[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 d<Os TA  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of qck/b  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ]xG8vy  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear cP1jw%3P  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 UIl
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%fid=fopen('e21.dat','w'); q KM]wu0Et  
N = 128;                       % Number of Fourier modes (Time domain sampling points) .+Ej%|l%  
M1 =3000;              % Total number of space steps W.|6$hRl)  
J =100;                % Steps between output of space JqUVGEg  
T =10;                  % length of time windows:T*T0 c6HU'%v  
T0=0.1;                 % input pulse width #$w#"Nr9k  
MN1=0;                 % initial value for the space output location 2mUu3fZ  
dt = T/N;                      % time step wB)+og-^1f  
n = [-N/2:1:N/2-1]';           % Index 3CE8+PnT  
t = n.*dt;   nnG2z@$-  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Q 8rtZ  
u20=u10.*0.0;                  % input to waveguide 2 Oi0;.<kX  
u1=u10; u2=u20;                 +V@=G &Ou0  
U1 = u1;   ;}~=W!yz  
U2 = u2;                       % Compute initial condition; save it in U "Y!
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. $vBU}~l7  
w=2*pi*n./T; Nd_@J&  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T BFOFes`>~  
L=4;                           % length of evoluation to compare with S. Trillo's paper 6p"c^  
dz=L/M1;                       % space step, make sure nonlinear<0.05 o"FiM5L^.  
for m1 = 1:1:M1                                    % Start space evolution #Qr4Ke$g[l  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS *d@Hnu"q  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; F}]_/cY7B  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform `t1$Ew
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   ca2 = fftshift(fft(u2)); pxxFm~"d  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation j7 =3\SO  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   pK9^WT@  
   u2 = ifft(fftshift(c2));                        % Return to physical space 2&0<$>  
   u1 = ifft(fftshift(c1)); XO#)i6}G  
if rem(m1,J) == 0                                 % Save output every J steps. )$B+3f  
    U1 = [U1 u1];                                  % put solutions in U array #/Fu*0/)`  
    U2=[U2 u2]; 38rZ`O*D  
    MN1=[MN1 m1]; D:E~yh)$-  
    z1=dz*MN1';                                    % output location }+4Bf+u:  
  end b0b9#9x  
end qb4;l\SfT  
hg=abs(U1').*abs(U1');                             % for data write to excel $Je"z]cy-  
ha=[z1 hg];                                        % for data write to excel &H&P)Px*_  
t1=[0 t']; 5%+}rSn7  
hh=[t1' ha'];                                      % for data write to excel file 3Jm'q,TC  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 'd^gRH<z  
figure(1) .w_`d'}  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 7J;~&x  
figure(2) ^<\} Y  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 3DAGW"F  
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非线性超快脉冲耦合的数值方法的Matlab程序 kc'0NE4oq  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   h+3Z.WKhwP  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 
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%  This Matlab script file solves the nonlinear Schrodinger equations "&#WMi  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of OawrS{  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6 2`PK+  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ;Uqx&5P}  
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C=1;                           DRW.NL o  
M1=120,                       % integer for amplitude 2c~?UK[1  
M3=5000;                      % integer for length of coupler s#4ew}  
N = 512;                      % Number of Fourier modes (Time domain sampling points) !mxh]x<e  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. C^" Hj  
T =40;                        % length of time:T*T0. bsi q9$F  
dt = T/N;                     % time step DIqT>HHZ  
n = [-N/2:1:N/2-1]';          % Index aE\B
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t = n.*dt;   ,(0XsBL  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. y8hg8J|  
w=2*pi*n./T; ?>.g;3E$  
g1=-i*ww./2; )fMX!#KP  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; r\n h.}s  
g3=-i*ww./2; @`;Y/',  
P1=0; "h^#<bPN  
P2=0; PyT}}UKj:  
P3=1; H'0*CiHes  
P=0; g<iwxF  
for m1=1:M1                 k<'vP{  
p=0.032*m1;                %input amplitude 4 ?@uF[  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 S`c]Fc  
s1=s10; ?gR\A8:8  
s20=0.*s10;                %input in waveguide 2 22/?JWL>  
s30=0.*s10;                %input in waveguide 3 }1]!#yMfq  
s2=s20; BY4  R@)  
s3=s30; Iwt2}E(e  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   {1@4}R4  
%energy in waveguide 1 #HM\a  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ^wO_b'@v  
%energy in waveguide 2 "_1-IE  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   4ljvoJ}xjr  
%energy in waveguide 3 eY4
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for m3 = 1:1:M3                                    % Start space evolution siRnH(^J  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS EK8
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; \Qi#'c$5+a  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; V"7<[u]K|  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform LN.Bd,  
   sca2 = fftshift(fft(s2)); }r~v,KDb  
   sca3 = fftshift(fft(s3)); /G)KkB
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   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   _ 7BF+*T  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); X&9^&U=e  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); FU5LYXCs  
   s3 = ifft(fftshift(sc3)); ?K4.L?D#J  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 5xMA~I0c  
   s1 = ifft(fftshift(sc1)); 7TV>6i+7  
end tIxhSI^  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); j$|j8?  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); -Ap2NpZ"t  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Ho)t=qn  
   P1=[P1 p1/p10]; [>$\s=` h  
   P2=[P2 p2/p10]; V`g\ja*Y  
   P3=[P3 p3/p10]; bIb6yVnHi  
   P=[P p*p]; B_."?*|w  
end C,|
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figure(1) C`NBHRa>  
plot(P,P1, P,P2, P,P3); W(&Go'9e"  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~