[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 )X@Obg  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of !8yw!hA  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of /ZqBO*]  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear e48`cX\E  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 %;yDiQ!+  
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%fid=fopen('e21.dat','w'); -ZFeE[Z  
N = 128;                       % Number of Fourier modes (Time domain sampling points) gYVk5d|8@4  
M1 =3000;              % Total number of space steps sP$bp Z}  
J =100;                % Steps between output of space }ddwL  
T =10;                  % length of time windows:T*T0 AWHB^}!}  
T0=0.1;                 % input pulse width |-4C[5rM  
MN1=0;                 % initial value for the space output location 4r;!b;3  
dt = T/N;                      % time step 4o8uWS{`  
n = [-N/2:1:N/2-1]';           % Index ;F9<Yv  
t = n.*dt;   %ANo^~8  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 u.*@lGVW  
u20=u10.*0.0;                  % input to waveguide 2 g9|B-1[  
u1=u10; u2=u20;                 +5H9mk  
U1 = u1;   K-IXAdx  
U2 = u2;                       % Compute initial condition; save it in U ^8$CpAK]M  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. *(Y
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w=2*pi*n./T; jXvGL  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Y$b4Ga9j  
L=4;                           % length of evoluation to compare with S. Trillo's paper :LBG6J  
dz=L/M1;                       % space step, make sure nonlinear<0.05 drP2%u  
for m1 = 1:1:M1                                    % Start space evolution 1{4d)z UB  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS @iK=1\-2  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; s:lar4>kM  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform _ vVw2HH  
   ca2 = fftshift(fft(u2)); :'?%%P  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation vzJ69%E_  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   e`k6YO  
   u2 = ifft(fftshift(c2));                        % Return to physical space tt%Zwf  
   u1 = ifft(fftshift(c1)); TU$PAwn=  
if rem(m1,J) == 0                                 % Save output every J steps. c[E{9wp v  
    U1 = [U1 u1];                                  % put solutions in U array RR!(,j^M  
    U2=[U2 u2]; y ,
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    MN1=[MN1 m1]; J_YbeZ]  
    z1=dz*MN1';                                    % output location 1MHP#X;|  
  end \}xK$$f2,  
end fiz2544  
hg=abs(U1').*abs(U1');                             % for data write to excel ;8/w'oe*j  
ha=[z1 hg];                                        % for data write to excel #P*%FgROl  
t1=[0 t']; *@o@>  
hh=[t1' ha'];                                      % for data write to excel file 26JP<&%L  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format R~8gw^w![  
figure(1) B!GpD@U  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn z_R^n#A~r  
figure(2) 6TJ5G8z_  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Y(GH/jw  
E@TX>M-&  
非线性超快脉冲耦合的数值方法的Matlab程序 4O_z|K_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。   vF"<r,pg  
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 E0[!jZ:c  
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%  This Matlab script file solves the nonlinear Schrodinger equations jUtrFl  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of .z&V!2zp  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear E9pKR+P  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 KK4>8zGR  
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C=1;                           ~r;da9  
M1=120,                       % integer for amplitude {dvrj<?  
M3=5000;                      % integer for length of coupler ^;+lsEW  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ~K%]9  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. z1}YoCj1  
T =40;                        % length of time:T*T0. [0.>:wT  
dt = T/N;                     % time step uXq?Z@af|f  
n = [-N/2:1:N/2-1]';          % Index fl _k5Q'&p  
t = n.*dt;   J0zudbP  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. yveyAsN`B  
w=2*pi*n./T; hPr*<2mp  
g1=-i*ww./2; N[X%tf\L]F  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 9qD/q?Hh$  
g3=-i*ww./2; hj64E
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P1=0; aGVzg$  
P2=0; >"?HbR9  
P3=1; 8+Al+6d|!  
P=0; ;5^grr@,4  
for m1=1:M1                 `%;nHQ"  
p=0.032*m1;                %input amplitude F7a &-  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 W=M&U  
s1=s10; vLR)B@O,2  
s20=0.*s10;                %input in waveguide 2 f/Km$#xOr  
s30=0.*s10;                %input in waveguide 3 @z"Zj 3ti  
s2=s20; ;OQ-T+(T  
s3=s30; lz\{ X  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   1Uz'=a  
%energy in waveguide 1 vM~/|)^0sW  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   *E0+!  
%energy in waveguide 2 fOiLb.BW  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   C&D]!ZvF  
%energy in waveguide 3 !_E E|#`n  
for m3 = 1:1:M3                                    % Start space evolution L]B]~Tw  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS -cyJjLL*  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; _/ j44q  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; TFb

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   sca1 = fftshift(fft(s1));                       % Take Fourier transform ^!k^=ST1J  
   sca2 = fftshift(fft(s2)); 'j#oMA{0  
   sca3 = fftshift(fft(s3)); dgd&ymRm :  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   v}A] R9TY  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); OP |{R7uC  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); R<LW*8  
   s3 = ifft(fftshift(sc3)); z/ T|  
   s2 = ifft(fftshift(sc2));                       % Return to physical space a8M.EFa:  
   s1 = ifft(fftshift(sc1)); 0K>rc1dy  
end Dn$zwksSs  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); OQ#gQ6;?
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   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); .Y'kDuUu  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); !Y=s_)X  
   P1=[P1 p1/p10]; q9pBS1Ej  
   P2=[P2 p2/p10]; ;w4rwL  
   P3=[P3 p3/p10]; \F,?ptu  
   P=[P p*p]; o"[P++qd  
end z%ljEI"<C  
figure(1) Gcg`Knr  
plot(P,P1, P,P2, P,P3); 7qon:]b4  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~