[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 pzaU'y#PM  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of H=w):kL|  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 2`j{n\/  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear N%ccy?B  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 <&gs)BY  
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%fid=fopen('e21.dat','w'); n
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N = 128;                       % Number of Fourier modes (Time domain sampling points) uPapINj  
M1 =3000;              % Total number of space steps Dsn=fht  
J =100;                % Steps between output of space uqU&k@  
T =10;                  % length of time windows:T*T0 *SIYZE'  
T0=0.1;                 % input pulse width DVMdRfA  
MN1=0;                 % initial value for the space output location e+F$fQt>  
dt = T/N;                      % time step i$`o,m#  
n = [-N/2:1:N/2-1]';           % Index *wY+yoj  
t = n.*dt;   *po o.Zz  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 e|5@7~Vi  
u20=u10.*0.0;                  % input to waveguide 2
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u1=u10; u2=u20;                 "A&A?%  
U1 = u1;   f F)M'C
  
U2 = u2;                       % Compute initial condition; save it in U >;R`Q9s7  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. <2L,+  
w=2*pi*n./T; ?1c7wEk  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T )UpVGT
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L=4;                           % length of evoluation to compare with S. Trillo's paper Bha("kG  
dz=L/M1;                       % space step, make sure nonlinear<0.05 c q[nqjC=  
for m1 = 1:1:M1                                    % Start space evolution aG#d41O  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS e$WAf`*  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
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   ca1 = fftshift(fft(u1));                        % Take Fourier transform J\w4N",  
   ca2 = fftshift(fft(u2)); BfCn
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation :uB?h1|  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   6R^32VeK($  
   u2 = ifft(fftshift(c2));                        % Return to physical space -mGG:#yP  
   u1 = ifft(fftshift(c1)); /5z,G r  
if rem(m1,J) == 0                                 % Save output every J steps. :
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    U1 = [U1 u1];                                  % put solutions in U array <66%(J>  
    U2=[U2 u2]; LwxJ:Kz.  
    MN1=[MN1 m1]; esE!i0%  
    z1=dz*MN1';                                    % output location &-p~UZy  
  end /;/:>c  
end ],[<^=|  
hg=abs(U1').*abs(U1');                             % for data write to excel MRK=\qjD  
ha=[z1 hg];                                        % for data write to excel Y\WVkd(+G  
t1=[0 t']; 8~t8^eBg  
hh=[t1' ha'];                                      % for data write to excel file HeO&p@  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format n7G`b'  
figure(1) 3c7i8b$  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn OcPgw/ I  
figure(2) S)wP];]`K  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn GnUD<P=I  
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非线性超快脉冲耦合的数值方法的Matlab程序 cYe2a"  
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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。   CL
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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 On~KTt3Mp  
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%  This Matlab script file solves the nonlinear Schrodinger equations 3**t'iWQ  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of y!}XlllV  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 1 I.P7_/  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8#tuB8>  
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C=1;                           r-L& ee  
M1=120,                       % integer for amplitude oqysfLJ  
M3=5000;                      % integer for length of coupler lF.kAEC  
N = 512;                      % Number of Fourier modes (Time domain sampling points) kZ)}tA7j  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ?PTXgIC  
T =40;                        % length of time:T*T0.
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dt = T/N;                     % time step xP9h$!  
n = [-N/2:1:N/2-1]';          % Index ,ayJgAD  
t = n.*dt;   $N}t)iA  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. YEaT_zWG0  
w=2*pi*n./T; d0ht*b  
g1=-i*ww./2; g[t paQ  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; [q3zs_nz  
g3=-i*ww./2; mVYfyLZ,(  
P1=0; i^iu#WC  
P2=0; Oso**WUOZ&  
P3=1; trrK6(p  
P=0; _izjvg  
for m1=1:M1                 ^VG].6  
p=0.032*m1;                %input amplitude IzUpkwN  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ~8mz.ZdY  
s1=s10; W^xO/xu1/  
s20=0.*s10;                %input in waveguide 2 i/'bpGrQ(  
s30=0.*s10;                %input in waveguide 3 TIl 'Z7  
s2=s20; yhbU;qEG9  
s3=s30;
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p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Ug546Bz  
%energy in waveguide 1 +^esL9RG:  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   U_izKvEh  
%energy in waveguide 2 y9R
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   :;+_<pk  
%energy in waveguide 3 @MTv4eC}e  
for m3 = 1:1:M3                                    % Start space evolution |94o P>d  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS +_pfBJ_$%  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; U?{oxy_[2  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ;
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   sca1 = fftshift(fft(s1));                       % Take Fourier transform o@.{|j  
   sca2 = fftshift(fft(s2)); 'NCqI  
   sca3 = fftshift(fft(s3)); j\bp#+  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   6s~B2t:Y  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); :2==7u7v?  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); N*$GP3]  
   s3 = ifft(fftshift(sc3)); ys`oHSf  
   s2 = ifft(fftshift(sc2));                       % Return to physical space hF@%k ;I  
   s1 = ifft(fftshift(sc1));
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end hbvcIGaT  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); FNF`Z  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); S#8)N`  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); %PB{jo  
   P1=[P1 p1/p10]; &ck}3\sQ  
   P2=[P2 p2/p10]; =<Sn&uL  
   P3=[P3 p3/p10]; =JfwHFHd#  
   P=[P p*p]; h0k?(O  
end }}]Lf3;  
figure(1) =:w,wI.  
plot(P,P1, P,P2, P,P3); (2>q  
pKq[F*Lut  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~