[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 y ?]GOQI  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of #p}I 84Q  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Ej>5PXp'2  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear {tMpI\>S  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 M~7gUb|  
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%fid=fopen('e21.dat','w'); o:jLM7$=  
N = 128;                       % Number of Fourier modes (Time domain sampling points) xM}lX(V!w  
M1 =3000;              % Total number of space steps :<f7;.  
J =100;                % Steps between output of space j_c0oclSz  
T =10;                  % length of time windows:T*T0 q:@$$}FjL  
T0=0.1;                 % input pulse width W&dYH 4O  
MN1=0;                 % initial value for the space output location szN`"Yi){  
dt = T/N;                      % time step $]EG|]"Ns  
n = [-N/2:1:N/2-1]';           % Index B'>(kZYMs  
t = n.*dt;   zz3Rld!b[  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 V6Ie\+@.\  
u20=u10.*0.0;                  % input to waveguide 2 hK*:pf  
u1=u10; u2=u20;                 X(kyu,w  
U1 = u1;   E$]7w4,n  
U2 = u2;                       % Compute initial condition; save it in U <<!XWV*m  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. y)o!F^  
w=2*pi*n./T; 833KU_ N  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 6=a($s!   
L=4;                           % length of evoluation to compare with S. Trillo's paper .dwb@$  
dz=L/M1;                       % space step, make sure nonlinear<0.05 @1ZLr  
for m1 = 1:1:M1                                    % Start space evolution 
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS {
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; +[M5x[[$  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ';4DUhp  
   ca2 = fftshift(fft(u2)); T<kyxbjR  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation AHX_I  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ]@_M
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   u2 = ifft(fftshift(c2));                        % Return to physical space j/_@~MJBt  
   u1 = ifft(fftshift(c1)); M0g!"0?  
if rem(m1,J) == 0                                 % Save output every J steps. :[P>e ox  
    U1 = [U1 u1];                                  % put solutions in U array Rdao  
    U2=[U2 u2]; g-j`Ex%  
    MN1=[MN1 m1]; &>43l+  
    z1=dz*MN1';                                    % output location G>f-w F6  
  end 5#/"0:2  
end QWG?^T fi  
hg=abs(U1').*abs(U1');                             % for data write to excel $$`E@\5P  
ha=[z1 hg];                                        % for data write to excel @bU(z$eB  
t1=[0 t']; ]X/1u"  
hh=[t1' ha'];                                      % for data write to excel file o!EPF-:  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format qV0C2jZ2  
figure(1) "J^M@k\!  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn NY(c4fzl  
figure(2) #]bWE$sU<  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn U WYLT-^x  
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非线性超快脉冲耦合的数值方法的Matlab程序 r168ft?c  
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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。   q5J6d+  
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 Ga0= G&/  
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%  This Matlab script file solves the nonlinear Schrodinger equations -:wC920+  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ?'uxYeX6  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear xb$eFiQ  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 7Fb |~In<Z  
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C=1;                           fbp
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M1=120,                       % integer for amplitude xq1=O  
M3=5000;                      % integer for length of coupler F3[3~r  
N = 512;                      % Number of Fourier modes (Time domain sampling points) u(V4KUk  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. /]4[b!OTJ  
T =40;                        % length of time:T*T0. f;M7y:A8q,  
dt = T/N;                     % time step (m|w&oA/  
n = [-N/2:1:N/2-1]';          % Index ~L j[xP  
t = n.*dt;   <*u[<  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. \2,7fy'  
w=2*pi*n./T; H^P uC (  
g1=-i*ww./2; p\5DW'  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; o<2H~2/  
g3=-i*ww./2; )u~LzE]{_  
P1=0; 9Cbf[\J!bq  
P2=0; o =)hUr  
P3=1; l(|@ dp  
P=0; D/C,Q|Ya6  
for m1=1:M1                 |KFRC)g  
p=0.032*m1;                %input amplitude .r!:` 6  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 `ZL~k  
s1=s10; }WXO[ +l  
s20=0.*s10;                %input in waveguide 2 t.B%7e  
s30=0.*s10;                %input in waveguide 3 R:HF~}  
s2=s20; z;`o>Ja2  
s3=s30; !l1UpJp  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   6u^MfOc  
%energy in waveguide 1 i_8q!CL@{  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   xJ H]>#XJ  
%energy in waveguide 2 n`<YhV  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Nq %@(K  
%energy in waveguide 3 sE7!U|  
for m3 = 1:1:M3                                    % Start space evolution </0@7  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS LO
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; tEP~`$9  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; "C 7-^R#  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform @#[<5ld  
   sca2 = fftshift(fft(s2)); $OU,| D  
   sca3 = fftshift(fft(s3)); z$OKn#%T  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   9fR`un)f}  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); D4WvRxki  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ;A)w:"m  
   s3 = ifft(fftshift(sc3)); R<aF;Rvb5  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 8/cD7O  
   s1 = ifft(fftshift(sc1)); +$
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end lrg3n[y-l  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); I_66q7U"0  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Zhb)n
 
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); W.b?MPy]  
   P1=[P1 p1/p10]; "bZ{W(h  
   P2=[P2 p2/p10]; J WaI[n}  
   P3=[P3 p3/p10]; %7WQb]y  
   P=[P p*p]; '?Fw]z1$  
end (izGF;N+  
figure(1) YB{hQ<W
 
plot(P,P1, P,P2, P,P3); eZ+pZq  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~