[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 VTD'D+t  
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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 Io| 72W}rg  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear U2!9Tl9".  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 voCQ_~*)9  
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%fid=fopen('e21.dat','w'); eFbr1IV  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Zs)HzOP)9  
M1 =3000;              % Total number of space steps RBiDU}j  
J =100;                % Steps between output of space 3%'$AM}+s  
T =10;                  % length of time windows:T*T0 }F**!%4d  
T0=0.1;                 % input pulse width O']-<E`1k  
MN1=0;                 % initial value for the space output location k_$w+Q  
dt = T/N;                      % time step vxK}f*d  
n = [-N/2:1:N/2-1]';           % Index YG<?|AS/  
t = n.*dt;   Q+gQ"l,95  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 'Aai.PE:  
u20=u10.*0.0;                  % input to waveguide 2 |no '^  
u1=u10; u2=u20;                 =p:D_b  
U1 = u1;   #\o VbVq  
U2 = u2;                       % Compute initial condition; save it in U 1+v)#Wj  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. b4i=eI8  
w=2*pi*n./T; DTPYCG&%  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T #%Uk}5;-  
L=4;                           % length of evoluation to compare with S. Trillo's paper sZ7{_}B  
dz=L/M1;                       % space step, make sure nonlinear<0.05 !bS:!Il9=  
for m1 = 1:1:M1                                    % Start space evolution T/UhZ4(V  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ]xbR:CYJ  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; }5FdX3YR  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 5 J61PuH   
   ca2 = fftshift(fft(u2)); UC3?XoT\  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation yiiYq(\{  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   p'ukV(B  
   u2 = ifft(fftshift(c2));                        % Return to physical space
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   u1 = ifft(fftshift(c1)); \Xh
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if rem(m1,J) == 0                                 % Save output every J steps. 1\TXb!OtL  
    U1 = [U1 u1];                                  % put solutions in U array D`2Iy.|!  
    U2=[U2 u2]; %5NfF65'  
    MN1=[MN1 m1]; ZFY t[:  
    z1=dz*MN1';                                    % output location CUaI66  
  end fXEF]C  
end G(EiDo&  
hg=abs(U1').*abs(U1');                             % for data write to excel :"|}oKT%mP  
ha=[z1 hg];                                        % for data write to excel
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t1=[0 t']; /T!S)FD\/v  
hh=[t1' ha'];                                      % for data write to excel file #B_ ``XV  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format -P^ 6b(  
figure(1) +K])&}Dw  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Szsq|T  
figure(2) oyiEOC  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Re0ma%~LP  
udMDE=1~L  
非线性超快脉冲耦合的数值方法的Matlab程序 M`-.0  
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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。   VZ5EV'D8!  
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 "}Of f  
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%  This Matlab script file solves the nonlinear Schrodinger equations DP6M4  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 7loIX Qw  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear qCi6kEr  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 prV:Kq;O  
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C=1;                           "qYPi  
M1=120,                       % integer for amplitude VPx"l5\  
M3=5000;                      % integer for length of coupler _=Ed>2M)no  
N = 512;                      % Number of Fourier modes (Time domain sampling points) : " 9F.U  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. :n4?  
T =40;                        % length of time:T*T0. &9g4/c-?$  
dt = T/N;                     % time step hz
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n = [-N/2:1:N/2-1]';          % Index hiZE8?0+~N  
t = n.*dt;   N{U``LV  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ( 6|S42  
w=2*pi*n./T; (,#Rj$W  
g1=-i*ww./2; {+_pyL  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; E"ijNs  
g3=-i*ww./2; ;I1}g]  
P1=0; dlsVE~_G  
P2=0; s-!Bpr16o0  
P3=1; 8M9 &CsT6  
P=0; B`3RyM"J@  
for m1=1:M1                 03Pa; n  
p=0.032*m1;                %input amplitude rnz9TmN:*1  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ?4GI19j  
s1=s10; <2Lcy&w_M  
s20=0.*s10;                %input in waveguide 2 Z6F>SL  
s30=0.*s10;                %input in waveguide 3 0*o)k6?q3  
s2=s20; ^|M\vO  
s3=s30; 1bs8fUPB3  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ~$-Nl  
%energy in waveguide 1 20h|e+3  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ]:m>pI*z.  
%energy in waveguide 2 L8("1_  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   }YH@T]O}  
%energy in waveguide 3 l3dGe'  
for m3 = 1:1:M3                                    % Start space evolution b1Bu5%bt,:  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS q] eSDRW  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; #-?pY"N,  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ]@)T]  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform m&(yx|a4+  
   sca2 = fftshift(fft(s2)); *&]x-p1m  
   sca3 = fftshift(fft(s3)); SV*h9LL  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   k$1ya7-@  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); *$mDu,'8  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); y1z<{'2x  
   s3 = ifft(fftshift(sc3)); Z".mEF-b  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 8@S7_x  
   s1 = ifft(fftshift(sc1)); HL-zuZa`Ju  
end @|kBc.(]  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); >Q':+|K}  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Ej\EuX  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ug*#rpb  
   P1=[P1 p1/p10]; ,b!!h]t  
   P2=[P2 p2/p10]; 'wB6-  
   P3=[P3 p3/p10]; oxT..=-  
   P=[P p*p]; 72@lDY4cE  
end e]R`B}vO  
figure(1) CMn&1  
plot(P,P1, P,P2, P,P3); /Ud<4j-  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~