[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 8<o(z'&y  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of AvwX 2?tc  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of P--#5W;^oB  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ei"FN3Rm  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 1,/oS&?E  
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%fid=fopen('e21.dat','w'); ^o{O5&i]  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Axcm~!uf  
M1 =3000;              % Total number of space steps :xA'X+d/'  
J =100;                % Steps between output of space >Qi2;t~G  
T =10;                  % length of time windows:T*T0 'Kq%tM26!  
T0=0.1;                 % input pulse width {:"bX~<^  
MN1=0;                 % initial value for the space output location LsmC/+7r$1  
dt = T/N;                      % time step YlYTH_L>E  
n = [-N/2:1:N/2-1]';           % Index phNv^R+  
t = n.*dt;   v3[ 2!UXq  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 1ptPey  
u20=u10.*0.0;                  % input to waveguide 2 EBn7waBS  
u1=u10; u2=u20;                 S4\T (  
U1 = u1;   [#.QDe  
U2 = u2;                       % Compute initial condition; save it in U d6Z;\f7[  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. P!-9cd1C,  
w=2*pi*n./T; N"
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g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T uh GL1{  
L=4;                           % length of evoluation to compare with S. Trillo's paper | 0&~fY  
dz=L/M1;                       % space step, make sure nonlinear<0.05 , n+dB2\  
for m1 = 1:1:M1                                    % Start space evolution sqkPC_;A  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS toP7b  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; $
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   ca1 = fftshift(fft(u1));                        % Take Fourier transform PB`94W  
   ca2 = fftshift(fft(u2)); X09&S4  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation gXF.e.uU  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   PsTwJLY   
   u2 = ifft(fftshift(c2));                        % Return to physical space x&kF;UC  
   u1 = ifft(fftshift(c1)); p( z.[  
if rem(m1,J) == 0                                 % Save output every J steps. 0uj3kr?cv  
    U1 = [U1 u1];                                  % put solutions in U array C^uXJ~8  
    U2=[U2 u2]; yJ?4B?p(  
    MN1=[MN1 m1]; x=9drKIw>  
    z1=dz*MN1';                                    % output location -()CgtSR  
  end eE7+fMP{  
end oo/#]a  
hg=abs(U1').*abs(U1');                             % for data write to excel _RAPXU~ 6-  
ha=[z1 hg];                                        % for data write to excel )WD<Q x&  
t1=[0 t']; Xo'_|-N+  
hh=[t1' ha'];                                      % for data write to excel file 5I@< 6S&X  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format -l^u1z
 
figure(1) ]r|X[9  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn LB-4
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figure(2) t.3b\RV[  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn mgg/
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非线性超快脉冲耦合的数值方法的Matlab程序 8*lVO2  
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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。   +$P0&YaQ  
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 h19c*,0z!  
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%  This Matlab script file solves the nonlinear Schrodinger equations =%p0rz|b  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of \y{C>!WX4  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear s<aJ pi{n4  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Lxs  
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C=1;                           ;QS-a  
M1=120,                       % integer for amplitude /u5MAl.<[  
M3=5000;                      % integer for length of coupler fgq#Oi}  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 
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dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. R9^Vk*`gFU  
T =40;                        % length of time:T*T0. 7]62=p2R  
dt = T/N;                     % time step M2{{B^*$6  
n = [-N/2:1:N/2-1]';          % Index 6gNsh  
t = n.*dt;   3+0$=ef  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. h#B%'9r  
w=2*pi*n./T; [a`89'"z  
g1=-i*ww./2; A+_361KH  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Ic P]EgB  
g3=-i*ww./2; X=8y$Yy  
P1=0; UXvUU^k"v  
P2=0; H)ud?vB6  
P3=1; I& DEF*  
P=0; ]-
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for m1=1:M1                 RNiFLD%5  
p=0.032*m1;                %input amplitude w9G (^jS6  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Rq|7$O5  
s1=s10; WRe9ki=R  
s20=0.*s10;                %input in waveguide 2 `O5wM\Z  
s30=0.*s10;                %input in waveguide 3 @l41'?m  
s2=s20; j KGfm9|zj  
s3=s30; I r]#u]Ap  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));    At@H  
%energy in waveguide 1 Y{ijSOl3  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   gY|f[M|  
%energy in waveguide 2 UP'~D]J  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Y23- Im  
%energy in waveguide 3 *eK\W00  
for m3 = 1:1:M3                                    % Start space evolution 0}$Zr*|;Y  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS >g+yw1nC  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; VKqIFM1b  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; }OL?k/w  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform o<cg9  
   sca2 = fftshift(fft(s2)); Pqu]?X  
   sca3 = fftshift(fft(s3)); $KHw=<:)/  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   LDc?/ Z1  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); C9OEB6  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); +Nn $  
   s3 = ifft(fftshift(sc3)); l!qhK'']V"  
   s2 = ifft(fftshift(sc2));                       % Return to physical space jlXzfDT  
   s1 = ifft(fftshift(sc1)); `ECY:3"$KA  
end RUco3fZ   
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); W T~UEK'  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 2@~.FBby7@  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 4}.PQ{  
   P1=[P1 p1/p10]; /<C}v~r  
   P2=[P2 p2/p10]; P|j|0o,8p  
   P3=[P3 p3/p10]; S#Q0aGj  
   P=[P p*p]; *hWpJEV  
end *@)0TL(03  
figure(1) .Q!_.LX  
plot(P,P1, P,P2, P,P3); [`J91=  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~