[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 [ MyE2^  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of cn`iX(ZgR  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of fCw*$:O  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear h6v077qG  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 !*{q^IO9v&  
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%fid=fopen('e21.dat','w'); >IfV\w32  
N = 128;                       % Number of Fourier modes (Time domain sampling points) *O~e T  
M1 =3000;              % Total number of space steps G~,:2 o3  
J =100;                % Steps between output of space vXE0%QE'Q  
T =10;                  % length of time windows:T*T0 iE].&>w  
T0=0.1;                 % input pulse width b:W-l?  
MN1=0;                 % initial value for the space output location j;0vAf  
dt = T/N;                      % time step sG7u}r  
n = [-N/2:1:N/2-1]';           % Index <vV_%uoM  
t = n.*dt;   8LzBh_J?  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 3Q^fVn$tk  
u20=u10.*0.0;                  % input to waveguide 2 GVGlVAo|@  
u1=u10; u2=u20;                 9+=gke  
U1 = u1;   ino:N5&;;  
U2 = u2;                       % Compute initial condition; save it in U Qzv
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 8\.b4FNJ  
w=2*pi*n./T; S\i@s_  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 7gF"=7{-  
L=4;                           % length of evoluation to compare with S. Trillo's paper a_~=#]a  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Kn`M4O  
for m1 = 1:1:M1                                    % Start space evolution ~`ny@WD9  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS p>w]rE:}  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; <AH1i@4  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform Yf@e=:  
   ca2 = fftshift(fft(u2)); Ifc]K?  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation #%0Bx3uM  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   QS[L~97m2M  
   u2 = ifft(fftshift(c2));                        % Return to physical space
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   u1 = ifft(fftshift(c1)); co8"sz0(U  
if rem(m1,J) == 0                                 % Save output every J steps. o\b-_E5"?  
    U1 = [U1 u1];                                  % put solutions in U array ia
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    U2=[U2 u2]; >Gml4vGK  
    MN1=[MN1 m1]; I#F!N6;  
    z1=dz*MN1';                                    % output location 'k0[rDFc#3  
  end =@&cHY  
end ElhRF{R  
hg=abs(U1').*abs(U1');                             % for data write to excel :KJ pk:<  
ha=[z1 hg];                                        % for data write to excel l e4?jQQ@L  
t1=[0 t']; 4`m~FNVS  
hh=[t1' ha'];                                      % for data write to excel file V"\0Y0  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format sUJ%x#u}Fk  
figure(1) O/s$SX%g  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 8BOZh6BV  
figure(2) %ts^Z*3u  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn IYn]U4P.  
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非线性超快脉冲耦合的数值方法的Matlab程序 g[RI.&?  
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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。   ,2
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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 !* Ti}oIo&  
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%  This Matlab script file solves the nonlinear Schrodinger equations R'EUV0KX>Y  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of %,Sf1fUJ
 
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear U$]|~41#  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 00v&lQBW  
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C=1;                           ?Nf>]|K:Q  
M1=120,                       % integer for amplitude %~L>1ShtU  
M3=5000;                      % integer for length of coupler eAv4FA4g  
N = 512;                      % Number of Fourier modes (Time domain sampling points) MYJg8 '[j  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 'o|30LzYgQ  
T =40;                        % length of time:T*T0. L^2FQti>  
dt = T/N;                     % time step r.3/
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n = [-N/2:1:N/2-1]';          % Index S5~VD?O,  
t = n.*dt;   f` =CpO*  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. w
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w=2*pi*n./T; (py]LBZ  
g1=-i*ww./2; { eCC$&"  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; I2nF-JzD2a  
g3=-i*ww./2; H 0+dV3  
P1=0; $o$ maA0  
P2=0;
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P3=1; ~U;rw&'H  
P=0; ^O^l(e!3  
for m1=1:M1                 0#w?HCx=  
p=0.032*m1;                %input amplitude B<j'm0a>B  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ?A(QyaKz  
s1=s10; DXz}YIEC  
s20=0.*s10;                %input in waveguide 2 -@T/b$]'n  
s30=0.*s10;                %input in waveguide 3 PV|uPuz  
s2=s20; 64hk2a8  
s3=s30; 4`JH&))}  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   \j&^aAp r  
%energy in waveguide 1 m[j70jYe  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   foJdu+^  
%energy in waveguide 2 Neg,qOt  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   x|yEtO&  
%energy in waveguide 3 FQ g~l4WX  
for m3 = 1:1:M3                                    % Start space evolution `PY>Hgb  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS >3z5
ww  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 6iCrRjY*  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; K|dso]b/  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 0eK*9S]  
   sca2 = fftshift(fft(s2)); %Gt.m  
   sca3 = fftshift(fft(s3)); z5)s/;Sc  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   jDQZQ NS  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); H54R8O$  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 2W4qBaG$=  
   s3 = ifft(fftshift(sc3)); Z!hafhcX  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 'fW6 .0fXa  
   s1 = ifft(fftshift(sc1)); 5nsq[Q`  
end ! u:Weoz  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ,"B+r6}EF  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ]Kr `9r),  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); &hRv
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   P1=[P1 p1/p10]; +nJUFc  
   P2=[P2 p2/p10]; 7)s^8+  
   P3=[P3 p3/p10]; D1__n6g[  
   P=[P p*p]; I1PuHf Qs  
end cReB~wk  
figure(1) CiB%B`,N  
plot(P,P1, P,P2, P,P3); HuOIFv  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~