[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 !LN8=u.  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of v03cQw\"WE  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Ap dXsL  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear x4
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 q
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%fid=fopen('e21.dat','w'); ]<f)Rf">:`  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 5CkG^9  
M1 =3000;              % Total number of space steps ;}46Uc#WS  
J =100;                % Steps between output of space d/7fJ8y8  
T =10;                  % length of time windows:T*T0 p&<Ssc  
T0=0.1;                 % input pulse width +vh|m5"7I7  
MN1=0;                 % initial value for the space output location @k?vbq  
dt = T/N;                      % time step Xsq@E#@S  
n = [-N/2:1:N/2-1]';           % Index ob.<j  
t = n.*dt;   7*5B  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 /Y7^!3uM  
u20=u10.*0.0;                  % input to waveguide 2 Ma^jy.  
u1=u10; u2=u20;                 $p0nq&4c  
U1 = u1;   uAO!fE}CJ  
U2 = u2;                       % Compute initial condition; save it in U 8MJJ w;  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Q]k<Y  
w=2*pi*n./T; N"S`9B1eD(  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T %~LY'cfPse  
L=4;                           % length of evoluation to compare with S. Trillo's paper j_8 YFz5  
dz=L/M1;                       % space step, make sure nonlinear<0.05 f@OH~4FG  
for m1 = 1:1:M1                                    % Start space evolution H5K Fm#  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 2@|`Ugjptl  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; uC'-: t#  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform oB:7R^a  
   ca2 = fftshift(fft(u2)); 11H`WOTQF  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation -+".ut:R  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   6j%%CWU{~  
   u2 = ifft(fftshift(c2));                        % Return to physical space P3zUaN\c  
   u1 = ifft(fftshift(c1)); O =Z}DGa+  
if rem(m1,J) == 0                                 % Save output every J steps. }.&nEi`  
    U1 = [U1 u1];                                  % put solutions in U array mrTf["K  
    U2=[U2 u2]; p*g Fr hm  
    MN1=[MN1 m1]; ='7m$,{(Q[  
    z1=dz*MN1';                                    % output location 7H7 Xbi@  
  end )@g[aRFa  
end b;i*}4h!  
hg=abs(U1').*abs(U1');                             % for data write to excel iM]O  
ha=[z1 hg];                                        % for data write to excel V%,,GmiU]  
t1=[0 t']; x5lVb$!G  
hh=[t1' ha'];                                      % for data write to excel file r&u1-%%9[  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ?WI v4
 
figure(1) q*hn5K*  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn .n 9.y8C  
figure(2) P3oYk_oW  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn PQHztS"  
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非线性超快脉冲耦合的数值方法的Matlab程序
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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。   ,1]UOQ>AP  
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 uyj!$}4  
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%  This Matlab script file solves the nonlinear Schrodinger equations Rk$7jZdTf  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of r_7%|T8  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 1[egCC\Mo_  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]cRvdUGv  
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C=1;                           MK#   
M1=120,                       % integer for amplitude -laH^<jm5  
M3=5000;                      % integer for length of coupler H
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N = 512;                      % Number of Fourier modes (Time domain sampling points) 1 iH@vd  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. :5kDc" =Z|  
T =40;                        % length of time:T*T0. (hc!!:N~q  
dt = T/N;                     % time step Jz8P':6[  
n = [-N/2:1:N/2-1]';          % Index Kw fd S(
 
t = n.*dt;   (:iMs) iO{  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. i\xs!QU  
w=2*pi*n./T; #$WnMJ@  
g1=-i*ww./2; re/-Yu$'  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; &8VH m?h  
g3=-i*ww./2; (B#FLoK  
P1=0; lxn/97rA  
P2=0; htB2?%S=T  
P3=1; ]OpGD5jZ  
P=0; HNZ$CaJh  
for m1=1:M1                 E~y8X9HZ)  
p=0.032*m1;                %input amplitude {4+/0\  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 [if(B\&  
s1=s10; D0J{pAJ  
s20=0.*s10;                %input in waveguide 2 B)q}]Qn  
s30=0.*s10;                %input in waveguide 3 9SC1A-nF  
s2=s20; ruaZ(R[  
s3=s30; C|y^{4|R  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   -x?Z2EA!  
%energy in waveguide 1 bdrE2m  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   c&;" Y{  
%energy in waveguide 2 )CXlPbhY?  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ".jO2GO^  
%energy in waveguide 3 u6C_*i{2  
for m3 = 1:1:M3                                    % Start space evolution Uz;^R@  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS v&:[?<6-  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; @3n!5XM{EE  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; l>*X+TpA,  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform DY`0 `T  
   sca2 = fftshift(fft(s2)); U&"L9o`2  
   sca3 = fftshift(fft(s3)); +v/y{8Fu  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   6jpzyf=~  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); \Fjasz5E'  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); PTHxvml  
   s3 = ifft(fftshift(sc3)); g9C-!X-<T  
   s2 = ifft(fftshift(sc2));                       % Return to physical space %)V=)l.j  
   s1 = ifft(fftshift(sc1)); C b'|  
end wPU5L*/*i  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Rd8mn'A  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); W2`3 p  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); WvU[9ME^)  
   P1=[P1 p1/p10]; GUL~k@:_k  
   P2=[P2 p2/p10]; aPJTH0u  
   P3=[P3 p3/p10]; Xau%v5r  
   P=[P p*p]; YusmMsN?  
end 1 F:bExQ  
figure(1) :U\*4l
 
plot(P,P1, P,P2, P,P3); .i\FK@2  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~