[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 bw P=f.  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of v1OVrk>s>  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of >3uNh:|>/  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Qo#]Lo> \g  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 BIWe Hx  
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%fid=fopen('e21.dat','w'); |UXSUP @s  
N = 128;                       % Number of Fourier modes (Time domain sampling points) [I *_0  
M1 =3000;              % Total number of space steps WywS1viD  
J =100;                % Steps between output of space 9eMle?pF  
T =10;                  % length of time windows:T*T0 %10ONe}  
T0=0.1;                 % input pulse width h3
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MN1=0;                 % initial value for the space output location (s3k2Z  
dt = T/N;                      % time step GTdoUSUq  
n = [-N/2:1:N/2-1]';           % Index HOP*QX8C%  
t = n.*dt;   )^ah, ;
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u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 B)JMughq_  
u20=u10.*0.0;                  % input to waveguide 2 5kiW@{m  
u1=u10; u2=u20;                 $tmdE)"&  
U1 = u1;   vE:*{G;Y  
U2 = u2;                       % Compute initial condition; save it in U uHgq"e  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 9
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w=2*pi*n./T; >yC=@Uq+  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T d_!Z /M,  
L=4;                           % length of evoluation to compare with S. Trillo's paper W+ S~__K  
dz=L/M1;                       % space step, make sure nonlinear<0.05 G4cgY|71  
for m1 = 1:1:M1                                    % Start space evolution i>Q!5  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ;'7(gAE
 
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; `B)@  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform aK_5@8+ZD  
   ca2 = fftshift(fft(u2)); YYe G9yR  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation m/=nz.  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   :$k*y%Z*N&  
   u2 = ifft(fftshift(c2));                        % Return to physical space oYqHl1cs  
   u1 = ifft(fftshift(c1)); CP7dn/  
if rem(m1,J) == 0                                 % Save output every J steps. ]fM|cN8(zM  
    U1 = [U1 u1];                                  % put solutions in U array E4X6f  
    U2=[U2 u2]; "-Q+!byh  
    MN1=[MN1 m1]; AF'<  
    z1=dz*MN1';                                    % output location q1}!Okr"2  
  end Q~,Mzt"}W  
end f^F;`;z  
hg=abs(U1').*abs(U1');                             % for data write to excel ALMsF2H  
ha=[z1 hg];                                        % for data write to excel |+nmOi,z  
t1=[0 t']; [}L~zn6>?a  
hh=[t1' ha'];                                      % for data write to excel file &QHJ%c  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format I C  
figure(1) gm9*z.S\'  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Uy?jVPL  
figure(2) meX2Y;  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn QG5WsuT  
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非线性超快脉冲耦合的数值方法的Matlab程序 e*:K79y  
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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。   (]
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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 $.`o  
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%  This Matlab script file solves the nonlinear Schrodinger equations TLwxP"  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of &;@L] o  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +z;*r8d<X  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 :iE b^F}  
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C=1;                           UoT`/.  
M1=120,                       % integer for amplitude :HY$x  
M3=5000;                      % integer for length of coupler :&BPKqKp  
N = 512;                      % Number of Fourier modes (Time domain sampling points) v=llg ^  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. t13V>9to  
T =40;                        % length of time:T*T0. 1:-'euA"  
dt = T/N;                     % time step s$M(-"mg  
n = [-N/2:1:N/2-1]';          % Index !ho^:}m  
t = n.*dt;   ] ?DU8  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1.
B>2R-pa4~  
w=2*pi*n./T; '<Zm>L&  
g1=-i*ww./2; noWF0+%  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; _b&|0j:Ud  
g3=-i*ww./2; <C`bf$ak  
P1=0; !rnjmc  
P2=0; hP6f  
P3=1; ]1 f^ SxSI  
P=0; #h;  
for m1=1:M1                 2`=jKt  
p=0.032*m1;                %input amplitude rq%]CsRY5  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 !Tnjha*  
s1=s10; wps/{h,  
s20=0.*s10;                %input in waveguide 2 }_+XN"}C  
s30=0.*s10;                %input in waveguide 3 5 ^{~xOM5  
s2=s20; =$'>VPQ  
s3=s30; @O#!W]6NT6  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   B!RfPk1B<*  
%energy in waveguide 1 e;.,x
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p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   l(>6Yq  
%energy in waveguide 2 ](r}`u%}y  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ~5HkDtI)  
%energy in waveguide 3 JQQyl:=  
for m3 = 1:1:M3                                    % Start space evolution 6"-$WUlg  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS xFu ,e  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ?|M-0{  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; _}R$h=YD  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform N3G9
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   sca2 = fftshift(fft(s2)); _U~R  
   sca3 = fftshift(fft(s3)); H{}&|;0  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift  
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   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Clf$EX;~  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); vXKL<  
   s3 = ifft(fftshift(sc3)); Y'/6T]a  
   s2 = ifft(fftshift(sc2));                       % Return to physical space c9/w{
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   s1 = ifft(fftshift(sc1)); E1QJ^]MG.  
end mb*Yw6q  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); )LP'
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   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); }c,b]!:  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); VEWW[T  
   P1=[P1 p1/p10]; ?1=.scmgDG  
   P2=[P2 p2/p10]; MIJuJ]U
}  
   P3=[P3 p3/p10]; =3(v4E':5  
   P=[P p*p]; S m(*<H  
end f`qy~M&  
figure(1) S1=P-Ao  
plot(P,P1, P,P2, P,P3); *BKD5EwS  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~