[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 P-ri=E}>  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 2Ry1b+\  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of D@!=d@V.  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear i;!H!-sM  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 IpP~Uz  
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%fid=fopen('e21.dat','w'); 1KjU ] r
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N = 128;                       % Number of Fourier modes (Time domain sampling points) rk)##)  
M1 =3000;              % Total number of space steps sg+uBCGB  
J =100;                % Steps between output of space Z!U)I-x&  
T =10;                  % length of time windows:T*T0 >3c@x  
T0=0.1;                 % input pulse width ezPz<iZ\N  
MN1=0;                 % initial value for the space output location ~#kT_*sw)  
dt = T/N;                      % time step UKM2AZ0lb  
n = [-N/2:1:N/2-1]';           % Index uL[.ND2._&  
t = n.*dt;   qL,tYJ<m%  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 dDF .qXq.  
u20=u10.*0.0;                  % input to waveguide 2 AE} )o)B  
u1=u10; u2=u20;                 OK\A</8r  
U1 = u1;   sP ls zC[  
U2 = u2;                       % Compute initial condition; save it in U H"qOSf{  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. yz0zFfiX  
w=2*pi*n./T; Yot?=T};3{  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T R58-wUto  
L=4;                           % length of evoluation to compare with S. Trillo's paper 'Y]mOD^p  
dz=L/M1;                       % space step, make sure nonlinear<0.05 )HX|S-qRU=  
for m1 = 1:1:M1                                    % Start space evolution TC<@e<-%Sq  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 1AU#%wIEP  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; R+Y4|  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform {l |E:>Q2  
   ca2 = fftshift(fft(u2)); !ET~KL!  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation fJ ,1Ef;Z  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ",!1m7[wF  
   u2 = ifft(fftshift(c2));                        % Return to physical space J9=m]R8T  
   u1 = ifft(fftshift(c1)); 9]e V?yoA8  
if rem(m1,J) == 0                                 % Save output every J steps. y
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    U1 = [U1 u1];                                  % put solutions in U array Q:5KZm[[  
    U2=[U2 u2]; l&[;rh  
    MN1=[MN1 m1]; B9wPU1  
    z1=dz*MN1';                                    % output location vBog0KD);s  
  end A\#iX
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end $ibuWb"a  
hg=abs(U1').*abs(U1');                             % for data write to excel hEw- O;T0  
ha=[z1 hg];                                        % for data write to excel CP6LHkM9  
t1=[0 t']; v'BZs   
hh=[t1' ha'];                                      % for data write to excel file ,u/aT5\_  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format f aLtdQi  
figure(1) -N"&/)  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn yR4|S2D3xn  
figure(2) lv]hTH 4T  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn :hM/f  
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非线性超快脉冲耦合的数值方法的Matlab程序 SI=yI-  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   A*um{E+  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 qkC/\![@  
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%  This Matlab script file solves the nonlinear Schrodinger equations 46 PoM  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ,13Lq-  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear /FIE:Io  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 W]nSR RWco  
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C=1;                           PnoPbk[<  
M1=120,                       % integer for amplitude |M+<m">E  
M3=5000;                      % integer for length of coupler )LyojwY_g  
N = 512;                      % Number of Fourier modes (Time domain sampling points) o";Z$tAJkC  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. rSJ9v:  
T =40;                        % length of time:T*T0. WH= EPOR,  
dt = T/N;                     % time step +gLPhX:`  
n = [-N/2:1:N/2-1]';          % Index `+uhy,  
t = n.*dt;   $k2*[sn,  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 3#TV5+x*"`  
w=2*pi*n./T; AU$Uxwz4  
g1=-i*ww./2; <^lRUw  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; K5XK%Gl"  
g3=-i*ww./2; =|YxDas  
P1=0; +9")KQT  
P2=0; t8dm)s[r8  
P3=1; sx`O8t  
P=0; QI3Nc8t_2  
for m1=1:M1                 pi ,eIm  
p=0.032*m1;                %input amplitude qk;{c
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 E8~}PQW:I  
s1=s10; >mjNmh7  
s20=0.*s10;                %input in waveguide 2 _C`K*u 6Z<  
s30=0.*s10;                %input in waveguide 3 l'TWkQ-  
s2=s20; Yk5}`d!:  
s3=s30; r}jGUe}d  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   n;:rf7hGY  
%energy in waveguide 1 aG92ay  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   6#QK%[1!>  
%energy in waveguide 2 J;f!!<l\  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   |
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%energy in waveguide 3 7Ddaf>  
for m3 = 1:1:M3                                    % Start space evolution yn/rW$  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 1Q.\s_2  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; E,f>1meN=  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; a!u rew#  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform %C=]1Q=T)  
   sca2 = fftshift(fft(s2)); pe{;~-|6  
   sca3 = fftshift(fft(s3)); NwZ@#D#[ Y  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   cJL'$`gWf  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ~mR'Q-hi<  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); npNB{J[  
   s3 = ifft(fftshift(sc3)); 6A=8+R'`F  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 4M^G`WA}t9  
   s1 = ifft(fftshift(sc1)); HVC>9_:]  
end (1NA  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 44F`$.v96  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); \R3H+W  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); mb!9&&2-t  
   P1=[P1 p1/p10]; r{rQu-|.  
   P2=[P2 p2/p10]; ^*fxR
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   P3=[P3 p3/p10]; ,-OCc!7K  
   P=[P p*p]; 3hK#'."`N  
end W[}s o6  
figure(1) T0]*{k(FR  
plot(P,P1, P,P2, P,P3); w&x!,yd;  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~