[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 {O[a+r.n  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 8
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ULNU'6  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear %[l5){:05  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 vg5i+ry<  
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%fid=fopen('e21.dat','w'); ML9ZS @  
N = 128;                       % Number of Fourier modes (Time domain sampling points) B~G?&"]  
M1 =3000;              % Total number of space steps :D""c*  
J =100;                % Steps between output of space !X*+Ct^  
T =10;                  % length of time windows:T*T0 o+r?N5  
T0=0.1;                 % input pulse width _Y?p =;  
MN1=0;                 % initial value for the space output location 7o-umZ}8  
dt = T/N;                      % time step YAYPof~A$l  
n = [-N/2:1:N/2-1]';           % Index R%=u<O  
t = n.*dt;   qH1[BsOx  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ]6bh#N;.  
u20=u10.*0.0;                  % input to waveguide 2 !?,7Cu.5#6  
u1=u10; u2=u20;                 ZEYT17g]  
U1 = u1;   Gb4k5jl  
U2 = u2;                       % Compute initial condition; save it in U E3@G^Y  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1.
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w=2*pi*n./T; omevF>b;  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T N =FX3Z  
L=4;                           % length of evoluation to compare with S. Trillo's paper P-o/ax  
dz=L/M1;                       % space step, make sure nonlinear<0.05 [+\=x[q  
for m1 = 1:1:M1                                    % Start space evolution UzTFT:\  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS j^-E,YMC  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; q$L=G  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform roSdcQTeT  
   ca2 = fftshift(fft(u2)); DO` K_B  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ">_<L.,I  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   S:aAR*<6  
   u2 = ifft(fftshift(c2));                        % Return to physical space I|8'#Q
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   u1 = ifft(fftshift(c1)); 1zqIB")s>  
if rem(m1,J) == 0                                 % Save output every J steps. gG*]|>M JI  
    U1 = [U1 u1];                                  % put solutions in U array 094~  s  
    U2=[U2 u2]; h8B:}_Cu  
    MN1=[MN1 m1]; AqnDsr!  
    z1=dz*MN1';                                    % output location / VypN,  
  end (&t741DN|  
end Fjch<gAofS  
hg=abs(U1').*abs(U1');                             % for data write to excel n,/eT,48`  
ha=[z1 hg];                                        % for data write to excel =;Ap+}  
t1=[0 t']; N1/)Fk-z  
hh=[t1' ha'];                                      % for data write to excel file . 7*k}@k  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format @-ps[b`z  
figure(1) B?n 6o|8  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn &.^(,pt  
figure(2) ]z3!hgTj  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn @{/GdB,}  
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非线性超快脉冲耦合的数值方法的Matlab程序 }.*"ezaZw  
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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。   &BTgISYi  
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 nYy%=B|>  
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%  This Matlab script file solves the nonlinear Schrodinger equations B}S!l>.z  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of B\^myg4
  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 LL% Aw)Q`  
p6S{OUiG  
C=1;                           +\Uq=@  
M1=120,                       % integer for amplitude n92*:Y  
M3=5000;                      % integer for length of coupler fL$U%I3  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ]]Bqte  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. R%Xhdcn7  
T =40;                        % length of time:T*T0. vX?MB  
dt = T/N;                     % time step _EHz>
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n = [-N/2:1:N/2-1]';          % Index fGdT2}gd  
t = n.*dt;   \iL{q^Im  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. B|I9Ex~L  
w=2*pi*n./T; M$J{clr  
g1=-i*ww./2; Z01BzIsR  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; '0b!lVe  
g3=-i*ww./2; t.\<Q#bN#  
P1=0; mH`K~8pRg  
P2=0; [pY1\$,  
P3=1; srL|Y&8p  
P=0; 4e`GMtp  
for m1=1:M1                 r<MW8  
p=0.032*m1;                %input amplitude yj$a0Rgkv  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ~W/|RP7S  
s1=s10; OKo)p`BX  
s20=0.*s10;                %input in waveguide 2 b?^CnMO  
s30=0.*s10;                %input in waveguide 3 =`st1K  
s2=s20; mv,p*0  
s3=s30; vQH6CB"  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   FH3^@@Y%  
%energy in waveguide 1 >PbB /->  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Ty&O
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%energy in waveguide 2 #3~hF)u&/  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   {u}d`%_.M  
%energy in waveguide 3 PP*',D3  
for m3 = 1:1:M3                                    % Start space evolution ^QG;:.3v  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS XfZ^,'z  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; l@W1bS  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; aw\0\'}  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform WY& [%r  
   sca2 = fftshift(fft(s2)); 'G)UIjl  
   sca3 = fftshift(fft(s3)); F=g+R~F  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   pLiGky  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); eo [eN.  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Dve+ #H6N  
   s3 = ifft(fftshift(sc3)); $-w&<U$E  
   s2 = ifft(fftshift(sc2));                       % Return to physical space GbB:K2  
   s1 = ifft(fftshift(sc1)); XM#xxf* Y  
end uN;]Fv@Z  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); mVsghDESJ)  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); b[/uSwvi  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); b
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   P1=[P1 p1/p10]; -dyN Ah?=  
   P2=[P2 p2/p10]; FW@(MIH  
   P3=[P3 p3/p10]; 3;%dn\ D  
   P=[P p*p]; Y=5}u&\   
end b+#A=Z+Pr  
figure(1) )`z{T  
plot(P,P1, P,P2, P,P3); $S'~UbmYU  
Dg=!d)\  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~