[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 |7
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of UUY-EC7X  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of *<U&DOYV:  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear asW1GZO  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 2ezuP F  
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%fid=fopen('e21.dat','w'); ooIMN =  
N = 128;                       % Number of Fourier modes (Time domain sampling points) .KT+,Y  
M1 =3000;              % Total number of space steps A0rdQmrOL  
J =100;                % Steps between output of space NI(`o8fN  
T =10;                  % length of time windows:T*T0 J6[x(T  
T0=0.1;                 % input pulse width 4_N)1u !  
MN1=0;                 % initial value for the space output location H]=3^g64  
dt = T/N;                      % time step z[v5hhI)4  
n = [-N/2:1:N/2-1]';           % Index _T5~B"*  
t = n.*dt;   9zO3KT2  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ,mYoxEB kl  
u20=u10.*0.0;                  % input to waveguide 2 vo`wYJ3W  
u1=u10; u2=u20;                 ].dTEzL9X  
U1 = u1;   @?Y^=0  
U2 = u2;                       % Compute initial condition; save it in U oAyk  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. {u.V8%8  
w=2*pi*n./T; -t6d`p;dR  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 0dkM72p  
L=4;                           % length of evoluation to compare with S. Trillo's paper X=\#n-*  
dz=L/M1;                       % space step, make sure nonlinear<0.05 4!k={Pd  
for m1 = 1:1:M1                                    % Start space evolution t48(GKF  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS $xu?zd"  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; #]eXI $HP  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform +zs6$OI]V  
   ca2 = fftshift(fft(u2)); `FJnR~d  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Xq>e]#gR  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   iY|YEi8  
   u2 = ifft(fftshift(c2));                        % Return to physical space \;7DS:d@  
   u1 = ifft(fftshift(c1)); b7AuKY{L  
if rem(m1,J) == 0                                 % Save output every J steps. U*&ZQw  
    U1 = [U1 u1];                                  % put solutions in U array 0"2 
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    U2=[U2 u2]; X^|oY]D  
    MN1=[MN1 m1]; o@>c[knJ  
    z1=dz*MN1';                                    % output location WQ5sC[&   
  end Ab2g),;c  
end (v4  
hg=abs(U1').*abs(U1');                             % for data write to excel H;sQ]:.*]  
ha=[z1 hg];                                        % for data write to excel V
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t1=[0 t']; k@8#Byl|  
hh=[t1' ha'];                                      % for data write to excel file 3yKI2en"  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 9uS7G*  
figure(1) Ox~'w0c,f  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ~o/^=:*  
figure(2) #>v7" <  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 'hekCZZ_I  
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非线性超快脉冲耦合的数值方法的Matlab程序 tt^ze|*&t  
m@O\Bi}=}  
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。   g?>AY2f[5  
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 bg HaheU  
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%  This Matlab script file solves the nonlinear Schrodinger equations __ mtZ{  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of sRZ:9de+  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear N6J$z\ P  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 4
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C=1;                           Vd?v"2S(9  
M1=120,                       % integer for amplitude /B!m|)h5~  
M3=5000;                      % integer for length of coupler tH'VV-!MZ  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 13QC
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dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 2YN`:"  
T =40;                        % length of time:T*T0. }=|ZEhtOp  
dt = T/N;                     % time step Oq2H>eW`f  
n = [-N/2:1:N/2-1]';          % Index Qi[D&47XO  
t = n.*dt;   bY2Mw8e%  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. !n{c#HfG  
w=2*pi*n./T; gPwp [  
g1=-i*ww./2; vLS9V/o  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; d_,tXV"z&  
g3=-i*ww./2; 5i^vN"J  
P1=0; %f-<ol  
P2=0; O5{XT]:  
P3=1; 2:N_c\Vi  
P=0; qE{cCS  
for m1=1:M1                 .]e6TFsrO  
p=0.032*m1;                %input amplitude w3w*"M  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 vf yva  
s1=s10; A pjqSz"  
s20=0.*s10;                %input in waveguide 2 0l6iv[qu5w  
s30=0.*s10;                %input in waveguide 3 SNU bY6  
s2=s20; cP2R24th  
s3=s30; yy
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p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   o3yqG#dA  
%energy in waveguide 1 `_'Dj>  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   d8kwW!m+  
%energy in waveguide 2 ]= NYvv>H  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   c_q+
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%energy in waveguide 3 be/1-=m  
for m3 = 1:1:M3                                    % Start space evolution  7q:bBS  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS N1!5J
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; >>bYg  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 5dp#\J@  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 5)zB/Ta<  
   sca2 = fftshift(fft(s2)); ,&?q}M  
   sca3 = fftshift(fft(s3)); W`'|&7~  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   iy82QNe  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); mG~y8nUtp  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); XC1lo4|  
   s3 = ifft(fftshift(sc3)); .:ZXtU  
   s2 = ifft(fftshift(sc2));                       % Return to physical space iFCH$!  
   s1 = ifft(fftshift(sc1)); &&]!+fTZ\(  
end |2<f<k/UT  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); V3W85_*  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); G r|@CZq  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); -NPkN%h  
   P1=[P1 p1/p10]; c2\vG  
   P2=[P2 p2/p10]; Cj1UD;  
   P3=[P3 p3/p10]; C55n  
   P=[P p*p]; DiQkT R  
end e-cb?.WU?  
figure(1) pInWKj[y1  
plot(P,P1, P,P2, P,P3); _*$B|%k   
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~