计算脉冲在非线性耦合器中演化的Matlab 程序 zg.'
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% This Matlab script file solves the coupled nonlinear Schrodinger equations of YKJk)%;+w
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of T@U_;v|rf
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 2Y(Phw2%
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 e=o<yf9>Q
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%fid=fopen('e21.dat','w'); z[M LMf[c
N = 128; % Number of Fourier modes (Time domain sampling points) K,&)\r kzD
M1 =3000; % Total number of space steps 9jDV]!N4
J =100; % Steps between output of space L
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T =10; % length of time windows:T*T0 s_hf,QH
T0=0.1; % input pulse width H~i+:X=I
MN1=0; % initial value for the space output location Op" \i
dt = T/N; % time step E
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n = [-N/2:1:N/2-1]'; % Index c+f~>AaI
t = n.*dt; xlp^XT6#
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 8Focs p2
u20=u10.*0.0; % input to waveguide 2 izebQVQO*
u1=u10; u2=u20; W#P)v{K
U1 = u1; Ett%Y*D+J
U2 = u2; % Compute initial condition; save it in U T6=c9f?7
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. B[F x2r`0
w=2*pi*n./T; zy(sekX;
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T gGxgU$`#c
L=4; % length of evoluation to compare with S. Trillo's paper 4'Z=T\:
dz=L/M1; % space step, make sure nonlinear<0.05 |#D3~au
for m1 = 1:1:M1 % Start space evolution +XLy Pj
u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS \zR@FOl`q
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; BKP XXR
ca1 = fftshift(fft(u1)); % Take Fourier transform btkD<1{g
ca2 = fftshift(fft(u2)); \l?\%aqm
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation +;c)GNQ)6:
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift \sEq
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u2 = ifft(fftshift(c2)); % Return to physical space ^ b{0|:
u1 = ifft(fftshift(c1)); e[$=5U~c
if rem(m1,J) == 0 % Save output every J steps. 0.'$U}#b
U1 = [U1 u1]; % put solutions in U array <.HX_z3l
U2=[U2 u2]; (TM1(<j
MN1=[MN1 m1]; N\ChA]Ck
z1=dz*MN1'; % output location =H%c/Jty
end 12U1DEd>-
end =Bcwd7+
hg=abs(U1').*abs(U1'); % for data write to excel #f0J.)M
ha=[z1 hg]; % for data write to excel %D< =6suW
t1=[0 t']; 5<wIJ5t
hh=[t1' ha']; % for data write to excel file y2;uG2IS_g
%dlmwrite('aa',hh,'\t'); % save data in the excel format Qh<_/X?
figure(1) }dQW-U
waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn %JeT,{
figure(2) V|e9G,z~A
waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn =+%QfuK
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非线性超快脉冲耦合的数值方法的Matlab程序 H:Y?(" k
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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。 [`Seh $
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 _CN5,mLNRk
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% This Matlab script file solves the nonlinear Schrodinger equations uDvZ]Q|.
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of -L%tiz`_
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear *`&4<>=n
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Z`y%#B6x.
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M1=120, % integer for amplitude |(G^3+5Uwm
M3=5000; % integer for length of coupler LlOUK2tZ
N = 512; % Number of Fourier modes (Time domain sampling points) *WdnP.'Y
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. {_T?0L
T =40; % length of time:T*T0. )F*;7]f
dt = T/N; % time step ,7-@eZ
n = [-N/2:1:N/2-1]'; % Index D]X&Va
t = n.*dt; $L%gQkz_
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. P7np
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w=2*pi*n./T; "I+71Ce
g1=-i*ww./2; }GI8p* ]o=
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; p?F%a;V3
g3=-i*ww./2; uvC ![j^~
P1=0; kEiWE|
P2=0; _]zm02|
P3=1; 6/e+=W2
P=0; ;U$Fz~rJ
for m1=1:M1 3"afrA
p=0.032*m1; %input amplitude U0>Uqk",
s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 Ot,eAiaX
s1=s10; o+Cd\D69S
s20=0.*s10; %input in waveguide 2 Q#!|h:K
s30=0.*s10; %input in waveguide 3 :+Ti^FF`w
s2=s20; bit@Kv1<C
s3=s30; [C_Dv-d
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); 9?W!E_
%energy in waveguide 1 LWwWxerZ
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); 0P)"_x_
%energy in waveguide 2 yvN;|R
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); e+416
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%energy in waveguide 3 F&pJ faig
for m3 = 1:1:M3 % Start space evolution Rf*cW&}%
s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS h|m>JDxn
s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; CjeAO 2
s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; =VXxQ\{
sca1 = fftshift(fft(s1)); % Take Fourier transform oY Y?`<N#
sca2 = fftshift(fft(s2)); Y243mq-
sca3 = fftshift(fft(s3)); [@K#BFA
sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift 1=NP=ZB
sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Vm6
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sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ZDffR:An
s3 = ifft(fftshift(sc3)); DX|yL!4[
s2 = ifft(fftshift(sc2)); % Return to physical space >2kjd
s1 = ifft(fftshift(sc1)); R8"qDj
end b@9>1d$
p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); [&_c.ti
p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ftr?@^
p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 7Qoy~=E
P1=[P1 p1/p10]; w&U>w@H^
P2=[P2 p2/p10]; uPZ<hG#K
P3=[P3 p3/p10]; r*I u6
P=[P p*p];
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