[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 ICm/9Onh&  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of uTvck6  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Rd:wMy$  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g1(`a`M  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 w;]~2$  
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%fid=fopen('e21.dat','w'); ]vUTb9>{?  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 57rH`UFXH  
M1 =3000;              % Total number of space steps DcX,o*ec!  
J =100;                % Steps between output of space 1gh<nn  
T =10;                  % length of time windows:T*T0 zOT(>1'  
T0=0.1;                 % input pulse width }1? 2  
MN1=0;                 % initial value for the space output location gF8n
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dt = T/N;                      % time step CSNfLGA
 
n = [-N/2:1:N/2-1]';           % Index 3!2TE-  
t = n.*dt;   xSL%1>MrN  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 L0EF CQ7  
u20=u10.*0.0;                  % input to waveguide 2 rFU|oDF  
u1=u10; u2=u20;                 vj4n=F,Z  
U1 = u1;   C ]
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U2 = u2;                       % Compute initial condition; save it in U ?nV& :~eY  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. !)+8:8H'  
w=2*pi*n./T;  KSB{Z TE  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T cUK
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L=4;                           % length of evoluation to compare with S. Trillo's paper MrFi0G7u  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Y=tx kN  
for m1 = 1:1:M1                                    % Start space evolution 5,u'p8}.  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS $Oi@B)=4d+  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; tZqy \_G  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform a534@U4,  
   ca2 = fftshift(fft(u2)); C">w3#M%  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation PA<<{\dp  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   $pGdGV\H  
   u2 = ifft(fftshift(c2));                        % Return to physical space KL4vr|i,  
   u1 = ifft(fftshift(c1)); 1:VbbOu->V  
if rem(m1,J) == 0                                 % Save output every J steps. 5*IfI+}  
    U1 = [U1 u1];                                  % put solutions in U array i{5,mS&  
    U2=[U2 u2]; iQ
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    MN1=[MN1 m1]; +ew9%={zB  
    z1=dz*MN1';                                    % output location 
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  end +`s%-}-r  
end ZQ'bB5I  
hg=abs(U1').*abs(U1');                             % for data write to excel 'mR9Uqq\  
ha=[z1 hg];                                        % for data write to excel #I] ^Wo  
t1=[0 t']; k7\ ,No}  
hh=[t1' ha'];                                      % for data write to excel file
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format SFQYrY  
figure(1) [9>h! khs  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn @.SuHd  
figure(2) .,$<waGD  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn : ZWKrnG  
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非线性超快脉冲耦合的数值方法的Matlab程序 W`2Xn?g  
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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。   1QPS=;|)  
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 d?Y|w
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%  This Matlab script file solves the nonlinear Schrodinger equations -xk.wWpV  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of mIy|]e`SJ  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ^}PG*h|  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 _>k&M7OU4  
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C=1;                           h]{V/  
M1=120,                       % integer for amplitude l1?$quM^V  
M3=5000;                      % integer for length of coupler , A@uSfC(  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Q2(K+!Oe  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. rUL_=>3  
T =40;                        % length of time:T*T0. gFQ\zOlY8a  
dt = T/N;                     % time step :{Mr~Co*  
n = [-N/2:1:N/2-1]';          % Index (.Th?p%>7  
t = n.*dt;   ^_rBEyz@  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. cKM#0dq  
w=2*pi*n./T; P]mJ01@'  
g1=-i*ww./2; _yN&+]c  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; rY,zZR+@  
g3=-i*ww./2; FMNT0  
P1=0; Krw'|<  
P2=0; .X](B~\!  
P3=1; 3"O&IY<  
P=0; m<liPl uv  
for m1=1:M1                 &rbkw<=j  
p=0.032*m1;                %input amplitude vBLs88  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ]*]#I?&'Hx  
s1=s10; ]]^r)&pox  
s20=0.*s10;                %input in waveguide 2 e,DRQ2AU  
s30=0.*s10;                %input in waveguide 3 k((kx:  
s2=s20; 9cXL4  
s3=s30; TR&7AiqB  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   [O@U@bD9  
%energy in waveguide 1 B".3NQ  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   's\rQ-TV  
%energy in waveguide 2 9 Eqv^0u  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   A)80qx:  
%energy in waveguide 3 E4N"|u|  
for m3 = 1:1:M3                                    % Start space evolution 95.s,'0  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS )CoJ9PO7  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; x }.&?m  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; MZ:Ty,pw:O  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform f3SAK!V+s  
   sca2 = fftshift(fft(s2)); Bp/k{7  
   sca3 = fftshift(fft(s3)); 6g)X&pZ  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   7b*9 Th*a  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); us )NgG  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); )(h<vo)-zX  
   s3 = ifft(fftshift(sc3)); o@qI!?p&  
   s2 = ifft(fftshift(sc2));                       % Return to physical space (G 9Ku 8Y  
   s1 = ifft(fftshift(sc1)); b8h6fB:2  
end BWLeitS/  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ZW ZKyJQ  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); oR}'I  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ar
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   P1=[P1 p1/p10]; Wl{wY,u  
   P2=[P2 p2/p10]; l-q.VY2  
   P3=[P3 p3/p10]; J\Z\q  
   P=[P p*p]; G\Q0{4w8  
end 5[A4K%EL  
figure(1) #IxCI)!I{[  
plot(P,P1, P,P2, P,P3); Jm3iYR+,  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~