[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 &Z
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of ;B7>/q;g  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of v+\E%H  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear }$b/g  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 h IGa);g  
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%fid=fopen('e21.dat','w'); Tp9LBF  
N = 128;                       % Number of Fourier modes (Time domain sampling points) / {A]('t  
M1 =3000;              % Total number of space steps AKS(WNGEp  
J =100;                % Steps between output of space 2[WQq)\  
T =10;                  % length of time windows:T*T0 D,X$66T ^  
T0=0.1;                 % input pulse width ']qC,;2  
MN1=0;                 % initial value for the space output location \f+R!  
dt = T/N;                      % time step B$7lL
  
n = [-N/2:1:N/2-1]';           % Index ag] nVE/  
t = n.*dt;   wv1?v_4  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 <,LeFy\zW  
u20=u10.*0.0;                  % input to waveguide 2 !Dz:6r  
u1=u10; u2=u20;                 <q_H 3|  
U1 = u1;   z9VQsC'K  
U2 = u2;                       % Compute initial condition; save it in U 3Hq0\Y"Y  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. xvgIYc{  
w=2*pi*n./T; eNXpRvY  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 1Ce:<.99B  
L=4;                           % length of evoluation to compare with S. Trillo's paper S;CT:kG6Y{  
dz=L/M1;                       % space step, make sure nonlinear<0.05 mNV4"lNR  
for m1 = 1:1:M1                                    % Start space evolution X-t4irZ)  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Ir]b.6B  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; zO!`sPP  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform u<+;]8[o  
   ca2 = fftshift(fft(u2)); 0}aJCJ9sx=  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 4h(aTbHaQ  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   NMOTWA}2  
   u2 = ifft(fftshift(c2));                        % Return to physical space /Fk0j
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   u1 = ifft(fftshift(c1)); +[*UC"  
if rem(m1,J) == 0                                 % Save output every J steps. 60hf)er  
    U1 = [U1 u1];                                  % put solutions in U array ;1"K79  
    U2=[U2 u2]; 8fdOV&&D~i  
    MN1=[MN1 m1]; tl#hCy  
    z1=dz*MN1';                                    % output location J,IOp-  
  end ytJ |jgp'  
end jkfI,T  
hg=abs(U1').*abs(U1');                             % for data write to excel gAR];(*  
ha=[z1 hg];                                        % for data write to excel FxD
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t1=[0 t']; Th"7p:SE?  
hh=[t1' ha'];                                      % for data write to excel file qHvW{0E  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format %S@XY3jZY  
figure(1) {5*+  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn sX@e1*YE_  
figure(2) gzw[^d  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn o6{XT.z5qx  

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非线性超快脉冲耦合的数值方法的Matlab程序 +K+ == mO&  
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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。   SqEO ]~  
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 :?lSa6de  
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%  This Matlab script file solves the nonlinear Schrodinger equations m.lNKIknQ  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Xf#uK\f  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear .%
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 sYXVSNonm  
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C=1;                           S$V'_  
M1=120,                       % integer for amplitude KX*e2 /0  
M3=5000;                      % integer for length of coupler <Qwi 0$  
N = 512;                      % Number of Fourier modes (Time domain sampling points) p%j@2U  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. UY>{e>/H9  
T =40;                        % length of time:T*T0. ULsz<Hj  
dt = T/N;                     % time step ]jM D'vg^b  
n = [-N/2:1:N/2-1]';          % Index pvcf_w`n
 
t = n.*dt;   Ndx='j0  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. r Cmqq/hZ  
w=2*pi*n./T; >R.~'A/$F  
g1=-i*ww./2; d{DlW |_  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ~lQ]PKJ"  
g3=-i*ww./2; \7W {/v4^  
P1=0; Z73 ysn}  
P2=0; hWuq  
P3=1; GfVMj7{  
P=0; /GCSC8T  
for m1=1:M1                 Be-gGJG  
p=0.032*m1;                %input amplitude I8?egDkk  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 _"z#I CT(  
s1=s10; y*_g1q$  
s20=0.*s10;                %input in waveguide 2 EEF}Wf$f  
s30=0.*s10;                %input in waveguide 3 #r0A<+t{T  
s2=s20; Vd|/]Zj  
s3=s30; w6Ue5Ix,!  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   \QYs(nm?k  
%energy in waveguide 1 'O2{0  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   RU[{!E  
%energy in waveguide 2 q-p4k`]  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   +}z T][9w  
%energy in waveguide 3 '0?5K0 2(  
for m3 = 1:1:M3                                    % Start space evolution NW^}u~-f  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS W5sVQ`S-  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; w)3LYF  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; R-Uj\M>  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform cj5pI?@e)  
   sca2 = fftshift(fft(s2)); Z;lE-`Z*(F  
   sca3 = fftshift(fft(s3)); {"s9A&  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   u;y1leG  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); TS@EE&Wq  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); D*_ F@}=  
   s3 = ifft(fftshift(sc3)); vO <;Gnh~  
   s2 = ifft(fftshift(sc2));                       % Return to physical space bQ_i&t\yzB  
   s1 = ifft(fftshift(sc1)); *:)#'cenI  
end gTiDV{Ip  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); gM_Z/$  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); qCIZW  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); &>sG xK  
   P1=[P1 p1/p10]; .viA+V  
   P2=[P2 p2/p10]; Bxz{rR0XV  
   P3=[P3 p3/p10]; J6\<>5A?  
   P=[P p*p]; } %rF}>$A  
end lD\lFN(:
 
figure(1) <XGOcekG  
plot(P,P1, P,P2, P,P3); 3Q
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~