[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`lLqV<[cB  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of e[Tu.$f-  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of +b9gP\Hke  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear h()Ok9]  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 p#]D-
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%fid=fopen('e21.dat','w'); v$P<:M M  
N = 128;                       % Number of Fourier modes (Time domain sampling points) hS( )OY  
M1 =3000;              % Total number of space steps E1=WH-iA0  
J =100;                % Steps between output of space kF1Tg KSd  
T =10;                  % length of time windows:T*T0 }o'WR'LX  
T0=0.1;                 % input pulse width ~]d3 f  
MN1=0;                 % initial value for the space output location ~6<'cun@x  
dt = T/N;                      % time step BE#s@-zR=p  
n = [-N/2:1:N/2-1]';           % Index |4slG  
t = n.*dt;   jMpV c E#  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 LU7ia[T  
u20=u10.*0.0;                  % input to waveguide 2 l{2Y[&%  
u1=u10; u2=u20;                 hxXl0egI  
U1 = u1;   2b[R^O}   
U2 = u2;                       % Compute initial condition; save it in U 8Hdm(>  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. vFz#A/1  
w=2*pi*n./T; "%mu~&Ga  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T }#b[@3/T  
L=4;                           % length of evoluation to compare with S. Trillo's paper gsSUmf1  
dz=L/M1;                       % space step, make sure nonlinear<0.05 hB!>*AsG  
for m1 = 1:1:M1                                    % Start space evolution Xcy Xju#"p  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 6JCq?:#ab  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; :vsF4  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform oZ/z{`  
   ca2 = fftshift(fft(u2)); [?=Vqd  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation zL%ruWNG  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   HW
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   u2 = ifft(fftshift(c2));                        % Return to physical space ik;S!S\
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   u1 = ifft(fftshift(c1)); u>K(m))5W3  
if rem(m1,J) == 0                                 % Save output every J steps. #},4m  
    U1 = [U1 u1];                                  % put solutions in U array |e]2 >NjQa  
    U2=[U2 u2]; "u H VX|`  
    MN1=[MN1 m1]; &nRbI:R  
    z1=dz*MN1';                                    % output location cl'#nLPz;  
  end =B/Ac0Y  
end 8+?|4'\
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hg=abs(U1').*abs(U1');                             % for data write to excel @[s+5_9nk  
ha=[z1 hg];                                        % for data write to excel 8F;r$i2  
t1=[0 t']; Jtv~
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hh=[t1' ha'];                                      % for data write to excel file *!wBn  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format Hy*_4r  
figure(1) k>'c4ay290  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn IHrG!owf  
figure(2) TA~FP#.  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn -Y{=bZS u  
$#HPwmd  
非线性超快脉冲耦合的数值方法的Matlab程序 &|LP>'H;  
T\ cJn>kCn  
在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   ZDhl$m[m  
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 CZ~%qPwDw  
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%  This Matlab script file solves the nonlinear Schrodinger equations CkHifmc(u-  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 0o>l+c  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear c:@lR/oe"  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 F.DR
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E[nJ'h<h  
C=1;                           v!~;QO  
M1=120,                       % integer for amplitude 5>nbA8  
M3=5000;                      % integer for length of coupler  &3:U&}I  
N = 512;                      % Number of Fourier modes (Time domain sampling points) fPj*qi  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ?S~@Ea8/M  
T =40;                        % length of time:T*T0. kzb%=
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dt = T/N;                     % time step k/`WfSM\.  
n = [-N/2:1:N/2-1]';          % Index +YNN$i  
t = n.*dt;   (v2.8zrJ  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. pAY[XN  
w=2*pi*n./T; UD+r{s/%  
g1=-i*ww./2; $.g)%#h:  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; sT;:V  
g3=-i*ww./2; Tl%n|pc  
P1=0; h=7eOK]  
P2=0; H*
H=a  
P3=1; >(9"D8  
P=0; @Q%g#N  
for m1=1:M1                 R3<2Z0lqy  
p=0.032*m1;                %input amplitude X^%E"{!nU  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 )2YZ [~3  
s1=s10; ZQ_&HmgRy  
s20=0.*s10;                %input in waveguide 2 f'-) 3T  
s30=0.*s10;                %input in waveguide 3 V1 :aR3*!  
s2=s20; <8?jn*$;\  
s3=s30; 6tDCaB  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ss4<s 5:y  
%energy in waveguide 1 |E7)s;}D  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   d=$1Z.]  
%energy in waveguide 2 M,WC+")Z=  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   yrgb6)]nm@  
%energy in waveguide 3 /qeSR3WC  
for m3 = 1:1:M3                                    % Start space evolution `(dRb  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS %CaUC'  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; M9J^;3Lrh  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; F# a)"$j;  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform L74Sx0nk=  
   sca2 = fftshift(fft(s2)); zB@@Gs>  
   sca3 = fftshift(fft(s3)); BGSqfr1F  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   D,)^l@UP  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); xdV $dDCT  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); {R{Io|  
   s3 = ifft(fftshift(sc3)); LqOjVQxz  
   s2 = ifft(fftshift(sc2));                       % Return to physical space \~{b;$N}  
   s1 = ifft(fftshift(sc1)); S^/:O.X)c,  
end {zj<nu  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); zr1,A#BV  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); X"z!52*3]  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ;^cc-bLvF  
   P1=[P1 p1/p10]; P:3%#d~q  
   P2=[P2 p2/p10]; 50Kv4a"  
   P3=[P3 p3/p10]; uJX(s6["=  
   P=[P p*p]; 320g!r  
end UB7H`)C}  
figure(1) Pp9nilb_(  
plot(P,P1, P,P2, P,P3); Pqc+pE  
4[$D3,A  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~