[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 \S2'3SDd/  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of MDCf(LhEH  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of C,z]q$4  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear W]*wxzf!5z  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 FRF}V@~  
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%fid=fopen('e21.dat','w'); 4-n.4j|  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 3 \WdA$Wx  
M1 =3000;              % Total number of space steps ;~q)^.K3  
J =100;                % Steps between output of space ?%0i,p@<  
T =10;                  % length of time windows:T*T0 dX3>j{_  
T0=0.1;                 % input pulse width (c_hX(  
MN1=0;                 % initial value for the space output location XF$C)id2p  
dt = T/N;                      % time step XZT( :(  
n = [-N/2:1:N/2-1]';           % Index 1Q$ M/}  
t = n.*dt;   BZ T%+s;u9  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 hg>YOf&RG  
u20=u10.*0.0;                  % input to waveguide 2 e)bqE^JP  
u1=u10; u2=u20;                 Ek.j@79  
U1 = u1;   V7v,)a" L  
U2 = u2;                       % Compute initial condition; save it in U FxT [4  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. =f p(hX"  
w=2*pi*n./T; Y{'G2)e  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T DpR%s",Q  
L=4;                           % length of evoluation to compare with S. Trillo's paper [(K^x?\Y0'  
dz=L/M1;                       % space step, make sure nonlinear<0.05 \ a<Ye T  
for m1 = 1:1:M1                                    % Start space evolution p5'\< gQ  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 7I
 
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; xMh&C{q  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform `'QPe42  
   ca2 = fftshift(fft(u2)); n#fg7d%  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 5V
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   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   =
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   u2 = ifft(fftshift(c2));                        % Return to physical space lqs_7HhvRS  
   u1 = ifft(fftshift(c1)); *]=)mM#  
if rem(m1,J) == 0                                 % Save output every J steps. }bTMeCgI  
    U1 = [U1 u1];                                  % put solutions in U array #>V;ZV5"  
    U2=[U2 u2]; uQNoIy J)  
    MN1=[MN1 m1]; tpctz~ .  
    z1=dz*MN1';                                    % output location KKzvoc?Bt  
  end J.d `tiN  
end `F@yZ4L3S  
hg=abs(U1').*abs(U1');                             % for data write to excel lb('r"*.  
ha=[z1 hg];                                        % for data write to excel {Q"<q`c  
t1=[0 t']; XDGZqkt  
hh=[t1' ha'];                                      % for data write to excel file -d~'tti  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format WveFB%@`;  
figure(1) /_|1,x-Kx  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn #]'xUgcE9  
figure(2) (qrT0D6  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn {m?x},  
+1%6-g4"  
非线性超快脉冲耦合的数值方法的Matlab程序 )qIK7;  
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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。   FRW.  
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 S7vE[VF5  
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%  This Matlab script file solves the nonlinear Schrodinger equations ;z>YwRV  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 2vC=.1k  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ;<A/e  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 #u$z-M !  
Ah`dt8t  
C=1;                           ccSSau5N  
M1=120,                       % integer for amplitude ;=OH=+Rl  
M3=5000;                      % integer for length of coupler _;{-w%Vf  
N = 512;                      % Number of Fourier modes (Time domain sampling points) &?nF';&  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. kR]SxG9  
T =40;                        % length of time:T*T0. \YS?}! 0  
dt = T/N;                     % time step hz%IxI9  
n = [-N/2:1:N/2-1]';          % Index +q$|6?  
t = n.*dt;   as4NvZ@+r  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. *&]l
 
w=2*pi*n./T; ?r<F\rBT7*  
g1=-i*ww./2; !Xi>{nV  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; D,/9rH  
g3=-i*ww./2; -wfV  
P1=0; =*Xf(mhc  
P2=0; pS;d
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P3=1; +IYSWR  
P=0; MV}]i@V  
for m1=1:M1                 )|x5#b-lz  
p=0.032*m1;                %input amplitude b*KZe[#M1  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 aw1J#5j`n  
s1=s10; : 4WbDeR  
s20=0.*s10;                %input in waveguide 2 G m! ]   
s30=0.*s10;                %input in waveguide 3 ltR^IiA}  
s2=s20; h :R)KM  
s3=s30; 1\0
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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))));   uw!|G>  
%energy in waveguide 1 (xed(uFEK  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   H)Ge#=;ckQ  
%energy in waveguide 2 :\_MA^<  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   6,1|y%(f  
%energy in waveguide 3 m9@n  
for m3 = 1:1:M3                                    % Start space evolution 59J9V3na  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS zQ}N mlk  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; rgKn=8+a  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Y;Gm,  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ~*[4DQ[\  
   sca2 = fftshift(fft(s2)); `F8;{`a  
   sca3 = fftshift(fft(s3)); RfG$Px '  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   C:MGi7f  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); +=Wdn)T  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); /H@")je  
   s3 = ifft(fftshift(sc3)); ycD.:w p\'  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Els=:4  
   s1 = ifft(fftshift(sc1)); Q0\5j<'e  
end QL18MbfqP  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); >:&p(eu)L0  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); `r(J6,O  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); $:II@=  
   P1=[P1 p1/p10]; :0/o?'s  
   P2=[P2 p2/p10]; +lJ]-U|P  
   P3=[P3 p3/p10]; , vyx`wDd  
   P=[P p*p]; .6o y>4  
end \|`Pul$  
figure(1) agT[y/gb  
plot(P,P1, P,P2, P,P3); %nf=[f
 
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~