[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 j#rjYiYKy  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of hOG9  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of OrNi<TY>  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 2r4owB?  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 u_shC"X:  
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%fid=fopen('e21.dat','w'); F jsnFX;  
N = 128;                       % Number of Fourier modes (Time domain sampling points) @i U@JE`C  
M1 =3000;              % Total number of space steps YMb\v4  
J =100;                % Steps between output of space rl"$6{Z}  
T =10;                  % length of time windows:T*T0 p~Di\AQ/  
T0=0.1;                 % input pulse width yhxen  
MN1=0;                 % initial value for the space output location I&%{%*y  
dt = T/N;                      % time step 4>x]v!d  
n = [-N/2:1:N/2-1]';           % Index ;6P#V`u  
t = n.*dt;   }86&? 0j.  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 l+`f\},  
u20=u10.*0.0;                  % input to waveguide 2 o."k7fLB  
u1=u10; u2=u20;                 Z<jio  
U1 = u1;   ]zK'aod  
U2 = u2;                       % Compute initial condition; save it in U Y>W$n9d&G2  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. >zx]% W  
w=2*pi*n./T; 4LO4SYW7  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T u_ou,RF  
L=4;                           % length of evoluation to compare with S. Trillo's paper O<}3\O )G(  
dz=L/M1;                       % space step, make sure nonlinear<0.05 5G  @  
for m1 = 1:1:M1                                    % Start space evolution ~QzUQYG*  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS RrB)u?  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ])Rs.Y{Q5  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform Z1Y/2MVSb  
   ca2 = fftshift(fft(u2)); 4 JC*c  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 7m='-_w)?w  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   "u^%~2  
   u2 = ifft(fftshift(c2));                        % Return to physical space tjLp;%6e  
   u1 = ifft(fftshift(c1)); d^b(Uo=$  
if rem(m1,J) == 0                                 % Save output every J steps. cC@.&  
    U1 = [U1 u1];                                  % put solutions in U array k%2woHSu&  
    U2=[U2 u2];
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    MN1=[MN1 m1]; }Rl^7h<!  
    z1=dz*MN1';                                    % output location Q5Yy \M  
  end [=/Yo1:v  
end FVY$A=G  
hg=abs(U1').*abs(U1');                             % for data write to excel H[oCI|k  
ha=[z1 hg];                                        % for data write to excel ^<u9I5?  
t1=[0 t']; "$P|!k45(  
hh=[t1' ha'];                                      % for data write to excel file xAlyik  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format Tx)!qpZ  
figure(1) (S<Z@y+d  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn j`H5S  
figure(2) sVzU
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 3jR>  
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非线性超快脉冲耦合的数值方法的Matlab程序 ={'*C7K)oK  
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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。   M( euwy  
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 H|UGR~&  
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%  This Matlab script file solves the nonlinear Schrodinger equations MawWgd*  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of [-X

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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Wb
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 [l`_2{:
 
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C=1;                           6(M^`&fl
 
M1=120,                       % integer for amplitude 8VWkUsOoI  
M3=5000;                      % integer for length of coupler J~jxmh  
N = 512;                      % Number of Fourier modes (Time domain sampling points) &Hl*Eg f  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 4k7 LM]  
T =40;                        % length of time:T*T0. E8gbm&x*  
dt = T/N;                     % time step fC4#b?Q  
n = [-N/2:1:N/2-1]';          % Index &<Iyb}tA?  
t = n.*dt;   LA +BH_t&  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. pYxdE|2j  
w=2*pi*n./T; :NCY6? [Dz  
g1=-i*ww./2; =P}BAJ  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; hwD;1n  
g3=-i*ww./2; xY_<D+OV  
P1=0; At t~NTL  
P2=0; Q85Y6',  
P3=1; %jBI*WzR  
P=0; N'5AU (  
for m1=1:M1                 a ](Jc)  
p=0.032*m1;                %input amplitude I38j[Xk  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 {.HFB:<!}  
s1=s10; F]qX}  
s20=0.*s10;                %input in waveguide 2 <i1.W!%  
s30=0.*s10;                %input in waveguide 3 dRhsnT+KX  
s2=s20; g %ZKn  
s3=s30; xPcH]Gs^b  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   {e/6iSpT  
%energy in waveguide 1 HxE`"/~.7k  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   $ap6Vxjr  
%energy in waveguide 2 Sd9%tO9mf  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   g %e"KnU  
%energy in waveguide 3 bdxmJ9a:R  
for m3 = 1:1:M3                                    % Start space evolution 3Yb2p!o  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS R3dt
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; hQFF%xl  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; *LA2@9l  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform E0lro+'lS  
   sca2 = fftshift(fft(s2)); bMCy=5  
   sca3 = fftshift(fft(s3)); <H]1 6  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   _+0QQ{'N  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 8am/5o  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); sI,S(VWor  
   s3 = ifft(fftshift(sc3)); {=Y3[  
   s2 = ifft(fftshift(sc2));                       % Return to physical space /4xp?Lo:  
   s1 = ifft(fftshift(sc1)); 6xC$R q  
end sM _m  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); .ou#BWav/  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ",Ge:\TR=  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 4k6,pt"  
   P1=[P1 p1/p10]; lYq/ n&@_1  
   P2=[P2 p2/p10]; Vmb `%k20'  
   P3=[P3 p3/p10]; S!JwF&EW  
   P=[P p*p]; wJ}
9(>id*  
end CHGV1X,  
figure(1) y]YUuJ9a  
plot(P,P1, P,P2, P,P3); %fzZpd]v=,  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~