[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 Jq'8"  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of bTaKB-  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Tz,9>uN  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear QH9t |l  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 _b~{/[s  

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%fid=fopen('e21.dat','w'); SscB&{f  
N = 128;                       % Number of Fourier modes (Time domain sampling points) c Rq2 re  
M1 =3000;              % Total number of space steps x1.S+:  
J =100;                % Steps between output of space p/HDG ^T:u  
T =10;                  % length of time windows:T*T0 ^U*y*l$  
T0=0.1;                 % input pulse width p2i?)+z  
MN1=0;                 % initial value for the space output location WYUDD_m  
dt = T/N;                      % time step Q,&Li+u|  
n = [-N/2:1:N/2-1]';           % Index RDp  
t = n.*dt;   akzGJ3g  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 WK>|IgK  
u20=u10.*0.0;                  % input to waveguide 2 Yg^ &4ZF  
u1=u10; u2=u20;                 d}[cX9U/  
U1 = u1;   -SrZ^  
U2 = u2;                       % Compute initial condition; save it in U ;mG*Rad  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. rR> X<  
w=2*pi*n./T; 3c=kYcj  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 2M-[x"\1/  
L=4;                           % length of evoluation to compare with S. Trillo's paper 20|`jxp  
dz=L/M1;                       % space step, make sure nonlinear<0.05 xV)[C )6  
for m1 = 1:1:M1                                    % Start space evolution tg/UtE`V  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS eyCZ[SC  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; tX{yR'Qhu  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 'p&,'+x  
   ca2 = fftshift(fft(u2)); MYWkEv7  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation vA1YyaB  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ,_Z(!| rW  
   u2 = ifft(fftshift(c2));                        % Return to physical space 5QMra5Nk  
   u1 = ifft(fftshift(c1)); s{Z)<n03  
if rem(m1,J) == 0                                 % Save output every J steps. 5 8bW  
    U1 = [U1 u1];                                  % put solutions in U array (90/,@66l  
    U2=[U2 u2]; D0r viO  
    MN1=[MN1 m1]; (jM0YtrD  
    z1=dz*MN1';                                    % output location I+8n;I)]X  
  end 50^ux:Uv+N  
end *j%x  
hg=abs(U1').*abs(U1');                             % for data write to excel qz-QVY,  
ha=[z1 hg];                                        % for data write to excel N T`S)P*?  
t1=[0 t']; ~|V^IJZ22  
hh=[t1' ha'];                                      % for data write to excel file Wh)D_  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format h+FM?ct6}  
figure(1) <1D|TrP  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn sS>b}u+v#!  
figure(2) AI-*5[w#A  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn *VZ|Idp  
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非线性超快脉冲耦合的数值方法的Matlab程序 x#>V50E  
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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。   +xFn~b/  
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 Lgg
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%  This Matlab script file solves the nonlinear Schrodinger equations $5R2QNg n  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of pH1!6X  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ,QY$:f<  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9P?
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C=1;                           b(Nv`'O  
M1=120,                       % integer for amplitude w&p
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M3=5000;                      % integer for length of coupler jf~](TK  
N = 512;                      % Number of Fourier modes (Time domain sampling points) G,u=ngZ]  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05.  \i%'M%  
T =40;                        % length of time:T*T0. va6Fp2n<1*  
dt = T/N;                     % time step >t+U`6xK  
n = [-N/2:1:N/2-1]';          % Index 7n8nJTU{4j  
t = n.*dt;   !6!)H8rX  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. /Z:
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w=2*pi*n./T; z5
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g1=-i*ww./2; /( Wq  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; T8XrmR&?PX  
g3=-i*ww./2; ge~@}&#iO@  
P1=0; IiU>VLa  
P2=0; [jMN*p?  
P3=1; xE/?ncTK^  
P=0; e97G]XLR  
for m1=1:M1                 |N.2iN:  
p=0.032*m1;                %input amplitude 7oE0;'  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 |R`"Zu`  
s1=s10; f9.?+.^_  
s20=0.*s10;                %input in waveguide 2 !J$r|IX5  
s30=0.*s10;                %input in waveguide 3 sh<Q2X  
s2=s20; IDohv[#  
s3=s30; i?x gV_q;  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   1[%3kY-h  
%energy in waveguide 1 k# [!; <  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   #-/W?kD  
%energy in waveguide 2 iQ'*QbP'Z  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Ez3fL&*  
%energy in waveguide 3 >>U>'
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for m3 = 1:1:M3                                    % Start space evolution 3_(_yEKx  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS gjS|3ED  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; @)Qgy}*5  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; hFrMOc&  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 3SVGx<,2  
   sca2 = fftshift(fft(s2)); U0x A~5B  
   sca3 = fftshift(fft(s3)); J<$@X JLS  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   nV'1 $L#  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); acd[rjeT  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); osW"wh_
  
   s3 = ifft(fftshift(sc3)); 3:J>-MO  
   s2 = ifft(fftshift(sc2));                       % Return to physical space dSM\:/t  
   s1 = ifft(fftshift(sc1)); OF-k7g7  
end .wfydu)3  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); $J[( 3  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); VY?9|};f  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); "Xq_N4  
   P1=[P1 p1/p10]; ~6G `k^!  
   P2=[P2 p2/p10]; As:O|!F  
   P3=[P3 p3/p10]; iq#{*:1  
   P=[P p*p]; D6"=2XR4n  
end e4z`:
%vy  
figure(1) >)>f~>  
plot(P,P1, P,P2, P,P3); &f*orM:  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~