[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 ZhCd**  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of XE_Lz2H`  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Q0"?TSY  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear <m
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 M{orw;1Isy  
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%fid=fopen('e21.dat','w'); j)8$hK/e0.  
N = 128;                       % Number of Fourier modes (Time domain sampling points) rF[-4t %  
M1 =3000;              % Total number of space steps 0#Gm# =F  
J =100;                % Steps between output of space H2|'JA#v  
T =10;                  % length of time windows:T*T0 >x%HqP#_V  
T0=0.1;                 % input pulse width 8Y8bFWuc  
MN1=0;                 % initial value for the space output location 4 ;_g9]  
dt = T/N;                      % time step nW
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n = [-N/2:1:N/2-1]';           % Index 6, j60`f)  
t = n.*dt;   #Ev}Gf+5Q  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 MzB.Vvsy%9  
u20=u10.*0.0;                  % input to waveguide 2 #@-dT
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u1=u10; u2=u20;                 r{?qvl!q  
U1 = u1;   BYdGK@ouk  
U2 = u2;                       % Compute initial condition; save it in U {.oz^~zs]g  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. U*{0,Ue'  
w=2*pi*n./T; qGN>a[D  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 00IW9B-  
L=4;                           % length of evoluation to compare with S. Trillo's paper g]h@U&`~u_  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Ndl{f=sjX-  
for m1 = 1:1:M1                                    % Start space evolution }>AA[ba"'  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS *MfH\X379  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; A-B>VX  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform cg^~P-i@*  
   ca2 = fftshift(fft(u2)); 4xT /8>v2|  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation :mDOqlXW/  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   TR*vZzoy  
   u2 = ifft(fftshift(c2));                        % Return to physical space }BW&1*M{  
   u1 = ifft(fftshift(c1)); S=S/]]e  
if rem(m1,J) == 0                                 % Save output every J steps. o_=4Ex "  
    U1 = [U1 u1];                                  % put solutions in U array ?A\+s,9  
    U2=[U2 u2]; Iu0GOy*[  
    MN1=[MN1 m1]; :Nf(:D8  
    z1=dz*MN1';                                    % output location 19[oXyFI  
  end %I`'it2d  
end zQO 1%g  
hg=abs(U1').*abs(U1');                             % for data write to excel o3Yb2Nw  
ha=[z1 hg];                                        % for data write to excel 2A|mXWG}~  
t1=[0 t']; Pbbi*&i  
hh=[t1' ha'];                                      % for data write to excel file qYVeFSS  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 2s,cyCw&  
figure(1) /ho7~C+H*e  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn \;_tXb}F  
figure(2) s^6,"C  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn uj\&-9gEi  
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非线性超快脉冲耦合的数值方法的Matlab程序 };}N1[D  
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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。   sRBfLN2C  
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 WoNJF6=?  
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%  This Matlab script file solves the nonlinear Schrodinger equations T ;84Sv  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of qmPu D/c  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ^h=gaNL  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 r91i :  
3NZK$d=4  
C=1;                           DfGq m-c  
M1=120,                       % integer for amplitude &)Zv>P8z`  
M3=5000;                      % integer for length of coupler Nk%$;
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N = 512;                      % Number of Fourier modes (Time domain sampling points) ]!1HN3  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 3HR)H-@6@7  
T =40;                        % length of time:T*T0. #~m^RoE  
dt = T/N;                     % time step N&G(`]  
n = [-N/2:1:N/2-1]';          % Index QA~F  
t = n.*dt;   u f<%!=e  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. v`'Iew }  
w=2*pi*n./T; kuLur)^
 
g1=-i*ww./2; o*d(;  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; l| \ -d  
g3=-i*ww./2; @o}J)  
P1=0; YsiH=x  
P2=0; 2|1CGHj\  
P3=1; 45Zh8k  
P=0;
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for m1=1:M1                 >D##94PZ  
p=0.032*m1;                %input amplitude afaQb  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 {#@[ttw$U  
s1=s10; dci,[TEGu  
s20=0.*s10;                %input in waveguide 2 K'Wv$[~Dc  
s30=0.*s10;                %input in waveguide 3 S+eu3nMq  
s2=s20; dF! B5(  
s3=s30; p}I\H ^"8+  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Q>\DM'{:4  
%energy in waveguide 1 FW3E UC)P  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   6_rgRo&  
%energy in waveguide 2 e8_EB/)_Z  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   I3Z\]BI  
%energy in waveguide 3 i-WP#\s  
for m3 = 1:1:M3                                    % Start space evolution C[
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   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS v3n T@ra'  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;  fOsvOC  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; XdlA)0S)  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform tK+JmbB\  
   sca2 = fftshift(fft(s2)); #{k+^7aQ  
   sca3 = fftshift(fft(s3)); \Q|,0`  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   d}?KPJ{  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Jfv'M<I  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); *[jq&  
   s3 = ifft(fftshift(sc3)); FSkX95  
   s2 = ifft(fftshift(sc2));                       % Return to physical space OYa9f[$  
   s1 = ifft(fftshift(sc1)); \|]+sQWQ  
end 7;6'=0(  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); cV`NQt<W  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); <O-R  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ?c_:S]^  
   P1=[P1 p1/p10]; ?< Ma4yl</  
   P2=[P2 p2/p10]; ^x(s!4d]  
   P3=[P3 p3/p10]; 0x&L'&SpN  
   P=[P p*p]; Kj?hcGl[  
end `6NcE-oJ  
figure(1) ]haQ#e}WH  
plot(P,P1, P,P2, P,P3); W=HHTvK9Hh  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~