[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 '97)c7E  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Q&(?D  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of vxUJ4|Qz  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Vyj>&"28  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 C@pDX>~2=b  
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%fid=fopen('e21.dat','w'); idGkX ?  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 4en&EWUr  
M1 =3000;              % Total number of space steps $%;NX[>j  
J =100;                % Steps between output of space 4S 2I]d  
T =10;                  % length of time windows:T*T0 }CsUZ&*&  
T0=0.1;                 % input pulse width VPys  
MN1=0;                 % initial value for the space output location + h`:qB  
dt = T/N;                      % time step [aO"9
 
n = [-N/2:1:N/2-1]';           % Index T=VVK6Lc:  
t = n.*dt;   EYGJDv(S  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 sa#=#0yg  
u20=u10.*0.0;                  % input to waveguide 2 9Vzk:zOT  
u1=u10; u2=u20;                 :KgLjhj|)  
U1 = u1;   q]<Xx{_  
U2 = u2;                       % Compute initial condition; save it in U XT{1!I(  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 9Lk.\.  
w=2*pi*n./T; eQcy'GA06  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T >G' NI?$  
L=4;                           % length of evoluation to compare with S. Trillo's paper PH
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dz=L/M1;                       % space step, make sure nonlinear<0.05 hrZ~7 0r  
for m1 = 1:1:M1                                    % Start space evolution da\K
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS LN?T$H  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ;ZjQy,H%  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 2s-f?WetbP  
   ca2 = fftshift(fft(u2)); R{!s%K&  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation >m}.}g8  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   8
f,jC+(  
   u2 = ifft(fftshift(c2));                        % Return to physical space >+u5%5-wr  
   u1 = ifft(fftshift(c1)); Bf1GHnXv  
if rem(m1,J) == 0                                 % Save output every J steps. v6s8 p  
    U1 = [U1 u1];                                  % put solutions in U array =_%:9FnQ0  
    U2=[U2 u2]; BTjF^&`  
    MN1=[MN1 m1]; w#Nn(!VR  
    z1=dz*MN1';                                    % output location A6lf-8ncx  
  end Yr-,0${m  
end Ng'f u|  
hg=abs(U1').*abs(U1');                             % for data write to excel lqX]'gu]\  
ha=[z1 hg];                                        % for data write to excel 7X|&:V.s|  
t1=[0 t']; wH|\;M{0V1  
hh=[t1' ha'];                                      % for data write to excel file X?>S24I"9  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format {nryAXK  
figure(1) }y=7r!{@  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn rRT9)wDa  
figure(2) S31:}   
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 'G-VhvMv  
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非线性超快脉冲耦合的数值方法的Matlab程序 k B2+Tr  
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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。   OMKEn!Wq  
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 .4_~ku  
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%  This Matlab script file solves the nonlinear Schrodinger equations JFYeOmR+l  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ~p'/Z@Atu  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear . s? ''/(  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ik&loM_  
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C=1;                           cB -XmX/  
M1=120,                       % integer for amplitude Qx.E+n\  
M3=5000;                      % integer for length of coupler >#!n"i;  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Fi7pq2  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. c?q#?K aF  
T =40;                        % length of time:T*T0. 1-w1k^e  
dt = T/N;                     % time step !m_'<=)B4~  
n = [-N/2:1:N/2-1]';          % Index }
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t = n.*dt;   (6 0,0|s  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. OEB_LI'  
w=2*pi*n./T; L?al2aopF  
g1=-i*ww./2; 4+v~{  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; L x9`y t6  
g3=-i*ww./2; O~qB  
P1=0; zKT \i  
P2=0; 3c9v~5og4  
P3=1; s?0r\cc|:  
P=0; xg3G  
for m1=1:M1                 0Fbq/63  
p=0.032*m1;                %input amplitude ?\c*DNM'  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 $#KSvo{otI  
s1=s10; h!d#=.R  
s20=0.*s10;                %input in waveguide 2 T*YdGIFO  
s30=0.*s10;                %input in waveguide 3 YjHGdacs  
s2=s20; RCxqqUS\C  
s3=s30; bZ3CJ f&mE  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   W>B:W0A  
%energy in waveguide 1 Ui?
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p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   )Xg#x:  
%energy in waveguide 2 7Kh+m@q.  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Qz<v. _  
%energy in waveguide 3 ](T*f'LN  
for m3 = 1:1:M3                                    % Start space evolution q=96Ci_a  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS A`OU}'v?L  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 4[Oy3.-c  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; `^_.E:f  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform &,e@pvc3  
   sca2 = fftshift(fft(s2)); D}3E1`)W  
   sca3 = fftshift(fft(s3)); Cs*u{O  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ]^j)4us  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); zH|!O!3"4  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); > ]6Eb`v  
   s3 = ifft(fftshift(sc3)); ^[qmELW#7  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Mb$&~!  
   s1 = ifft(fftshift(sc1)); hV=)T^Q  
end 66z1_lA  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); p&ZD1qa  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ,Hj=]e2?  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Gc SX5c  
   P1=[P1 p1/p10]; rJ<v1Yb  
   P2=[P2 p2/p10]; L#NPt4Sz+  
   P3=[P3 p3/p10]; uV%7|/fD  
   P=[P p*p]; $e<3z6  
end r--"JO%
2  
figure(1) U)c,ZxE  
plot(P,P1, P,P2, P,P3); #]:nQ(  
L0uN|?}  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~