[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 B&<5VjZ\  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of V~Z)
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 'o*\N%  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear j]`hy"  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 a=x&sz\x  
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%fid=fopen('e21.dat','w'); m-+>h:1b|9  
N = 128;                       % Number of Fourier modes (Time domain sampling points) VS_\bIC  
M1 =3000;              % Total number of space steps ]YfG`0e
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J =100;                % Steps between output of space _qpIdQBo  
T =10;                  % length of time windows:T*T0 j9GKz1
 
T0=0.1;                 % input pulse width .*xO/pn  
MN1=0;                 % initial value for the space output location 7GG`9!l]D  
dt = T/N;                      % time step #3eI4KJ4+l  
n = [-N/2:1:N/2-1]';           % Index mG\9Qkom|  
t = n.*dt;   ;]=@;? 9  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 [eBt Dc*w  
u20=u10.*0.0;                  % input to waveguide 2 R
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u1=u10; u2=u20;                 #7]>ozKm  
U1 = u1;   ="f-I9y  
U2 = u2;                       % Compute initial condition; save it in U vpOGyvI  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 6W3."};  
w=2*pi*n./T; ~E_irzOFP  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T p_e x  
L=4;                           % length of evoluation to compare with S. Trillo's paper /v|b]Ji  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ;=E}PbZt2  
for m1 = 1:1:M1                                    % Start space evolution RBg2iG$8|  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS *CAz_s<  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; C8YStT  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform &gJ@"`r4  
   ca2 = fftshift(fft(u2)); k.Gt}\6zP  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Y5B!*+h  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   SB5qm?pT8<  
   u2 = ifft(fftshift(c2));                        % Return to physical space odJE~\\hw  
   u1 = ifft(fftshift(c1)); Zm|il9y4m  
if rem(m1,J) == 0                                 % Save output every J steps. 1=E}X5  
    U1 = [U1 u1];                                  % put solutions in U array DYC2bs>  
    U2=[U2 u2]; z|Xt'?9&n  
    MN1=[MN1 m1]; ,zH\P+*  
    z1=dz*MN1';                                    % output location ]W%rhppC  
  end !U(KQ:j  
end :D>flZi  
hg=abs(U1').*abs(U1');                             % for data write to excel {ehYE^%N  
ha=[z1 hg];                                        % for data write to excel bNtOqhi  
t1=[0 t']; eb,QT\/G  
hh=[t1' ha'];                                      % for data write to excel file iEy2z+/"^  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format #)#'^MZX  
figure(1) IM[=]j.?  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn I\rjw$V#  
figure(2) `/wXx5n5<  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn A)d0Z6G`  
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非线性超快脉冲耦合的数值方法的Matlab程序 N[O_}_  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   h"}F3E  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 }v?l0Gk(  
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%  This Matlab script file solves the nonlinear Schrodinger equations NcX-*o  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of a{%EHL,F  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 20`XklV  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 vt5>>rl  
W&Xi&[Ux  
C=1;                           rEU1 VvE  
M1=120,                       % integer for amplitude 6Q+VW_~  
M3=5000;                      % integer for length of coupler "/U
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N = 512;                      % Number of Fourier modes (Time domain sampling points) |L-- j  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. zx"0^r}  
T =40;                        % length of time:T*T0. gq~`!tW'  
dt = T/N;                     % time step kjQI=:i=  
n = [-N/2:1:N/2-1]';          % Index tEibxE  
t = n.*dt;   o(t`XE['<  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. CaoQPb*  
w=2*pi*n./T; 5VfpeA`  
g1=-i*ww./2; X\<a|/{V A  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ~wGjr7Wt  
g3=-i*ww./2; 2Y=Q%  
P1=0; HDu|KW$o1  
P2=0; lb"T'}q  
P3=1; .Dr7YquW  
P=0; )_kEy>YscZ  
for m1=1:M1                 *t={9h  
p=0.032*m1;                %input amplitude AJzm/,
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 W^3'9nYU  
s1=s10; jd 8g0^  
s20=0.*s10;                %input in waveguide 2 'XSHl?+q  
s30=0.*s10;                %input in waveguide 3 7FP"]\x  
s2=s20; )%!X,  
s3=s30; mj9]M?]  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   %U1HvmyK  
%energy in waveguide 1 ~i}/
 
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   9@*4^Ks p  
%energy in waveguide 2 A+3=OBpkW0  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   %u]>K(tU  
%energy in waveguide 3 xlW>3'uHfa  
for m3 = 1:1:M3                                    % Start space evolution FOcDBCrOe  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ,-Lv3  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; i l%9j  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; EkN>5).  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform V<REcII.  
   sca2 = fftshift(fft(s2)); ^$lsmF]^  
   sca3 = fftshift(fft(s3)); er!+QD,EM  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   _)#~D*3  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); [|HQfTp$  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ):Ekf2  
   s3 = ifft(fftshift(sc3)); `7',RUj|D  
   s2 = ifft(fftshift(sc2));                       % Return to physical space jqoU;u`  
   s1 = ifft(fftshift(sc1)); HsK52<  
end / pR,l5  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 9x9E+DG#(  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); uQW d1>  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); b55G1w  
   P1=[P1 p1/p10]; %,)Xi  
   P2=[P2 p2/p10]; 8ZO~=e  
   P3=[P3 p3/p10]; j7HOh
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   P=[P p*p]; %E2C4UbY  
end ra\|c>[%  
figure(1) i{>YQ  
plot(P,P1, P,P2, P,P3); WF<*rl  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~