[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 k?`Q
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of >IEc
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ?Y'r=Q{w  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Rq,Fp/  
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%fid=fopen('e21.dat','w'); V2BsvR`
  
N = 128;                       % Number of Fourier modes (Time domain sampling points) *vP:+]  
M1 =3000;              % Total number of space steps _v +At;Y  
J =100;                % Steps between output of space gtJCvVj>g  
T =10;                  % length of time windows:T*T0 _0!<iN L  
T0=0.1;                 % input pulse width -< }#ImTN  
MN1=0;                 % initial value for the space output location 4<y|SI!  
dt = T/N;                      % time step E9#.!re|^  
n = [-N/2:1:N/2-1]';           % Index [A46WF>L  
t = n.*dt;    !AFii:#  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 apd"p{  
u20=u10.*0.0;                  % input to waveguide 2 c%x.cbu>  
u1=u10; u2=u20;                 a 8.Xy])!  
U1 = u1;   %tZ[wwt  
U2 = u2;                       % Compute initial condition; save it in U S<nbNSu6+  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ~
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w=2*pi*n./T; ;%Rp=&J  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T <hzuPi@  
L=4;                           % length of evoluation to compare with S. Trillo's paper T8\%+3e.  
dz=L/M1;                       % space step, make sure nonlinear<0.05 #u$Z/,  
for m1 = 1:1:M1                                    % Start space evolution D[bPm:\0M  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS uoe>T:  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; (5&l<u"K~  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform -`d(>ok  
   ca2 = fftshift(fft(u2)); I oFtfb[  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation LAPCL&Z  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ]]lM)  
   u2 = ifft(fftshift(c2));                        % Return to physical space F>c
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   u1 = ifft(fftshift(c1)); }I ^e:,{  
if rem(m1,J) == 0                                 % Save output every J steps. XaR(~2  
    U1 = [U1 u1];                                  % put solutions in U array {pM3f  
    U2=[U2 u2]; Cswa5l`af  
    MN1=[MN1 m1]; egy#8U)Z  
    z1=dz*MN1';                                    % output location R4Si{J*O  
  end P<s:dH"  
end kH>^3(Q\  
hg=abs(U1').*abs(U1');                             % for data write to excel WDQw)EUl&  
ha=[z1 hg];                                        % for data write to excel u}BN)%`B  
t1=[0 t']; oLz9mqp2%  
hh=[t1' ha'];                                      % for data write to excel file `%Uz0hF  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format C;.+ kE  
figure(1) ?,Zc{  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn aFVd}RO0  
figure(2) 3:G94cp5  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 9Qhk~^ngg  
HP*AN@>Kw  
非线性超快脉冲耦合的数值方法的Matlab程序 NZ?|#53  
{GM8}M~D&  
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。   /dt'iai~l  
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 ~L=Idt!9  
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DsH`I%w{  
%  This Matlab script file solves the nonlinear Schrodinger equations 7z4u?>pne*  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of {;j@-=pV  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear sKuPV
  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 +jpC%o}C  
Il,^/qvIY  
C=1;                           9\[A%jp#K@  
M1=120,                       % integer for amplitude "J (.dg]"  
M3=5000;                      % integer for length of coupler n*U+jc  
N = 512;                      % Number of Fourier modes (Time domain sampling points) W_z?t;  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. b1`(f"&l  
T =40;                        % length of time:T*T0. hg=BXe4:  
dt = T/N;                     % time step {
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n = [-N/2:1:N/2-1]';          % Index 60St99@O  
t = n.*dt;   *,=WaODO%  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. %l8nTcL_?  
w=2*pi*n./T; :i_kA'dl&  
g1=-i*ww./2; !%_H1jk  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; hr] :bR  
g3=-i*ww./2; (6Sf#M  
P1=0; J((
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P2=0; ,"!P{c  
P3=1; HJ,sZ4*]]  
P=0; m+/-SG  
for m1=1:M1                 1*Ui=M4  
p=0.032*m1;                %input amplitude WxFrqUz  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 DG $._  
s1=s10; a>{b'X^LV  
s20=0.*s10;                %input in waveguide 2 MJ:>ZRXCE  
s30=0.*s10;                %input in waveguide 3 -O=a"G=  
s2=s20; ^"d!(npw  
s3=s30; 4x JOPu
 
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   d.3O1TXK  
%energy in waveguide 1 [ZP8l'?  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   &JpFt^IHi  
%energy in waveguide 2 %Pb 5PIk4  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   {!C';^  
%energy in waveguide 3 (gl/NH!  
for m3 = 1:1:M3                                    % Start space evolution 6:Nz=sw8  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS $N#f)8v  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; SEc3`y;j%  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; =Xc[EUi<;g  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform c=T^)~$$  
   sca2 = fftshift(fft(s2)); Sr`gQ#b@r}  
   sca3 = fftshift(fft(s3)); 3=r8kh7,  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   aQEMCWxZ  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Svmyg]  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); icf[.  
   s3 = ifft(fftshift(sc3)); ReCmv/AE  
   s2 = ifft(fftshift(sc2));                       % Return to physical space
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   s1 = ifft(fftshift(sc1)); 
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end $z+iB;x  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); !$>d75zli  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); nJ|8#U7  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 2b]'KiX  
   P1=[P1 p1/p10]; $e|G#mMd-  
   P2=[P2 p2/p10]; 7FVu[Qu  
   P3=[P3 p3/p10]; qYW{$K  
   P=[P p*p]; xi=qap=S^9  
end eYurg6Ob~  
figure(1) X"W%(x`w  
plot(P,P1, P,P2, P,P3); kQ$Q}3f  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~