[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 |~CnELF)  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of kWz%v  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Q#r 0DWo\  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Y@\5gZ&T  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 0j/81Y}p  
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%fid=fopen('e21.dat','w'); Pd;ClMa%  
N = 128;                       % Number of Fourier modes (Time domain sampling points) IFTW,9hh  
M1 =3000;              % Total number of space steps tB3CX\e  
J =100;                % Steps between output of space z|?R=;,u`  
T =10;                  % length of time windows:T*T0 I2DmM"-|  
T0=0.1;                 % input pulse width Cw|SY  
MN1=0;                 % initial value for the space output location PrKlwhi#  
dt = T/N;                      % time step 8k`z
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n = [-N/2:1:N/2-1]';           % Index 6uXYZ.A
  
t = n.*dt;   \
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u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 t5Mo'*j =  
u20=u10.*0.0;                  % input to waveguide 2 W=\dsdnu*  
u1=u10; u2=u20;                 9iy|=  
U1 = u1;   G\p; bUF  
U2 = u2;                       % Compute initial condition; save it in U k51s*U6=  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. XZ&v3ul  
w=2*pi*n./T; BD0-v`  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T `pMI[pLZe  
L=4;                           % length of evoluation to compare with S. Trillo's paper mfN@tMp  
dz=L/M1;                       % space step, make sure nonlinear<0.05 D5m\u$~V  
for m1 = 1:1:M1                                    % Start space evolution 6qJB"_.  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS C|J1x4sb@  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; `s_TY%&_}g  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ` ;=Se_  
   ca2 = fftshift(fft(u2)); 9h(hx7]  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation X[
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   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ;2|H6IN"  
   u2 = ifft(fftshift(c2));                        % Return to physical space [;f"',)y,  
   u1 = ifft(fftshift(c1)); W7o/  
if rem(m1,J) == 0                                 % Save output every J steps. WO9/rF_  
    U1 = [U1 u1];                                  % put solutions in U array m8PB2h  
    U2=[U2 u2]; bN&da [K  
    MN1=[MN1 m1]; K)@}Ok"#\4  
    z1=dz*MN1';                                    % output location 7:<Ed"rdE  
  end _D4}
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end R*0F)M  
hg=abs(U1').*abs(U1');                             % for data write to excel EG.C2]Fi  
ha=[z1 hg];                                        % for data write to excel y)E2=JQA/  
t1=[0 t']; !gf3%!%  
hh=[t1' ha'];                                      % for data write to excel file 5w1[KO#K|  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ,AM-cwwT:u  
figure(1) 0cUt"(]  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ;LE @Ezx  
figure(2) OJ 5 !+#>  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ?$c  
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非线性超快脉冲耦合的数值方法的Matlab程序 EvmmQ  
TMCA?r%Y\  
在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   m_ m@>}ud  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ~Wm}M  
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%  This Matlab script file solves the nonlinear Schrodinger equations n5/Tn7hY  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of QZox3LM1&.  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear NF!1)  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 "%t`I)  
CWQ2iu<_0  
C=1;                           DZ.trtK  
M1=120,                       % integer for amplitude 5z ^UQq  
M3=5000;                      % integer for length of coupler # :w2Hf6Q  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ONiI:Z>%  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. S\;.nAR  
T =40;                        % length of time:T*T0. k#*yhG,]'  
dt = T/N;                     % time step /*^|5>-`i1  
n = [-N/2:1:N/2-1]';          % Index 9/(c cj  
t = n.*dt;   iBC>w+t14  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. X$iJ|=vW  
w=2*pi*n./T; UiZp-Y%ki  
g1=-i*ww./2; wP0+Xv,  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; >?eTbtP  
g3=-i*ww./2; ;S`-9}6  
P1=0; '\B"g@if  
P2=0; '2$!thm  
P3=1; ~!9Px j*  
P=0; .<^YE%  
for m1=1:M1                 WcO,4:  
p=0.032*m1;                %input amplitude {b0&qV   
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 7O{O')o!  
s1=s10; A=d$ir K[  
s20=0.*s10;                %input in waveguide 2 kseJm+Hc  
s30=0.*s10;                %input in waveguide 3 wKS-O%?  
s2=s20; WAXts]=  
s3=s30; hUvuq,LH_  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   EvQwGt1)P  
%energy in waveguide 1 D8AIVK]  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   `{lAhZ5  
%energy in waveguide 2 IKzRM|/  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   D#Yx,`Ui  
%energy in waveguide 3 EQ63VF
  
for m3 = 1:1:M3                                    % Start space evolution 355Sd;*  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS F*JvpI[7n  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; =/JF-#n/MA  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; |EV\a[  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform l()MYuLNV  
   sca2 = fftshift(fft(s2)); qJXsf M6  
   sca3 = fftshift(fft(s3)); oXlxPN39  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   vd7N&c9  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); L@n6N|[_  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); h<'5q&y  
   s3 = ifft(fftshift(sc3));
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   s2 = ifft(fftshift(sc2));                       % Return to physical space zB6u-4^wT  
   s1 = ifft(fftshift(sc1)); wYO"znd  
end m_!vIUOz  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); k3>ur>aW  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); v<3o[mq  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));  +iH30v  
   P1=[P1 p1/p10]; Z\=04[  
   P2=[P2 p2/p10]; .d~]e2x  
   P3=[P3 p3/p10]; !\#Wk0Ku  
   P=[P p*p]; K+@eH#Cv,(  
end  Ep\  
figure(1) EhIV(q9x  
plot(P,P1, P,P2, P,P3); A?IZ( Zx(`  

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转自：http://blog.163.com/opto_wang/

谢谢哈~！~