[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 ?8$`GyjS  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 0m1V@3]7>  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of z(c8]Wu#  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear lrc%GU):  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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%fid=fopen('e21.dat','w'); wxBHlgK4z  
N = 128;                       % Number of Fourier modes (Time domain sampling points) lO\HchGzB  
M1 =3000;              % Total number of space steps PW@ :fM:q  
J =100;                % Steps between output of space l'm|**  
T =10;                  % length of time windows:T*T0 ,W+=N"`a'  
T0=0.1;                 % input pulse width J8\l'}?&  
MN1=0;                 % initial value for the space output location U{
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dt = T/N;                      % time step xppnBnu$7  
n = [-N/2:1:N/2-1]';           % Index Up%XBA  
t = n.*dt;   Z?S?O#FED  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Q^<amM!  
u20=u10.*0.0;                  % input to waveguide 2 q/:]+  
u1=u10; u2=u20;                 d(}? \|  
U1 = u1;   >]_6|Wfl  
U2 = u2;                       % Compute initial condition; save it in U dlyGgaV*X  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. }{+?>!qDt  
w=2*pi*n./T; 7}qxWz  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 3US`6Y"  
L=4;                           % length of evoluation to compare with S. Trillo's paper v1i-O'  
dz=L/M1;                       % space step, make sure nonlinear<0.05
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for m1 = 1:1:M1                                    % Start space evolution A ___| #R  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS i9 CQ~  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ;fV"5H)U\  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform -`ljKp  
   ca2 = fftshift(fft(u2)); "E7<S5cr  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation D|U bh]  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   k
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   u2 = ifft(fftshift(c2));                        % Return to physical space W`LG.`JW  
   u1 = ifft(fftshift(c1)); |{|B70v3Co  
if rem(m1,J) == 0                                 % Save output every J steps. 512p\x@  
    U1 = [U1 u1];                                  % put solutions in U array gjD|f2*x  
    U2=[U2 u2]; fiC0'4.,  
    MN1=[MN1 m1]; 6|Dtx5 "r  
    z1=dz*MN1';                                    % output location LV9R ]  
  end ({Yfsf,  
end A/9<} m  
hg=abs(U1').*abs(U1');                             % for data write to excel Hwd^C2v  
ha=[z1 hg];                                        % for data write to excel Y\<w|LkD8  
t1=[0 t']; `[E-V  
hh=[t1' ha'];                                      % for data write to excel file 'N6oXE
  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format z( ^?xv  
figure(1) >~7XBb08  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn .>,Y |  
figure(2) 5o{U$  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ~Ih` ayVq  
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非线性超快脉冲耦合的数值方法的Matlab程序 o *U-.&  
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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。   r]}6iF.  
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 \+Qd=,!i(  
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%  This Matlab script file solves the nonlinear Schrodinger equations 9pi{)PDJ  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of  0zr%8Q(Q  
%  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 S_*Gv O  
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C=1;                           !iHC++D  
M1=120,                       % integer for amplitude k
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M3=5000;                      % integer for length of coupler Mx0~^l
 
N = 512;                      % Number of Fourier modes (Time domain sampling points) l`6.(6  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ~f[;(?39xZ  
T =40;                        % length of time:T*T0. 3J8>r|u;1'  
dt = T/N;                     % time step ,|8aDL?
 
n = [-N/2:1:N/2-1]';          % Index FW2x  
t = n.*dt;   ]ZR` 6|"VO  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. r1.zURY  
w=2*pi*n./T; v:!TqfI  
g1=-i*ww./2; V]]!0ugvk(  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Nz"K`C>/  
g3=-i*ww./2; z<P?p  
P1=0; r4K_Wp  
P2=0; %Y/;jCY  
P3=1; [T'[7Z  
P=0; 1QhQ#`$<1  
for m1=1:M1                 [Djx@x  
p=0.032*m1;                %input amplitude >^W6'Q$P<  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 TWRnty-C  
s1=s10; n<)A5UB5-  
s20=0.*s10;                %input in waveguide 2 FP y}Wc*UA  
s30=0.*s10;                %input in waveguide 3 GM8>u
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s2=s20; MdEds|D  
s3=s30; LH`$<p2''r  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ETX>wZ  
%energy in waveguide 1 O\oRM2^u}  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   $zhvI*0  
%energy in waveguide 2 y_Gs_xg  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   8.%wnH  
%energy in waveguide 3 7On.y*  
for m3 = 1:1:M3                                    % Start space evolution :|&6x!  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS U![$7k>,pr  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 247vU1  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; gs.+|4dv  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform xHx_! )7  
   sca2 = fftshift(fft(s2)); %PPy0RZ^  
   sca3 = fftshift(fft(s3)); 7N5M=f.DS(  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   a3:45[SO4e  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 4QPHT#eqX  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); } nIYNeP?D  
   s3 = ifft(fftshift(sc3)); a
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   s2 = ifft(fftshift(sc2));                       % Return to physical space @^# 9N!Fj]  
   s1 = ifft(fftshift(sc1)); VWYNq^<AT  
end a>6M{C@pd  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); TR `C|TV>  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); QYj 4D  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ;$]a.9 -  
   P1=[P1 p1/p10]; VD!PF'  
   P2=[P2 p2/p10]; ]$.w I~J%  
   P3=[P3 p3/p10]; |Ul4n@+2  
   P=[P p*p]; ::GW  
end 9N2.:<so  
figure(1) KB^GC5L>  
plot(P,P1, P,P2, P,P3); TgLr4Ex  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~