[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 jWNF3\  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of l:- <CbG  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of m4~>n(  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear /n-!dXi  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 +b_o2''  
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%fid=fopen('e21.dat','w'); ~b;u1;ne  
N = 128;                       % Number of Fourier modes (Time domain sampling points) W
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M1 =3000;              % Total number of space steps L)yc_ d5  
J =100;                % Steps between output of space 7Q>bJ Ek7  
T =10;                  % length of time windows:T*T0 >&`;@ZOH  
T0=0.1;                 % input pulse width #Pr w2u  
MN1=0;                 % initial value for the space output location HyGu3  
dt = T/N;                      % time step _Y _v&  
n = [-N/2:1:N/2-1]';           % Index 2C[xrZa^  
t = n.*dt;   X]+z:!  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 w tSX(LNY  
u20=u10.*0.0;                  % input to waveguide 2 4D=^24f`0  
u1=u10; u2=u20;                 !Y^3%B%  
U1 = u1;   %Rm`+  
U2 = u2;                       % Compute initial condition; save it in U uRCZGg&V?#  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 1WUlBr/k  
w=2*pi*n./T; hmp!|Q[)  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T x.kIzI5  
L=4;                           % length of evoluation to compare with S. Trillo's paper WWjc.A$  
dz=L/M1;                       % space step, make sure nonlinear<0.05 XpIl-o&re  
for m1 = 1:1:M1                                    % Start space evolution "(+p1  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS KybrSa  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; n@_aTY  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 05s{Z.aK  
   ca2 = fftshift(fft(u2)); Q/]t$  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation $iMbtA5aQ  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   2#)z%K6T  
   u2 = ifft(fftshift(c2));                        % Return to physical space &ieb6@RO`Q  
   u1 = ifft(fftshift(c1)); R q9(<'F  
if rem(m1,J) == 0                                 % Save output every J steps. SL5QhP  
    U1 = [U1 u1];                                  % put solutions in U array J. $U_k  
    U2=[U2 u2]; Xv2Q8-}w  
    MN1=[MN1 m1]; +<rWYF(ii/  
    z1=dz*MN1';                                    % output location \V%l.P4>e  
  end pKkBAr,  
end Ye]-RN/W  
hg=abs(U1').*abs(U1');                             % for data write to excel ]
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ha=[z1 hg];                                        % for data write to excel JIU8~D  
t1=[0 t']; s6(bTO.  
hh=[t1' ha'];                                      % for data write to excel file sh)[|?7
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format =58:e7(df  
figure(1) _"h1#E  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn TrR=3_;.7  
figure(2) ZW%;"5uVm)  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ,d@FO|G#pt  
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非线性超快脉冲耦合的数值方法的Matlab程序 2g HRfTF  
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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。   "'*Qq@!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 s_ %LU:WC  
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w=k
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%  This Matlab script file solves the nonlinear Schrodinger equations 
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%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of bY}:!aR<mK  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear |Ng}ZLBM  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 &\e8c g  
se*!OiOt  
C=1;                           EI8KKo *  
M1=120,                       % integer for amplitude l5FKw;=K}:  
M3=5000;                      % integer for length of coupler s(pNg?R  
N = 512;                      % Number of Fourier modes (Time domain sampling points) N?v}\PU  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. {4>N2mP{M  
T =40;                        % length of time:T*T0. Xk`'m[  
dt = T/N;                     % time step tvcM< e20  
n = [-N/2:1:N/2-1]';          % Index "R^0eNv$  
t = n.*dt;   qCy SL lp0  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. I78Q8W(5  
w=2*pi*n./T; W%@0Ym`7  
g1=-i*ww./2; -0>s`ruor  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; JYrOE"!h  
g3=-i*ww./2; pcNpr`  
P1=0; ?wpl 88z  
P2=0; TEQs9-Uy  
P3=1; n8Rsle`a  
P=0; q$kx/6=k  
for m1=1:M1                  :X 9_~  
p=0.032*m1;                %input amplitude Odr<fvV,>  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ODKHI\U  
s1=s10; {r
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s20=0.*s10;                %input in waveguide 2 6r)B|~,OA  
s30=0.*s10;                %input in waveguide 3 _Lgi5B%   
s2=s20; i|!W;2KL5  
s3=s30; sI`oz
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p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   `>u^Pm  
%energy in waveguide 1 
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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))));   +6s6QeNS8  
%energy in waveguide 2 thSXri?kl  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   d,E2l~s  
%energy in waveguide 3 9a]JQ  
for m3 = 1:1:M3                                    % Start space evolution ONMR2J(  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS DHVfb(H5e  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; eE" *c>I  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; l4AXjq2  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform Zb:S IJ  
   sca2 = fftshift(fft(s2)); O'S9y  
   sca3 = fftshift(fft(s3)); ^%NjdZuDO  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ZM_-g4[H  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 
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   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); grE'ySX0  
   s3 = ifft(fftshift(sc3)); d RHw]!.  
   s2 = ifft(fftshift(sc2));                       % Return to physical space  / !aVv  
   s1 = ifft(fftshift(sc1)); zO((FQ  
end zcOG[-  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); &W%fsy<  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); &IP`j~b  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); #YK=e&da  
   P1=[P1 p1/p10]; G$t:#2  
   P2=[P2 p2/p10]; }b+$S'`Bv  
   P3=[P3 p3/p10]; Qn \=P*j  
   P=[P p*p]; 9>ML;$T&  
end H,;9' *84  
figure(1) WD|pG;Gq  
plot(P,P1, P,P2, P,P3); uo3o[H&#  
QJ,~K&?  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~