[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 Q*&k6A"jx  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of <a_ytSoG1  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ^N#z&oh  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear R<]f[  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 m%7T ~  
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%fid=fopen('e21.dat','w'); apmZ&Ab  
N = 128;                       % Number of Fourier modes (Time domain sampling points) II;   
M1 =3000;              % Total number of space steps Ts)ox}rYVm  
J =100;                % Steps between output of space DNwqi"  
T =10;                  % length of time windows:T*T0 O7,)#{  
T0=0.1;                 % input pulse width 4@0y$Dv\  
MN1=0;                 % initial value for the space output location ]fiAV|'^  
dt = T/N;                      % time step qGivR
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n = [-N/2:1:N/2-1]';           % Index '
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t = n.*dt;   pT ]:TRPS  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 m6+4}=Cn  
u20=u10.*0.0;                  % input to waveguide 2 ~
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u1=u10; u2=u20;                 q#pD}Xe$  
U1 = u1;   -0P(lkylf  
U2 = u2;                       % Compute initial condition; save it in U wB%N}bi!  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. S1SsJo2\  
w=2*pi*n./T; NRIp@PIF:"  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T s\/$`fuhx  
L=4;                           % length of evoluation to compare with S. Trillo's paper \A#YL1hh  
dz=L/M1;                       % space step, make sure nonlinear<0.05 iC(&U YL  
for m1 = 1:1:M1                                    % Start space evolution _|1m]2'9  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Wks?9)Is  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; pA?kv]l(  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ;Gnk8lIsb  
   ca2 = fftshift(fft(u2)); C]dK/~Z#r  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation S29k IJ  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   3]MSS\uB  
   u2 = ifft(fftshift(c2));                        % Return to physical space @3g$H[}  
   u1 = ifft(fftshift(c1)); Z~[EZgIg  
if rem(m1,J) == 0                                 % Save output every J steps. R%EpF'[~[  
    U1 = [U1 u1];                                  % put solutions in U array K."%PdC  
    U2=[U2 u2]; E=3UaYr  
    MN1=[MN1 m1]; S:F8`Gh  
    z1=dz*MN1';                                    % output location (:h#H[F  
  end T#OrsJdu  
end iCXKi7  
hg=abs(U1').*abs(U1');                             % for data write to excel SOg>0VH)  
ha=[z1 hg];                                        % for data write to excel 0cF+4,5  
t1=[0 t']; K3*8-Be  
hh=[t1' ha'];                                      % for data write to excel file r P1FM1"M  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format !TwH;#U w  
figure(1) =]F;{x  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ))NiX^)8^  
figure(2) QJ%[6S  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Yt3+o<  
V(#z{!  
非线性超快脉冲耦合的数值方法的Matlab程序 8 o^ h\9I  
hH.X_X?d%  
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。   IVY{N/ 3|  
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 'O:QS)  
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%  This Matlab script file solves the nonlinear Schrodinger equations V!&O5T(~  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Or:a\qQ1  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear n-)Xs;`2  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 'h*^;3@*  
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N!,|)8s  
C=1;                           d(t$riFX}  
M1=120,                       % integer for amplitude Ec4+wRWk85  
M3=5000;                      % integer for length of coupler !Zi_4 .(4  
N = 512;                      % Number of Fourier modes (Time domain sampling points) w+_pq6\V  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. =G<i6%(^g  
T =40;                        % length of time:T*T0. B&},W*p  
dt = T/N;                     % time step ;;{!wA+"D  
n = [-N/2:1:N/2-1]';          % Index =jEh#  
t = n.*dt;   *f ;">(`o*  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. F?y4 L9|e  
w=2*pi*n./T; iVdY\+N!<  
g1=-i*ww./2; ^hyY,X  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 0Z,a3)jcc  
g3=-i*ww./2; ~9Jlb-*I5  
P1=0; 9vL n#_  
P2=0; GYJ lX  
P3=1; Li2-G  
P=0; {37v.4d;  
for m1=1:M1                 2leTEs5aK`  
p=0.032*m1;                %input amplitude ZNN^  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 h
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s1=s10; w$fP$ \+  
s20=0.*s10;                %input in waveguide 2 YYs/
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s30=0.*s10;                %input in waveguide 3 %V;B{?>9zB  
s2=s20; H4Lvw8G  
s3=s30; y} W-OLE  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   QKVFH:"3  
%energy in waveguide 1 ^6kE tTO*  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   }:zTz%_K  
%energy in waveguide 2 XI/LVP,.  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Bkaupvv9S  
%energy in waveguide 3 WETnrA"N  
for m3 = 1:1:M3                                    % Start space evolution \LbBK ~l-I  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS -#agWqUM|T  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; BK/_hNz  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; PYhRP00}M  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform qW"  
   sca2 = fftshift(fft(s2)); }^a" >$DU  
   sca3 = fftshift(fft(s3)); tX'2 $}  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ='z4bU  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 0*{2
^\  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); [5T{`&  
   s3 = ifft(fftshift(sc3)); )Bo]+\2  
   s2 = ifft(fftshift(sc2));                       % Return to physical space uJ@C-/BD!M  
   s1 = ifft(fftshift(sc1)); 8H7=vk+  
end ~A-Y%P  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 6aq=h`Y  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); N:% }KAc  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); *k^'xL  
   P1=[P1 p1/p10]; _GF{Duxh  
   P2=[P2 p2/p10]; cy{ ado2  
   P3=[P3 p3/p10]; P+2@,?9#  
   P=[P p*p]; )/mBq#ZS  
end Mep ct  
figure(1) c80!Ub@  
plot(P,P1, P,P2, P,P3); o>Faq+@  
F!*tE&Se+  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~