[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 &&nvv&a  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of l#Ipo5
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of [sy~i{Bm  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear bzF>Efza  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 tMR&>hM  
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%fid=fopen('e21.dat','w'); zgI!S6q  
N = 128;                       % Number of Fourier modes (Time domain sampling points) .hzzoLI2  
M1 =3000;              % Total number of space steps 6c$ so  
J =100;                % Steps between output of space SDwTGQ/0  
T =10;                  % length of time windows:T*T0 hs!a'
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T0=0.1;                 % input pulse width anxgD?<+B  
MN1=0;                 % initial value for the space output location G%jgr"]\z  
dt = T/N;                      % time step  iVu  
n = [-N/2:1:N/2-1]';           % Index - 0R5g3^*/  
t = n.*dt;   (y*7 gf  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 K`{P/w  
u20=u10.*0.0;                  % input to waveguide 2 3CL/9C>  
u1=u10; u2=u20;                 4>-'wMW")  
U1 = u1;   :PE{2*  
U2 = u2;                       % Compute initial condition; save it in U 'y[74?1  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. #>iBu:\J  
w=2*pi*n./T; @.0>gmY;:  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T _kg<KD=P  
L=4;                           % length of evoluation to compare with S. Trillo's paper @a$_F3W  
dz=L/M1;                       % space step, make sure nonlinear<0.05 w$[&ejFb  
for m1 = 1:1:M1                                    % Start space evolution &kUEnwQ-  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS j)xRzImu  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; rofj&{w  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform )S@e&a|  
   ca2 = fftshift(fft(u2)); #s>AiD  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ]Wr2IM  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   R
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   u2 = ifft(fftshift(c2));                        % Return to physical space kw{dvE\K  
   u1 = ifft(fftshift(c1)); ~"|MwR!0  
if rem(m1,J) == 0                                 % Save output every J steps. 6 <XQ'tM]N  
    U1 = [U1 u1];                                  % put solutions in U array `@TWZ%f6  
    U2=[U2 u2]; ]^:sV)  
    MN1=[MN1 m1]; -@L7!,j  
    z1=dz*MN1';                                    % output location 5.! OC5tO  
  end gR1vUad7  
end q)te/J@  
hg=abs(U1').*abs(U1');                             % for data write to excel `yF6-F  
ha=[z1 hg];                                        % for data write to excel diHK  
t1=[0 t']; -LzkM"  
hh=[t1' ha'];                                      % for data write to excel file X .,Lmh  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format mh#NmW>n  
figure(1) @n2Dt d  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn |?v(?  
figure(2) yC\dM1X  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ]Q0m]O
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非线性超快脉冲耦合的数值方法的Matlab程序 "o_s=^U  
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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。   zUq ^  
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 [l44,!Z
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%  This Matlab script file solves the nonlinear Schrodinger equations Ey|{yUmU+  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of eJbZA&:  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 43wm_4C!H  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 >AK9F. _z  
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C=1;                           Lb]!TOl  
M1=120,                       % integer for amplitude d*$L$1S  
M3=5000;                      % integer for length of coupler 5PY4PT=G  
N = 512;                      % Number of Fourier modes (Time domain sampling points) /cHUqn30a  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. OSoIH`tA  
T =40;                        % length of time:T*T0. Me 5Xd|  
dt = T/N;                     % time step f$>KTb({B  
n = [-N/2:1:N/2-1]';          % Index R7\T.;8+  
t = n.*dt;   A1Ru&fd!  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1.  *^y,Gg/  
w=2*pi*n./T; B]2m(0Y>>v  
g1=-i*ww./2; <+y%k~("  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ycq+C8J+Ep  
g3=-i*ww./2; !$u:_8  
P1=0; 0oK_uY 4g  
P2=0; E)3Ah!  
P3=1; :$6mS[@|  
P=0; :+_uyp2V  
for m1=1:M1                 Bnp\G h  
p=0.032*m1;                %input amplitude B4@1WZn<8  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 +Y?)?  
s1=s10; 2dsXG$-W2  
s20=0.*s10;                %input in waveguide 2 7D(Eo{ue  
s30=0.*s10;                %input in waveguide 3
*82+GY]  
s2=s20; CCHGd&\Z  
s3=s30; !78P+i  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   _C@A>]GT  
%energy in waveguide 1 w#v-h3XcF  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   shgZru  
%energy in waveguide 2 *I:a\o~$[  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   o9rZ&Q<  
%energy in waveguide 3 GIb,y,PDB  
for m3 = 1:1:M3                                    % Start space evolution bvW3[ V  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS LpK? C<?x  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; BOflhoUX  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; s"UUo|hM  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform Pm7lP5  
   sca2 = fftshift(fft(s2)); IayF<y,8  
   sca3 = fftshift(fft(s3)); K 0e*K=UM  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   1%$t;R  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); oeYUsnsbi  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); }}qY,@eeX  
   s3 = ifft(fftshift(sc3)); `]`S"W7&  
   s2 = ifft(fftshift(sc2));                       % Return to physical space CKnPMvmz  
   s1 = ifft(fftshift(sc1)); 1B#iJZ}  
end U5 ia|V  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 9Y:Iha`$w  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Avww@$  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Cxd^i  
   P1=[P1 p1/p10]; uZM%F)  
   P2=[P2 p2/p10]; <a&w$Zc/  
   P3=[P3 p3/p10]; %Rt 5$+dNT  
   P=[P p*p]; +~>cAWZq_  
end tkYPfUvTE  
figure(1) D GL=\  
plot(P,P1, P,P2, P,P3); !hFzIp  
( Sjlm^bca  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~