(m1,J) == 0 % Save output every J steps. 9Sj:nn^/u
U1 = [U1 u1]; % put solutions in U array lu@>?,<
U2=[U2 u2]; ek;&<Z_ ]
MN1=[MN1 m1]; ah!O&ECh
z1=dz*MN1'; % output location 5[j!\d}U
end rO?x/{;ai
end |q.:hWYFpM
hg=abs(U1').*abs(U1'); % for data write to excel mZ0oa-Iy
ha=[z1 hg]; % for data write to excel ;MRC~F=
t1=[0 t']; pJ*#aH[ySP
hh=[t1' ha']; % for data write to excel file :?:j$
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%dlmwrite('aa',hh,'\t'); % save data in the excel format v<J;S9u=
figure(1) gt t$O
waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn N;`[R>Z~
figure(2) g0:4zeL
waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn !qw=I(
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非线性超快脉冲耦合的数值方法的Matlab程序 :!iPn%
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在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 Pq J*
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 c%LB|(@j{
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% This Matlab script file solves the nonlinear Schrodinger equations HT,kx
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of g=YiR/O1QN
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ,I&0#+}n
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 <
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C=1; -ynLuq#1A
M1=120, % integer for amplitude C}P
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M3=5000; % integer for length of coupler T;[c<gc/
N = 512; % Number of Fourier modes (Time domain sampling points) ~h^}W$pO
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. > v!c\
T =40; % length of time:T*T0. %Rsf6rJ
dt = T/N; % time step R5;eR(24G
n = [-N/2:1:N/2-1]'; % Index LI|HET_
t = n.*dt; Nj-rZ%&
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. lQ<n
dt~
w=2*pi*n./T; hHl-;%#
g1=-i*ww./2; ocuVDC
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; B{o\RNU
g3=-i*ww./2; nk3<]u
P1=0; +l?ro[#6&.
P2=0; ,f0g|5yDf
P3=1; \y )4`A
P=0; @oc%4~zl
for m1=1:M1 E e\-q
p=0.032*m1; %input amplitude +j: Ld(
s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 KJ^GUqVl
s1=s10; Ufe
s20=0.*s10; %input in waveguide 2 rUpAiZfz >
s30=0.*s10; %input in waveguide 3 %V1T!<
s2=s20; vgW1hWmHJ
s3=s30; (`y|AOs
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); I.0P7eA-
%energy in waveguide 1 W]}V<S$
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); = 4WZr
%energy in waveguide 2 kmr
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); "gikX/Co=
%energy in waveguide 3 -zLI!F 0
for m3 = 1:1:M3 % Start space evolution G1^!e j
s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS L8tLW09
s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
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s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 8Pdnw/W
sca1 = fftshift(fft(s1)); % Take Fourier transform DD$Pr&~=
sca2 = fftshift(fft(s2)); cASHgm
sca3 = fftshift(fft(s3)); ftH%, /,
sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift "sx&