计算脉冲在非线性耦合器中演化的Matlab 程序 /w|YNDA]j
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% This Matlab script file solves the coupled nonlinear Schrodinger equations of F>&8b^v bn
% soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ka (xU#;
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear >+1bTt/-F
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 h0GXN\xI
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%fid=fopen('e21.dat','w'); tIg_cY_y
N = 128; % Number of Fourier modes (Time domain sampling points) Uc/%4Gx
M1 =3000; % Total number of space steps |i|O9^*%
J =100; % Steps between output of space __a9}m4i7x
T =10; % length of time windows:T*T0 3KqylC&.
T0=0.1; % input pulse width m~}nM |m%
MN1=0; % initial value for the space output location GK)hK-
dt = T/N; % time step hfY2pG9N
n = [-N/2:1:N/2-1]'; % Index [P<oyd@#
t = n.*dt; u}pLO9V"`
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 ].$N@tC
u20=u10.*0.0; % input to waveguide 2 'rSM6j
u1=u10; u2=u20; ^*ZO@GNL
U1 = u1; D;Z\GnD
U2 = u2; % Compute initial condition; save it in U "Aynt_a.
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. #e=[W))
w=2*pi*n./T; B${Q Y)t
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T KjhOz%Yt[o
L=4; % length of evoluation to compare with S. Trillo's paper a^,Xm(Wb}
dz=L/M1; % space step, make sure nonlinear<0.05 ETmfy}V8
for m1 = 1:1:M1 % Start space evolution i#
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u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS Er{yQIi0L
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; j_k!9"bt
ca1 = fftshift(fft(u1)); % Take Fourier transform x]F:~(P
ca2 = fftshift(fft(u2)); #
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c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation m~2PpO
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift gI[xOK#
u2 = ifft(fftshift(c2)); % Return to physical space W &*0F~
u1 = ifft(fftshift(c1)); z+;+c$X
if rem(m1,J) == 0 % Save output every J steps. /:B!hvpw
U1 = [U1 u1]; % put solutions in U array $[H3O(B0*
U2=[U2 u2]; R+P1 +5
MN1=[MN1 m1]; SoCa_9*X
z1=dz*MN1'; % output location xw`Pq6
end Qv#]T,
end gVb;sk^
hg=abs(U1').*abs(U1'); % for data write to excel aK'BC>uFI
ha=[z1 hg]; % for data write to excel ?xIwQd0
t1=[0 t']; y<kW2<?
hh=[t1' ha']; % for data write to excel file orJN#0v4
%dlmwrite('aa',hh,'\t'); % save data in the excel format E-CZk_K9
figure(1) }s? 9Hnqa
waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn li(g?|AD
figure(2) U4Il1|
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waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn Zhf+u
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非线性超快脉冲耦合的数值方法的Matlab程序 3b~k)t4R
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在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 |
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Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 :W^
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% This Matlab script file solves the nonlinear Schrodinger equations ~~z}yCl
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Db@$'
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear |BN^5mqP6
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 .O@T#0&=_
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C=1; ]U82A**n
M1=120, % integer for amplitude 4'[/gMUkw
M3=5000; % integer for length of coupler 8!sl) R
N = 512; % Number of Fourier modes (Time domain sampling points) }Dp/K4
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. ^i:%0"[*^i
T =40; % length of time:T*T0. /d*d'3{c
dt = T/N; % time step ,Tjc\;~%
n = [-N/2:1:N/2-1]'; % Index OF-$*
t = n.*dt; "=@X>jUc
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ^-Bx zOp
w=2*pi*n./T; q-}qrg
g1=-i*ww./2; B^nE^"b
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; d#NG]V/
g3=-i*ww./2; ^\KZE|^3@
P1=0; WS6'R
P2=0; NH~\kV
P3=1; muc6gwBp
P=0; l$
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for m1=1:M1 >cJf D9-<h
p=0.032*m1; %input amplitude Yv>kToa\^
s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 (l}W\iB'd
s1=s10; F!ZE4S_
s20=0.*s10; %input in waveguide 2 ~Z-o2+xA
s30=0.*s10; %input in waveguide 3 Qh3BI?GZ'3
s2=s20; UU'0WIbY6
s3=s30; juIi-*R!
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); _Oc5g5_{
%energy in waveguide 1 _Fkz^B*
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); Kjzo>fIC{
%energy in waveguide 2 =S#9\W&