[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

计算脉冲在非线性耦合器中演化的Matlab 程序 @"H+QVJ@  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Ov)rsi
 
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of % ;2x.  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 3D k W  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 INrUvD/*  
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%fid=fopen('e21.dat','w'); c)M_&?J!5  
N = 128;                       % Number of Fourier modes (Time domain sampling points) SD6xi\8  
M1 =3000;              % Total number of space steps J+LFzl07q  
J =100;                % Steps between output of space 52>?l C  
T =10;                  % length of time windows:T*T0 'wX'}3_/g  
T0=0.1;                 % input pulse width EpCUL@+  
MN1=0;                 % initial value for the space output location x1$tS#lS  
dt = T/N;                      % time step G)?O!(_  
n = [-N/2:1:N/2-1]';           % Index F#Oqa^$(  
t = n.*dt;   8lt P)K4  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 3 $Uv  
u20=u10.*0.0;                  % input to waveguide 2 UPPDs"  
u1=u10; u2=u20;                 5HioxHL  
U1 = u1;   N@^
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U2 = u2;                       % Compute initial condition; save it in U ;EE*#"IJ  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 5Y)!q?#H  
w=2*pi*n./T; #T n~hnW  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T e4ajT  
L=4;                           % length of evoluation to compare with S. Trillo's paper ?PSm) ~Oa  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ]`y4n=L
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for m1 = 1:1:M1                                    % Start space evolution <Dt,FWWkv'  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 6pQ#Zg()vp  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; o_EXbS]C  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform |]]Xee]  
   ca2 = fftshift(fft(u2)); >\$qF  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation abCcZ<=|b  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   t4UKG&[a  
   u2 = ifft(fftshift(c2));                        % Return to physical space M>0=A  
   u1 = ifft(fftshift(c1)); ^C@uP9g  
if rem(m1,J) == 0                                 % Save output every J steps. r+>E`GGQ  
    U1 = [U1 u1];                                  % put solutions in U array U^~K-!0  
    U2=[U2 u2]; W9Bl'e  
    MN1=[MN1 m1]; ho@f}4jhQ3  
    z1=dz*MN1';                                    % output location rG
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  end vBQ5-00YY=  
end ~c :e0}  
hg=abs(U1').*abs(U1');                             % for data write to excel ?U2ed)zzw  
ha=[z1 hg];                                        % for data write to excel ?G
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t1=[0 t']; gV!Eotq  
hh=[t1' ha'];                                      % for data write to excel file co<){5zOT  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format #* 
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figure(1) M{:gc7%  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn < 7zyRm@S  
figure(2) z(>{"t<C  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn QO7> XHn  
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非线性超快脉冲耦合的数值方法的Matlab程序 C_PXh>H]'  
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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 m^O:k"+!  
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%  This Matlab script file solves the nonlinear Schrodinger equations #2I[F  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of V_~}7~ I  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 4G@vO{$  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 l`gRw4/$  
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C=1;                           R?>a UFM  
M1=120,                       % integer for amplitude )dJM  
M3=5000;                      % integer for length of coupler +fAAkO*GP  
N = 512;                      % Number of Fourier modes (Time domain sampling points) x7l)i!/$  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. vf~q%+UqK  
T =40;                        % length of time:T*T0. C\.?3  
dt = T/N;                     % time step FD#?pVyPn^  
n = [-N/2:1:N/2-1]';          % Index +sE81B  
t = n.*dt;   >?b/_O  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. =@binTC4  
w=2*pi*n./T; ~0|~Fg  
g1=-i*ww./2; eOD;@4lR  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; E[nWB"pxE  
g3=-i*ww./2; mv SNKS  
P1=0; X+P& up06  
P2=0; 1b;Aru~l  
P3=1; 5D-xm$8C  
P=0; . ~G>vVb  
for m1=1:M1                 _myam3[W  
p=0.032*m1;                %input amplitude |j^>6nE  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 REoFP;H~  
s1=s10; y= cBpC  
s20=0.*s10;                %input in waveguide 2 @6 gA4h  
s30=0.*s10;                %input in waveguide 3 >Bskw2  
s2=s20; Y$Js5K@F  
s3=s30; X LA  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   5p94b*l  
%energy in waveguide 1 9:fVHynr  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   JF%+T yMe  
%energy in waveguide 2 E} Uy-  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   :8E(pq|1PB  
%energy in waveguide 3 +%?_1bGX>  
for m3 = 1:1:M3                                    % Start space evolution 0}PW
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   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS l0tMdsz  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; n|SsV  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; $62ospR^Y  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 26o68U8&y  
   sca2 = fftshift(fft(s2)); ( y2%G=.j  
   sca3 = fftshift(fft(s3)); H`),PY2  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   1-r1hZ-  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); b,KQG|k  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); sA3 4`ZAa  
   s3 = ifft(fftshift(sc3));
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   s2 = ifft(fftshift(sc2));                       % Return to physical space 2ztP'  
   s1 = ifft(fftshift(sc1)); !(uyqplTk  
end h+,zfVJu  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); lY.FmF}k  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
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   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); PM7*@~.  
   P1=[P1 p1/p10]; `Kpn@Xg
 
   P2=[P2 p2/p10]; ud'r?QDM  
   P3=[P3 p3/p10]; ]*%0CDY6`N  
   P=[P p*p]; iZgv VH  
end k U*
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figure(1) 3PpycJ}  
plot(P,P1, P,P2, P,P3); %$`pD I)  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~