[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 Q{|_"sfJ  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 704_ehrlE  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of d@%PTSX  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear cT5BBR  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 NTo[di\_  
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%fid=fopen('e21.dat','w'); bcgXpP  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Zi?:< H}  
M1 =3000;              % Total number of space steps ,8.$!Zia  
J =100;                % Steps between output of space "TI>_~  
T =10;                  % length of time windows:T*T0 O\SH;y,N  
T0=0.1;                 % input pulse width ix hF,F
 
MN1=0;                 % initial value for the space output location Y P,>vzW  
dt = T/N;                      % time step hSz_e  
n = [-N/2:1:N/2-1]';           % Index T>pyYF1Q  
t = n.*dt;   2bOl`{x  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 a!EW[|[Q  
u20=u10.*0.0;                  % input to waveguide 2 ~.>8ww  
u1=u10; u2=u20;                 yl&s!I  
U1 = u1;   j#Qnu0D  
U2 = u2;                       % Compute initial condition; save it in U ;|`<B7xf  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ~s yWORiXm  
w=2*pi*n./T; S5kD|kJ  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T S17;;w0  
L=4;                           % length of evoluation to compare with S. Trillo's paper ~Ajst!Y7=  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Zoy)2E{  
for m1 = 1:1:M1                                    % Start space evolution +z[+kir  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS cm0$v8  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; &2Ef:RZF  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform yDJy'Z_F{  
   ca2 = fftshift(fft(u2)); D|amKW7  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation v>HOz\F  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   I$R
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   u2 = ifft(fftshift(c2));                        % Return to physical space .4ZOm'ko{  
   u1 = ifft(fftshift(c1)); (d/!M n6L  
if rem(m1,J) == 0                                 % Save output every J steps. /M JI^\CA  
    U1 = [U1 u1];                                  % put solutions in U array *\@RBJGF  
    U2=[U2 u2]; ftKL#9,s(  
    MN1=[MN1 m1]; Dlpmm2  
    z1=dz*MN1';                                    % output location yh/JHo;  
  end ^ir)z@P?V  
end sH>`eqY
 
hg=abs(U1').*abs(U1');                             % for data write to excel =~"X/>'  
ha=[z1 hg];                                        % for data write to excel F2\&rC4v  
t1=[0 t']; :T|9
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hh=[t1' ha'];                                      % for data write to excel file 6{{<+ o  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format
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figure(1)  +hKs  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn , @!X!L  
figure(2) I:HrBhI)wP  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn fs:yx'm
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# E_S..  
非线性超快脉冲耦合的数值方法的Matlab程序 6O,:I  
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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。   xXc>YTK'  
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 &CcW(-  
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%  This Matlab script file solves the nonlinear Schrodinger equations *u:,@io7'G  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of G"m?2$^-A  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear OR*JWW[]  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 d3|/&gDBK  
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C=1;                           :8]8
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M1=120,                       % integer for amplitude 8{QCW{K  
M3=5000;                      % integer for length of coupler -8Hc M\b  
N = 512;                      % Number of Fourier modes (Time domain sampling points) `U b*rOMu  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. I`*5z;Q!%@  
T =40;                        % length of time:T*T0. 4'=Q:o*w`  
dt = T/N;                     % time step <i4]qO(0u  
n = [-N/2:1:N/2-1]';          % Index Kc95yt  
t = n.*dt;   6PYm?i=p?  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. G0|}s&$yL  
w=2*pi*n./T; FZO&r60$E  
g1=-i*ww./2; 6T|Z4f|  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
g1|Pyt{  
g3=-i*ww./2; ^N[ Cip}8  
P1=0; ;ne`ppz0  
P2=0; Pc=ei  
P3=1;
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P=0; 4sntSlz)~k  
for m1=1:M1                 !'~Ldl  
p=0.032*m1;                %input amplitude ZG2EOy  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 CQNMCYjg(R  
s1=s10; ju'aUzn  
s20=0.*s10;                %input in waveguide 2 2J{vfF  
s30=0.*s10;                %input in waveguide 3 j~1K(=Ng  
s2=s20; -3i(N.)<;  
s3=s30; l`N4P  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   $ZGup"z)  
%energy in waveguide 1 MZ&.{SY7  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   tM
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%energy in waveguide 2 pi~5}bF!a  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   l"A/6r!Dp  
%energy in waveguide 3 Wh..QVv  
for m3 = 1:1:M3                                    % Start space evolution `,xO~_ e>  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS qqe"hruF
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ?gUraS
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   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ,*U-o}{8C?  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ;akW i]  
   sca2 = fftshift(fft(s2)); S*=^I2;  
   sca3 = fftshift(fft(s3)); l^ay*H  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   O
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   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); >qB`03>  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); $x`HmL3Sb  
   s3 = ifft(fftshift(sc3)); i+mU(/l2{  
   s2 = ifft(fftshift(sc2));                       % Return to physical space JZ`SV}\`  
   s1 = ifft(fftshift(sc1)); sZCK?  
end >!@D^3PPA  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 2w3LK2`ZL  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); s|H7;.3gp  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); "i(f+N,)  
   P1=[P1 p1/p10]; gk6R#  
   P2=[P2 p2/p10]; Zs79,*o+0M  
   P3=[P3 p3/p10]; XJPIAN~l  
   P=[P p*p]; XWAIW=.  
end |Vqm1.1/Zv  
figure(1) uP%VL}%0  
plot(P,P1, P,P2, P,P3); .z_nW1id  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~