[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 $Tur"_`I;  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of (;j7{(  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of UA8!?r-cR
 
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 4By-+C*  
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%fid=fopen('e21.dat','w'); IcoL/7k3  
N = 128;                       % Number of Fourier modes (Time domain sampling points) d$TW](Bby  
M1 =3000;              % Total number of space steps

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J =100;                % Steps between output of space F:@Ixk?E  
T =10;                  % length of time windows:T*T0 Na6z,TW  
T0=0.1;                 % input pulse width *@& "MZ/M  
MN1=0;                 % initial value for the space output location 1%@~J\qF  
dt = T/N;                      % time step )mPlB.  
n = [-N/2:1:N/2-1]';           % Index bvx:R
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t = n.*dt;   `@eH4}L*  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 l =yHx\  
u20=u10.*0.0;                  % input to waveguide 2 qC4-J)8Wk  
u1=u10; u2=u20;                 _)l %-*Z7p  
U1 = u1;   "P{&UwMmh  
U2 = u2;                       % Compute initial condition; save it in U =R'v]SXj  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 19.cf3Dh  
w=2*pi*n./T; :z\f.+MI  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ?},ItJ#>)q  
L=4;                           % length of evoluation to compare with S. Trillo's paper 1;P\mff3Y  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Ax0,7,8y  
for m1 = 1:1:M1                                    % Start space evolution (6BCFl:/Q<  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; if
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   ca1 = fftshift(fft(u1));                        % Take Fourier transform ]p!J]YV ]0  
   ca2 = fftshift(fft(u2)); !-c*lb  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Y2X1!Em>B  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Du>HF;Fv  
   u2 = ifft(fftshift(c2));                        % Return to physical space (OqJet2{
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   u1 = ifft(fftshift(c1)); >.iw8#l  
if rem(m1,J) == 0                                 % Save output every J steps. 1955(:I  
    U1 = [U1 u1];                                  % put solutions in U array HUC2RM?FN  
    U2=[U2 u2];  {K9E% ,w  
    MN1=[MN1 m1]; <yS"c5D6  
    z1=dz*MN1';                                    % output location [!&k?.*;<  
  end z\tJ~  
end \Wc/kY3&  
hg=abs(U1').*abs(U1');                             % for data write to excel Y*k<NeDyn  
ha=[z1 hg];                                        % for data write to excel OQ7c|O  
t1=[0 t']; uB1!*S1f  
hh=[t1' ha'];                                      % for data write to excel file ?i~/gjp  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format Y/0O9}hf  
figure(1) Fw9``{4w  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn wP/9z(US  
figure(2) 4QF
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ku
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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。  
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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 ({KAh?  
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%  This Matlab script file solves the nonlinear Schrodinger equations [T]qm7 ?  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of WWcm(q=  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear [\9
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 eH955[fVd4  
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C=1;                           .p9h$z^  
M1=120,                       % integer for amplitude F[=lA"F^  
M3=5000;                      % integer for length of coupler /JeqoM"x  
N = 512;                      % Number of Fourier modes (Time domain sampling points) a{HgIQg_>R  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. j{R|]SjW2H  
T =40;                        % length of time:T*T0. THgzT\_zq  
dt = T/N;                     % time step .eNwC.8i  
n = [-N/2:1:N/2-1]';          % Index 8.Ef5-m  
t = n.*dt;   HoE
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ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. kQd[E-b7  
w=2*pi*n./T; &NjZD4m`=  
g1=-i*ww./2; 8ex:OTzn|  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Y"kS!!C>[  
g3=-i*ww./2; P .4b+9Tx  
P1=0; "!Oh#Vf  
P2=0; {2k< k(,  
P3=1; %4|}&,%%r  
P=0; D2:a  
for m1=1:M1                 V1nZ M  
p=0.032*m1;                %input amplitude 1+t
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 }0*ra37z>  
s1=s10; C.)&FW2F_  
s20=0.*s10;                %input in waveguide 2 X,EYa>RSy_  
s30=0.*s10;                %input in waveguide 3 dh;M
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s2=s20; wu!_BCIy  
s3=s30; H.8CwsfP  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   p5;,/ |Ft  
%energy in waveguide 1 cvV?V\1f  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   a]
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%energy in waveguide 2 zg Y*|{4Sl  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   0/P-> n~  
%energy in waveguide 3 bC4*w O  
for m3 = 1:1:M3                                    % Start space evolution f9
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   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 0tm_}L$g=b  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; AzO3(1:  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ]7S7CVDk4  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform >)J47j7{c  
   sca2 = fftshift(fft(s2)); xDA,?i;T 0  
   sca3 = fftshift(fft(s3)); W[X!P)=w]  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   7! b)'W?  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); wy_;+ 'Y  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ?sf2h:\N  
   s3 = ifft(fftshift(sc3)); TQ\wHJ  
   s2 = ifft(fftshift(sc2));                       % Return to physical space :KV,:13`D  
   s1 = ifft(fftshift(sc1)); F `pyhc>1;  
end B
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   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); b8{h[YJL2  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); l`FR.)2h  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 9Ajgfy>  
   P1=[P1 p1/p10]; v>y8s&/  
   P2=[P2 p2/p10]; @@{_[ir  
   P3=[P3 p3/p10]; ;TV'PJ  
   P=[P p*p]; 9HNh*Gc=  
end ghobu}wuF  
figure(1) !/Bw,y ri<  
plot(P,P1, P,P2, P,P3); (m3I#L  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~