[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 KnaQhZ  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of se:]F/  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 4onRO!G,  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear vUk <z*  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 $-Lk,}s.*  
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%fid=fopen('e21.dat','w'); }te\) Yk.N  
N = 128;                       % Number of Fourier modes (Time domain sampling points) a^hDxeG  
M1 =3000;              % Total number of space steps SzR7:U  
J =100;                % Steps between output of space R4.$9_ui  
T =10;                  % length of time windows:T*T0 UA>UW!I  
T0=0.1;                 % input pulse width
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MN1=0;                 % initial value for the space output location T>7$<ulm  
dt = T/N;                      % time step PHU#$LG  
n = [-N/2:1:N/2-1]';           % Index dMK|l   
t = n.*dt;   rvgArFf}]  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Ikv@}^p 7  
u20=u10.*0.0;                  % input to waveguide 2 }1=V`N(  
u1=u10; u2=u20;                 7s+3^'  
U1 = u1;   u,mC`gz  
U2 = u2;                       % Compute initial condition; save it in U b_+dNoB  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 2Dgulx5kGZ  
w=2*pi*n./T; P~HzNC  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T TPEg>[  
L=4;                           % length of evoluation to compare with S. Trillo's paper =~}\g;K1Q  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Xxhzzm-B  
for m1 = 1:1:M1                                    % Start space evolution TUuw  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS r%\(5H f  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; =+HMPV6yg7  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform R>f$*T  
   ca2 = fftshift(fft(u2)); .
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation P(D0ru  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   SEu1M}+E  
   u2 = ifft(fftshift(c2));                        % Return to physical space do@`(f3g  
   u1 = ifft(fftshift(c1)); -T3 z@k  
if rem(m1,J) == 0                                 % Save output every J steps. 5i `q  
    U1 = [U1 u1];                                  % put solutions in U array X%w`:c&  
    U2=[U2 u2]; 0~ !).f  
    MN1=[MN1 m1]; "|ZC2Zu<  
    z1=dz*MN1';                                    % output location rG)K?B~  
  end hUN]Lm6M  
end }QrBN:a$(  
hg=abs(U1').*abs(U1');                             % for data write to excel X!#rw= Q  
ha=[z1 hg];                                        % for data write to excel &Z3g$R 9  
t1=[0 t']; *-0tj~)>  
hh=[t1' ha'];                                      % for data write to excel file "O@L IR7
 
%dlmwrite('aa',hh,'\t');                           % save data in the excel format =pSuyM'  
figure(1) .hO) R.  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ]U?)_P@}  
figure(2) iG*@(  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn WxO2  
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非线性超快脉冲耦合的数值方法的Matlab程序 6?GR+;/  
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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。   a k&G=a6^  
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 cXP*?N4Cf  
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%  This Matlab script file solves the nonlinear Schrodinger equations ^U1@ hq*u  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of YhQ;>Ko  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6_xPk`m  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 a;@
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C=1;                           )> >Tj7  
M1=120,                       % integer for amplitude B'sgCU  
M3=5000;                      % integer for length of coupler #Xdj:T<*  
N = 512;                      % Number of Fourier modes (Time domain sampling points) [H"\<"1o  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. _OR@
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T =40;                        % length of time:T*T0. pHO,][VZ  
dt = T/N;                     % time step J4Yu|E<&  
n = [-N/2:1:N/2-1]';          % Index Y'n+,g  
t = n.*dt;   ;.dyuKlI  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. N`o[iHUj \  
w=2*pi*n./T; p@`]9tLP(K  
g1=-i*ww./2; M`m-@z  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; CG!7BP\  
g3=-i*ww./2; z''ITX)oG  
P1=0; :<Z>?x  
P2=0; z#DgoA  
P3=1; F`C$F!GE  
P=0; bm`x;M^M  
for m1=1:M1                 f&5'1tG  
p=0.032*m1;                %input amplitude _c:}i\8R  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 VH*4fcT'D  
s1=s10; Lt8J^}kwl  
s20=0.*s10;                %input in waveguide 2 V@%:y tDf  
s30=0.*s10;                %input in waveguide 3 Obj?,O  
s2=s20; #H8% BZyV  
s3=s30; jEaU;  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   RH^!7W*  
%energy in waveguide 1 qhE1 7Hf  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   :_,oD  
%energy in waveguide 2 A.[~}ywH  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   @cc4]>4  
%energy in waveguide 3 yAyq-G"sO  
for m3 = 1:1:M3                                    % Start space evolution 4xYW?s(  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS r0xmDJ@y  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; LN!e_b  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; JSf \ApX  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform cUB+fH<B2  
   sca2 = fftshift(fft(s2)); 3$TU2-x;g  
   sca3 = fftshift(fft(s3)); #gQaNc?  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ~d.Z.AD  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); K*"Wq:T;B  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); TAE@KSPvo  
   s3 = ifft(fftshift(sc3)); \7\7i-Vo
 
   s2 = ifft(fftshift(sc2));                       % Return to physical space 8k.<xWDU  
   s1 = ifft(fftshift(sc1)); ZUg~8VVe  
end n^xB_DJ~  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 3=@lJ?Ym  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); .5s#JL  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 1Uy'TEk  
   P1=[P1 p1/p10]; x@aWvrL  
   P2=[P2 p2/p10]; iCZuE:I1K,  
   P3=[P3 p3/p10]; $F#eD0|  
   P=[P p*p]; jeu|9{iTVu  
end <F%c"Rkh  
figure(1) e]!`Cl-f80  
plot(P,P1, P,P2, P,P3); \H&8.<HJ  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~