[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 *6NO-T; -  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of l*$WX=h6n  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of bBA$}bv  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear =Nw2;TkB[  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 \M+MDT&  
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%fid=fopen('e21.dat','w'); >NJjS8f5  
N = 128;                       % Number of Fourier modes (Time domain sampling points) `Ac:f5a  
M1 =3000;              % Total number of space steps [:Be[pLC
 
J =100;                % Steps between output of space qpoquWZ  
T =10;                  % length of time windows:T*T0 Hr(6TLNw  
T0=0.1;                 % input pulse width DP|TIt,Rl  
MN1=0;                 % initial value for the space output location $2Kau 1  
dt = T/N;                      % time step 4S'[\ZJO  
n = [-N/2:1:N/2-1]';           % Index =.DTR5(_h  
t = n.*dt;   3voW  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 g4Y) Bz
 
u20=u10.*0.0;                  % input to waveguide 2 ]
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u1=u10; u2=u20;                 /j11,O?72  
U1 = u1;   PXa5g5!  
U2 = u2;                       % Compute initial condition; save it in U +-U@0&Y3M  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. w-r_H!-  
w=2*pi*n./T; {W-5:~?"  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T -<|Y1PQ  
L=4;                           % length of evoluation to compare with S. Trillo's paper nHnk#SAAu  
dz=L/M1;                       % space step, make sure nonlinear<0.05 w nWgy4:  
for m1 = 1:1:M1                                    % Start space evolution yDzdE;  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ZOp^`c9~  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; o\&~CW~@~  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform C9o$9 l+B  
   ca2 = fftshift(fft(u2)); WPtMds4  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Og=[4?Kpk  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   {wcO[bN  
   u2 = ifft(fftshift(c2));                        % Return to physical space J6DnPaw-G  
   u1 = ifft(fftshift(c1)); FtN}]@F  
if rem(m1,J) == 0                                 % Save output every J steps. :"VujvFX  
    U1 = [U1 u1];                                  % put solutions in U array 6eM6[  
    U2=[U2 u2]; z*RSMfRW  
    MN1=[MN1 m1]; `-o5&>'nf  
    z1=dz*MN1';                                    % output location F%Kp9I*  
  end 21ViHV  
end 8[oYZrg  
hg=abs(U1').*abs(U1');                             % for data write to excel r?\|f:M3  
ha=[z1 hg];                                        % for data write to excel $Y6 3!*  
t1=[0 t']; 4\\.n  
hh=[t1' ha'];                                      % for data write to excel file {$0&R$v3  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format NIaF5z  
figure(1) 3B;}j/h2  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn C
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figure(2) 2yvVeo&3  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ka#K [qI  
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非线性超快脉冲耦合的数值方法的Matlab程序 x)3~il5  
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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。   *!Y-!  
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 U_l7CCK +  
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%  This Matlab script file solves the nonlinear Schrodinger equations qc
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%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of +qhnP$vIe  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 7-X/>v  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 +TF8WZZF.d  
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C=1;                           nS.2C>A  
M1=120,                       % integer for amplitude )km7tA 0a  
M3=5000;                      % integer for length of coupler 'PpZ/ry$  
N = 512;                      % Number of Fourier modes (Time domain sampling points) N 'i,>  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. '#W_boN  
T =40;                        % length of time:T*T0. wdwp9r  
dt = T/N;                     % time step MxTmWsaW  
n = [-N/2:1:N/2-1]';          % Index 0cFn{q'u  
t = n.*dt;  
]IS;\~  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Ig9d#c  
w=2*pi*n./T; #]y5zi  
g1=-i*ww./2; DT\ym9  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; LWD#a~  
g3=-i*ww./2; #9\THfb  
P1=0; 4sIXO   
P2=0; M&f#wQ  
P3=1; `eC+% O  
P=0; =Dk7RKoHF  
for m1=1:M1                 '_0  
p=0.032*m1;                %input amplitude hVM2/j  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Xk,>l6vc  
s1=s10; kYlg4 .~M  
s20=0.*s10;                %input in waveguide 2 nP1GW6P
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s30=0.*s10;                %input in waveguide 3 1"YpO"Rh  
s2=s20; ^C7C$TZS  
s3=s30; /H)Br~ l  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   6,+nRiZ  
%energy in waveguide 1 gu<V(M\  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   %i"}x/CD[  
%energy in waveguide 2 5g>wV  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   =|,A%ZGF$  
%energy in waveguide 3 #\ #3r  
for m3 = 1:1:M3                                    % Start space evolution Ri @`a  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ^A!$i$NON  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; OH6n^WKY  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; >f$NzJ}  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform hcyO97@r  
   sca2 = fftshift(fft(s2)); "Pj}E=!k  
   sca3 = fftshift(fft(s3)); ,Sg33N?  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   X#ZgS!Mn  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 3=- })X;  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ARWZ; GX  
   s3 = ifft(fftshift(sc3)); 6Dst;:  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 8r^ ~0nm  
   s1 = ifft(fftshift(sc1)); %K1")s  
end QDE$E.a  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); K5`Rk"s  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); <2<87PU  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); QVtM.oi!Q  
   P1=[P1 p1/p10]; 9$RIH\*  
   P2=[P2 p2/p10]; 7
8]gtJ  
   P3=[P3 p3/p10]; Im)EDTm$  
   P=[P p*p]; cp%ii'  
end d#>y}H9  
figure(1) 2|{V,!/cvG  
plot(P,P1, P,P2, P,P3); h}&b+1{X  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~