计算脉冲在非线性耦合器中演化的Matlab 程序 KnaQhZ
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% This Matlab script file solves the coupled nonlinear Schrodinger equations of se:]F/
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 4onRO!G,
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear vUk <z*
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 $-Lk,}s.*
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%fid=fopen('e21.dat','w'); }te\)
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N = 128; % Number of Fourier modes (Time domain sampling points) a^hDxeG
M1 =3000; % Total number of space steps S zR7:U
J =100; % Steps between output of space R4.$9_ui
T =10; % length of time windows:T*T0 UA>UW!I
T0=0.1; % input pulse width s5F,*<
MN1=0; % initial value for the space output location T>7$<ulm
dt = T/N; % time step PHU#$LG
n = [-N/2:1:N/2-1]'; % Index dMK|l
t = n.*dt; rvgArFf}]
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 Ikv@}^p 7
u20=u10.*0.0; % input to waveguide 2 }1=V`N(
u1=u10; u2=u20; 7s+3^'
U1 = u1; u,mC`gz
U2 = u2; % Compute initial condition; save it in U b_ +dNoB
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. 2Dgulx5kGZ
w=2*pi*n./T; P~HzNC
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T T PEg>[
L=4; % length of evoluation to compare with S. Trillo's paper =~}\g;K1Q
dz=L/M1; % space step, make sure nonlinear<0.05 Xxhzzm-B
for m1 = 1:1:M1 % Start space evolution TUuw
u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS r%\(5H f
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; =+HMPV6yg7
ca1 = fftshift(fft(u1)); % Take Fourier transform R >f$*T
ca2 = fftshift(fft(u2)); .aTu]i3l_
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation P(D0ru
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift SEu1M}+E
u2 = ifft(fftshift(c2)); % Return to physical space do@`(f3g
u1 = ifft(fftshift(c1)); -T3 z@k
if rem(m1,J) == 0 % Save output every J steps. 5i `q
U1 = [U1 u1]; % put solutions in U array X%w` :c&
U2=[U2 u2]; 0~
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MN1=[MN1 m1]; " |ZC2Zu<
z1=dz*MN1'; % output location rG)K? B~
end hUN]Lm6M
end }QrBN:a$(
hg=abs(U1').*abs(U1'); % for data write to excel X!#rw= Q
ha=[z1 hg]; % for data write to excel &Z3g$R 9
t1=[0 t']; *-0tj~)>
hh=[t1' ha']; % for data write to excel file "O@L
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%dlmwrite('aa',hh,'\t'); % save data in the excel format =pSuyM'
figure(1) .hO) R.
waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn ]U?)_P@}
figure(2) iG*@(
waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn WxO2
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非线性超快脉冲耦合的数值方法的Matlab程序 6?GR+;/
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在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 a
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Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 cXP*?N4Cf
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% This Matlab script file solves the nonlinear Schrodinger equations ^U1@
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% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of YhQ;>Ko
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6_xPk`m
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 a;@G
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C=1; )> >Tj7
M1=120, % integer for amplitude B'sgCU
M3=5000; % integer for length of coupler #Xdj:T<*
N = 512; % Number of Fourier modes (Time domain sampling points) [ H"\<"1o
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. _OR@S%$
T =40; % length of time:T*T0. pHO,][VZ
dt = T/N; % time step J4Yu|E<&
n = [-N/2:1:N/2-1]'; % Index Y'n+,g
t = n.*dt; ;.dyuKlI
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. N`o[iHUj \
w=2*pi*n./T; p@`]9tLP(K
g1=-i*ww./2; M`m-@z
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; CG!7BP\
g3=-i*ww./2; z''ITX)oG
P1=0; :<Z>?x
P2=0; z#DgoA
P3=1; F`C$F!GE
P=0; bm`x;M^M
for m1=1:M1 f&5'1tG
p=0.032*m1; %input amplitude
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s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 VH*4fcT'D
s1=s10; Lt8J^}kwl
s20=0.*s10; %input in waveguide 2 V@%:y tDf
s30=0.*s10; %input in waveguide 3 Obj?, O
s2=s20; #H8% BZyV
s3=s30; jEaU;
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); R H^!7W*
%energy in waveguide 1 qhE1
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p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); :_,oD
%energy in waveguide 2 A.[~}ywH
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); @cc4]>4
%energy in waveguide 3 yAyq-G"sO
for m3 = 1:1:M3 % Start space evolution 4xYW?s(
s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS r0xmDJ@y
s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; LN!e_b
s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; JSf \ApX
sca1 = fftshift(fft(s1)); % Take Fourier transform cUB+fH<B2
sca2 = fftshift(fft(s2)); 3$TU2-x;g
sca3 = fftshift(fft(s3)); #gQaNc?
sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift ~d.Z.AD
sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); K*"Wq:T;B
sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); TAE@KSPvo
s3 = ifft(fftshift(sc3)); \7\7i-Vo
s2 = ifft(fftshift(sc2)); % Return to physical space 8k.<