[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 ]mc,FlhU@  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of (X8N?t
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Eg9502Bl~8  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear _k}b  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 r'8e"pTi  
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%fid=fopen('e21.dat','w'); %6n;B|!  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Wj3H  y4  
M1 =3000;              % Total number of space steps (*EN!-/  
J =100;                % Steps between output of space H$;\TG@,  
T =10;                  % length of time windows:T*T0 /oI''O%M  
T0=0.1;                 % input pulse width R'F|z{8  
MN1=0;                 % initial value for the space output location w8E,zH  
dt = T/N;                      % time step HG^8&uh]  
n = [-N/2:1:N/2-1]';           % Index lRrOoON  
t = n.*dt;   ovHbs^
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u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 5!Guf?i  
u20=u10.*0.0;                  % input to waveguide 2 1/gh\9h  
u1=u10; u2=u20;                 +,%x&L&I  
U1 = u1;   HqbTJ!a  
U2 = u2;                       % Compute initial condition; save it in U 4b#YpK$7U  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. [AU1JO`\"  
w=2*pi*n./T; a
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g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T JmBYD[h,  
L=4;                           % length of evoluation to compare with S. Trillo's paper \h yTcFb  
dz=L/M1;                       % space step, make sure nonlinear<0.05 h m"B kOA  
for m1 = 1:1:M1                                    % Start space evolution ^a(q7ZfY
 
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ?gkK*\x2  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; bi5'-.B  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform )yK!EK\  
   ca2 = fftshift(fft(u2)); #*~ (  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation oU2RxK->u  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Ro1l:P)C`  
   u2 = ifft(fftshift(c2));                        % Return to physical space QCjmg5bf'7  
   u1 = ifft(fftshift(c1)); J@$>d  
if rem(m1,J) == 0                                 % Save output every J steps. Ywni2-)<  
    U1 = [U1 u1];                                  % put solutions in U array cB<
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    U2=[U2 u2]; c>
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    MN1=[MN1 m1]; -H]svOX  
    z1=dz*MN1';                                    % output location 3"B|w^6'2  
  end aw,8'N)  
end H'P
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hg=abs(U1').*abs(U1');                             % for data write to excel 7(oxmv}#Q  
ha=[z1 hg];                                        % for data write to excel 8-m"]o3  
t1=[0 t']; rg $71Ir  
hh=[t1' ha'];                                      % for data write to excel file ,
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format I5e!vCG)  
figure(1) lmod8B  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn OZ-F+#d  
figure(2) %~eZrG.  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ;zGGT^Dn  
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非线性超快脉冲耦合的数值方法的Matlab程序 @P8q=j}l9  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   ?
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Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 4(Mt6{q  
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%  This Matlab script file solves the nonlinear Schrodinger equations osnDW aN  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of h;B'#$_  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Q8P;AN_JS  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 vzVl2  
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C=1;                           Yu8WmX,[  
M1=120,                       % integer for amplitude wp@c;gK7  
M3=5000;                      % integer for length of coupler KsHMAp3  
N = 512;                      % Number of Fourier modes (Time domain sampling points) F6fm{  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. c  xX  
T =40;                        % length of time:T*T0. NSxDCTw  
dt = T/N;                     % time step (;s\Ip0  
n = [-N/2:1:N/2-1]';          % Index 1sgoT f%  
t = n.*dt;   8*|
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ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. q k!Q2W  
w=2*pi*n./T; Q.5a"(d@  
g1=-i*ww./2; yJr'\(  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; JiRW|+`pe  
g3=-i*ww./2; Hiw{1E:rW  
P1=0; G;tIhq[$Vb  
P2=0; DB?[h
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P3=1; x*_c'\F|  
P=0; V57^0^Zp`  
for m1=1:M1                 8I@_X~R  
p=0.032*m1;                %input amplitude XX/cJp  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 <8H`y(S  
s1=s10; $ccI(J`zux  
s20=0.*s10;                %input in waveguide 2 C=.  
s30=0.*s10;                %input in waveguide 3 $biCm$a  
s2=s20; QjRVdb>  
s3=s30; e#08,wgW  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Ar>-xCTD  
%energy in waveguide 1 p[W8XX  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   \n/_P
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%energy in waveguide 2 Rk"_4zJk  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   M34*$>bk  
%energy in waveguide 3 _7 n+j  
for m3 = 1:1:M3                                    % Start space evolution YRB,jwne  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS R|Ykez!D  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; .lqo>Ta y  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; sYeZ.MacU  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform f^nogw<z!  
   sca2 = fftshift(fft(s2)); hv9s  
   sca3 = fftshift(fft(s3)); 1z*]MYU  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   TlM ]d;9G  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); @1rF9< 4g  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); _<xU"8b"5  
   s3 = ifft(fftshift(sc3)); =7Nm=5@  
   s2 = ifft(fftshift(sc2));                       % Return to physical space %vMi kibI  
   s1 = ifft(fftshift(sc1)); R$v{ p[  
end [ UQzCqV  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); =:5yRP  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 1!,lI?j,  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); _ 57m] ;&  
   P1=[P1 p1/p10]; hYF<Wn3L  
   P2=[P2 p2/p10]; qc@CV:  
   P3=[P3 p3/p10]; fU$zG"a_  
   P=[P p*p]; N=-hXgX^  
end MB:E/  
figure(1) , Lhgv1  
plot(P,P1, P,P2, P,P3); E5.)ro=$  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~