[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 {KODwP'~  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of RN!oflb  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of haB$W 4x  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Kx#G_N@  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Km-lWreTH  
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%fid=fopen('e21.dat','w'); $(C71M|CT  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 9;q@;)'5  
M1 =3000;              % Total number of space steps +dR$;!WB3  
J =100;                % Steps between output of space v!40>[?|p  
T =10;                  % length of time windows:T*T0 ptrLnJ|%  
T0=0.1;                 % input pulse width ]`+>{Sx 1  
MN1=0;                 % initial value for the space output location =@B9I<GKf  
dt = T/N;                      % time step u},<On  
n = [-N/2:1:N/2-1]';           % Index Z\TH=UA  
t = n.*dt;   #&&^5r-b-  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 KWU#Swa`  
u20=u10.*0.0;                  % input to waveguide 2 X%39
cXM C  
u1=u10; u2=u20;                 =q>eoXp  
U1 = u1;   ~I2IgEj>]  
U2 = u2;                       % Compute initial condition; save it in U } fSbH  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 2Xgn[oI{  
w=2*pi*n./T;
!%]]lxi  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T !MQo=k  
L=4;                           % length of evoluation to compare with S. Trillo's paper `}Q+:  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ~"{Kjr#R  
for m1 = 1:1:M1                                    % Start space evolution [b
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ;J2=6np  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 7nfQ=?XNK  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform Ma wio5  
   ca2 = fftshift(fft(u2)); 3u-j`7  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation T4._S:~  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   )%WS(S>8  
   u2 = ifft(fftshift(c2));                        % Return to physical space oZP:}= F  
   u1 = ifft(fftshift(c1)); CEZ*a 0}=  
if rem(m1,J) == 0                                 % Save output every J steps. q'{E $V)E  
    U1 = [U1 u1];                                  % put solutions in U array RIb< 7  
    U2=[U2 u2]; ;nSaZ$`5  
    MN1=[MN1 m1]; .(nq"&u-*  
    z1=dz*MN1';                                    % output location v5 $"v?PT  
  end @ttcFX1:W  
end 8V^gOUF.  
hg=abs(U1').*abs(U1');                             % for data write to excel efRa|7!HK  
ha=[z1 hg];                                        % for data write to excel naM4X@jl  
t1=[0 t']; kLADd"C  
hh=[t1' ha'];                                      % for data write to excel file A5B 5pJ  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ~ia#=|1}  
figure(1) <86upS6  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn JrS/"QSA  
figure(2) v"=^?5B  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn r'k-*I  
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非线性超快脉冲耦合的数值方法的Matlab程序 HrWXPac A  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   V#C
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Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 19&!#z  
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%  This Matlab script file solves the nonlinear Schrodinger equations cM.q^{d`  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of W!V06.  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear NuW9.6$Jrf  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 \Qz>us=G  
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C=1;                           .K;*uq:0  
M1=120,                       % integer for amplitude P[aB}<1f0  
M3=5000;                      % integer for length of coupler 1,9RfYV  
N = 512;                      % Number of Fourier modes (Time domain sampling points) jHTaG%oh  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. %\Ig{Rj;  
T =40;                        % length of time:T*T0. D("['`{  
dt = T/N;                     % time step XOVZ'V  
n = [-N/2:1:N/2-1]';          % Index ,Ix7Yg[  
t = n.*dt;   auaFP-$`f  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. _N0x&9S$  
w=2*pi*n./T; J1yy6Wq3
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g1=-i*ww./2; i#
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g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; jZe]zdml  
g3=-i*ww./2; \D>'  
P1=0;  H[fD >  
P2=0; 3zMmpeq  
P3=1; qS+'#Sn  
P=0; fh:=ja?bM3  
for m1=1:M1                 L&
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p=0.032*m1;                %input amplitude YtxBkKiJ2V  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 hFs0qPVY  
s1=s10; R qOEQ*k  
s20=0.*s10;                %input in waveguide 2 yV=hi?f-[V  
s30=0.*s10;                %input in waveguide 3 _Ev"/%  
s2=s20; ;x|4Tm  
s3=s30; -L</,>p  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   /$]dVvhX%  
%energy in waveguide 1 ir3iW*5k  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   a}El!7RO0  
%energy in waveguide 2 x
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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))));   rL&585  
%energy in waveguide 3 MoO jM&9  
for m3 = 1:1:M3                                    % Start space evolution LHR%dt|M  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS qA Jgz7=c  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 4,wdIdSm4  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; s[8<@I*u  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform _av%`bb&z9  
   sca2 = fftshift(fft(s2)); mzfj!0zR*  
   sca3 = fftshift(fft(s3)); fb&K.6"  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   %~ZOQ%c1  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); @fPiGu`L  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); I`p44}D3  
   s3 = ifft(fftshift(sc3)); m9.QGX\]  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Y
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   s1 = ifft(fftshift(sc1)); %fK"g2:  
end 'hg, W]  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 8mV`|2>  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); YmNBtGhT  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); }eULcgRG  
   P1=[P1 p1/p10]; kc1 *@<L6  
   P2=[P2 p2/p10]; 33s.p'  
   P3=[P3 p3/p10]; .#lQZo6$\|  
   P=[P p*p]; NrhU70y  
end 6(<M.U_ft  
figure(1) *.ZV.(  
plot(P,P1, P,P2, P,P3); &z&Jl#t-)  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~