[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 3T4HX|rC  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of v_WQ<G?  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of }N$f=:i
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear )58~2v
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |d*a~T0  
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%fid=fopen('e21.dat','w'); MtN!Xx  
N = 128;                       % Number of Fourier modes (Time domain sampling points) -V[x q  
M1 =3000;              % Total number of space steps af9KtX+  
J =100;                % Steps between output of space lI.oyR'  
T =10;                  % length of time windows:T*T0 |5X[/Q*K`W  
T0=0.1;                 % input pulse width $AE5n>ZD$  
MN1=0;                 % initial value for the space output location 1+XM1(|c`  
dt = T/N;                      % time step  Y#~A":A  
n = [-N/2:1:N/2-1]';           % Index e"NP]_vh,  
t = n.*dt;   ]t`SCsoo  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 $gD8[NAIx=  
u20=u10.*0.0;                  % input to waveguide 2 ; D/6e6  
u1=u10; u2=u20;                 UXJblo#  
U1 = u1;   q^Oj/ws  
U2 = u2;                       % Compute initial condition; save it in U 0BhcXHt  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. %DXBl:!Y`  
w=2*pi*n./T; q#8yU\J|,  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T '@Rk#=85Z  
L=4;                           % length of evoluation to compare with S. Trillo's paper BI%XF 9{  
dz=L/M1;                       % space step, make sure nonlinear<0.05 vB{iw}Hi!  
for m1 = 1:1:M1                                    % Start space evolution Y_!+Y<x7v  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS dr:x0>  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; m;MJ{"@A'  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 18QqZ,t  
   ca2 = fftshift(fft(u2)); CEc(2q+%i  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ]S[?tn  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   L+<h5>6  
   u2 = ifft(fftshift(c2));                        % Return to physical space m6n%?8t  
   u1 = ifft(fftshift(c1)); ~"SQwE|  
if rem(m1,J) == 0                                 % Save output every J steps. )E>yoUhN  
    U1 = [U1 u1];                                  % put solutions in U array n-l_PhPQ`  
    U2=[U2 u2]; vIOGDI>  
    MN1=[MN1 m1]; -bHlFNRm  
    z1=dz*MN1';                                    % output location %N fpEo  
  end Z_m<x!  
end m:[I$b6AY  
hg=abs(U1').*abs(U1');                             % for data write to excel =f{v:n6  
ha=[z1 hg];                                        % for data write to excel AguE)I&m  
t1=[0 t']; vJ^~J2#5  
hh=[t1' ha'];                                      % for data write to excel file }P.Z}n;Uj  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format A`Y^qXFb`  
figure(1) PDuBf&/e  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn D_
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figure(2) SM4`Hys;p  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 3-{BXht)  
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非线性超快脉冲耦合的数值方法的Matlab程序 `Y4Kw  
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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。   52tc|j6~#  
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 Q/ .LDye8  
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%  This Matlab script file solves the nonlinear Schrodinger equations PD.$a-t  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of $$1t4=Pz  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear rVNx2  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 fP|[4 ku
 
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C=1;                           7N[".V]c  
M1=120,                       % integer for amplitude wPjq B{!Q  
M3=5000;                      % integer for length of coupler Rq5'=L  
N = 512;                      % Number of Fourier modes (Time domain sampling points) :!oJmvy  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. yef\Y3X  
T =40;                        % length of time:T*T0. ~. vridH  
dt = T/N;                     % time step EXr2d"  
n = [-N/2:1:N/2-1]';          % Index %(/E `  
t = n.*dt;   cE 'LE1DK  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. nWIZ0Nde'  
w=2*pi*n./T; nJN-U+)u  
g1=-i*ww./2; W{"sB:E  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; \~E?;q!  
g3=-i*ww./2; $e7%>*?m  
P1=0; _) x{TnK  
P2=0; P|$n   
P3=1; U`qC.s(L  
P=0; g&xj(SMj-$  
for m1=1:M1                 6-
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p=0.032*m1;                %input amplitude %%s)D4sW  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 <.n,:ir  
s1=s10; 9,INyEyAL  
s20=0.*s10;                %input in waveguide 2 rz%~=Ca2j  
s30=0.*s10;                %input in waveguide 3 )-)rL@s.  
s2=s20; x:MwM?  
s3=s30; 5:IDl1f5  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   F%|P#CaB  
%energy in waveguide 1 *zrGrk:l  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   8>eYM  
%energy in waveguide 2 HfVHjF)  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   @Z ==B%`  
%energy in waveguide 3 9m)$^U>oz  
for m3 = 1:1:M3                                    % Start space evolution ?K[Y
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   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ,XEIg  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; mcd{:/^?  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; zK5&,/  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ?;CIS$$r  
   sca2 = fftshift(fft(s2)); V ,p~,rC  
   sca3 = fftshift(fft(s3)); ):G%o  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   =SLG N`m3  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); metn&  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); W:RjWn@<  
   s3 = ifft(fftshift(sc3)); p6<JpW5@_  
   s2 = ifft(fftshift(sc2));                       % Return to physical space b_~XTWP$l  
   s1 = ifft(fftshift(sc1)); LRu,_2"  
end >k\pSV[  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 'r]6 GC8Z$  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); F}u'A,Hc  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Q&]|W Xv  
   P1=[P1 p1/p10]; z;1dMQ,#  
   P2=[P2 p2/p10]; a*5KUj6/TL  
   P3=[P3 p3/p10]; *ai~!TR  
   P=[P p*p]; u @Ze@N%  
end $vu*# .w  
figure(1) q* R}yt5  
plot(P,P1, P,P2, P,P3); 9-T<gYl  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~