[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 6iQqOAG  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of <=uO*s>%  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 2;]tItd1  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ]Q^8 9?  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 NHZMH!=4:n  
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%fid=fopen('e21.dat','w'); 7# 'j>]  
N = 128;                       % Number of Fourier modes (Time domain sampling points) RGV{KL  
M1 =3000;              % Total number of space steps [9?
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J =100;                % Steps between output of space AO$aWyI  
T =10;                  % length of time windows:T*T0 UIQ=b;J9  
T0=0.1;                 % input pulse width hy"p8j7_  
MN1=0;                 % initial value for the space output location GmGq69]J*  
dt = T/N;                      % time step <.7W:s,f=  
n = [-N/2:1:N/2-1]';           % Index a(o[ bH.|;  
t = n.*dt;   /7*qaG  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 lSId<v?C>  
u20=u10.*0.0;                  % input to waveguide 2 d\z':d.Tt  
u1=u10; u2=u20;                 *7Sg8\wDn  
U1 = u1;   '9wD+'c=A  
U2 = u2;                       % Compute initial condition; save it in U `.6Jgfu  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. BJ/#V)  
w=2*pi*n./T; ;`bJgSCfo  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T a7NX~9g  
L=4;                           % length of evoluation to compare with S. Trillo's paper Pb D|7IM  
dz=L/M1;                       % space step, make sure nonlinear<0.05 \v_t: "  
for m1 = 1:1:M1                                    % Start space evolution ~?A,GalS  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS = &aD!nTx  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Y@%6*uTLa  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform xcIZ'V  
   ca2 = fftshift(fft(u2)); :kI x?cc  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation _jb"@TY  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   sXC]{] P  
   u2 = ifft(fftshift(c2));                        % Return to physical space 48%a${Nvvj  
   u1 = ifft(fftshift(c1)); Ll
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if rem(m1,J) == 0                                 % Save output every J steps. ;v+CQx  
    U1 = [U1 u1];                                  % put solutions in U array >-y&k^a=  
    U2=[U2 u2]; G@Zi3 5  
    MN1=[MN1 m1]; s: q15"  
    z1=dz*MN1';                                    % output location U7fE6&g  
  end Pq7tNM E  
end !r!Mq~X<=  
hg=abs(U1').*abs(U1');                             % for data write to excel 4_I,wG@  
ha=[z1 hg];                                        % for data write to excel XKU=VOY  
t1=[0 t']; <F.Ol/'h  
hh=[t1' ha'];                                      % for data write to excel file IO_H%/v"jC  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format _5YL !v&  
figure(1) 9'8oOBqm3%  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn $l[*Y  
figure(2) SS~Txt75m  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn %J%gXk}]  
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非线性超快脉冲耦合的数值方法的Matlab程序 =yNHJHRA#  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   +ow ^xiD  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ptq{$Y{_  
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%  This Matlab script file solves the nonlinear Schrodinger equations :3n.nKANr  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of et ~gO!1:*  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ?HcA&  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 )LhO}zQ  
&%r#eB?7  
C=1;                           YV940A-n  
M1=120,                       % integer for amplitude =,]J"n8|v  
M3=5000;                      % integer for length of coupler xNqQbkF  
N = 512;                      % Number of Fourier modes (Time domain sampling points) X9gC2iSs]  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. |f}NO~CA  
T =40;                        % length of time:T*T0. A>
g$[  
dt = T/N;                     % time step 7ER 2h*  
n = [-N/2:1:N/2-1]';          % Index `U1%d7[vY  
t = n.*dt;   f8^58]wx0  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. d=KOV;~);  
w=2*pi*n./T; Qy/bzO  
g1=-i*ww./2; v#+w<gRq  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; !^fJAtCN]  
g3=-i*ww./2; i }gxq  
P1=0; G-^ccdT  
P2=0; yl ;'Ru:  
P3=1; C;) xjZiR  
P=0; *_wef/==  
for m1=1:M1                 Fi/G, [q  
p=0.032*m1;                %input amplitude +e:ZN tr9  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 XZ&v3ul  
s1=s10; BD0-v`  
s20=0.*s10;                %input in waveguide 2 l9ihW^  
s30=0.*s10;                %input in waveguide 3 ,< icW&a  
s2=s20; (Sv%-8?gs  
s3=s30; `^_:  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   66Xt=US  
%energy in waveguide 1 '> Q$5R1  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   bX(*f>G'  
%energy in waveguide 2 J| '(;Ay4u  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   oX4uRc7wR  
%energy in waveguide 3 %Nn'p"  
for m3 = 1:1:M3                                    % Start space evolution V6{xX0'b*m  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Aii[=x8  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; RM+E  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ZO1J";>u  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform p,8Z{mLn  
   sca2 = fftshift(fft(s2)); w1_Ux<RF  
   sca3 = fftshift(fft(s3)); qi2dTB  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   \-0`%k"&  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Pvw%,=41O  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); R*0F)M  
   s3 = ifft(fftshift(sc3)); %$xFnGb  
   s2 = ifft(fftshift(sc2));                       % Return to physical space KxwLKaImI  
   s1 = ifft(fftshift(sc1)); dSZ#,Ea"  
end R4(8]oUW  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 9p4U\hx  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Z :+#3.4$3  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); %4Zy1{yKs_  
   P1=[P1 p1/p10]; -JENY|6  
   P2=[P2 p2/p10]; ;#i$0~lRl  
   P3=[P3 p3/p10]; ?63JQ.;  
   P=[P p*p]; Vgn1I(Gj4  
end fO>~V1  
figure(1) |]cDz  
plot(P,P1, P,P2, P,P3); OP}p;(  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~