[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 _ )^n[_E  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of WY~
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 9aqFdlbY  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear FHH2  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 $0iN43WSQ  
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%fid=fopen('e21.dat','w'); ^_ZQf  
N = 128;                       % Number of Fourier modes (Time domain sampling points) q14A'XW  
M1 =3000;              % Total number of space steps EZiGi[t7  
J =100;                % Steps between output of space .yj=*N.  
T =10;                  % length of time windows:T*T0 o9HDxS$~^  
T0=0.1;                 % input pulse width NU/~E"^I.  
MN1=0;                 % initial value for the space output location o:Z*F0qm  
dt = T/N;                      % time step 7 -V_)FK2c  
n = [-N/2:1:N/2-1]';           % Index .Lu=16  
t = n.*dt;   A[':O*iB  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 J>Rt2K  
u20=u10.*0.0;                  % input to waveguide 2 qXW2a'~  
u1=u10; u2=u20;                 >|I3h5\M  
U1 = u1;   zsRN\U  
U2 = u2;                       % Compute initial condition; save it in U uJp}9B60_  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. "Lpt@g[HF  
w=2*pi*n./T; k0D&F;a%  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T &akMj@4;R  
L=4;                           % length of evoluation to compare with S. Trillo's paper #WpO9[b>  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Mw5!9@Fc7  
for m1 = 1:1:M1                                    % Start space evolution |-aj$u%~  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS .r*b+rc;]  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ?R{?
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   ca1 = fftshift(fft(u1));                        % Take Fourier transform 6nSk,yE'hE  
   ca2 = fftshift(fft(u2)); TAC\2*bWje  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation WE~3(rs#X#  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   K6oXnz}  
   u2 = ifft(fftshift(c2));                        % Return to physical space LA@}{hU  
   u1 = ifft(fftshift(c1)); +`Bn]e8O  
if rem(m1,J) == 0                                 % Save output every J steps. s*YFN#Wuc  
    U1 = [U1 u1];                                  % put solutions in U array >a-+7{};  
    U2=[U2 u2]; ng<`2XgU  
    MN1=[MN1 m1]; quUJ%F  
    z1=dz*MN1';                                    % output location E:E&Wv?r  
  end $-AvH(@  
end n0i&P
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hg=abs(U1').*abs(U1');                             % for data write to excel qiF~I0_
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ha=[z1 hg];                                        % for data write to excel -MEz`7c~  
t1=[0 t']; Pd;ClMa%  
hh=[t1' ha'];                                      % for data write to excel file w+$gY?%  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format yEqmB4^-  
figure(1) X5/{Mx`8Oz  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn J+|ohA  
figure(2) qL+y8*  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn DVcu*UVw  
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非线性超快脉冲耦合的数值方法的Matlab程序 (MIw$)#^  
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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。   ipp_?5TL  
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 g^4FzJ  
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%  This Matlab script file solves the nonlinear Schrodinger equations 3ElpS^2W  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of t3>rf3v  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear O]g+z$2o  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 PC_4#6^5  
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C=1;                           !Cy2>6v7  
M1=120,                       % integer for amplitude ge oN4  
M3=5000;                      % integer for length of coupler N]<gHGj}  
N = 512;                      % Number of Fourier modes (Time domain sampling points) `k|nf9_  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 9|WWA%p  
T =40;                        % length of time:T*T0. S+y2eP G  
dt = T/N;                     % time step ,;-*q}
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n = [-N/2:1:N/2-1]';          % Index U[D<%7f  
t = n.*dt;   5#o,]tP  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. [;f"',)y,  
w=2*pi*n./T; W7o/  
g1=-i*ww./2; FOA%(5$4  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; U.F65KaKF  
g3=-i*ww./2; y4L9Cxvs  
P1=0; *a%PA(%6  
P2=0; T!a[@,)_  
P3=1; )\;r V';  
P=0; DS2$w9!  
for m1=1:M1                 cj#q7  
p=0.032*m1;                %input amplitude !v L:P2  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 \IfgL$+  
s1=s10; %nh'F6bNgv  
s20=0.*s10;                %input in waveguide 2 $bosGG  
s30=0.*s10;                %input in waveguide 3 k>CtWV5B  
s2=s20; fNJ;{&#  
s3=s30; _64@zdL+  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   j2Y(Q/i  
%energy in waveguide 1 $\!;*SSj  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   q_&IZ,{Vk  
%energy in waveguide 2 { bn#:75r  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   >2 qP  
%energy in waveguide 3 sK?-@  
for m3 = 1:1:M3                                    % Start space evolution }AqD0Qd2Hj  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS <pUou  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; #Vigu,zY  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; h,'+w  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 6S[D"Q94  
   sca2 = fftshift(fft(s2)); Dg+d=I?  
   sca3 = fftshift(fft(s3)); Gnt!!1_8L  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   "J{zfWr  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); & }}WP:U  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); DZ.trtK  
   s3 = ifft(fftshift(sc3)); 3]es$Jy  
   s2 = ifft(fftshift(sc2));                       % Return to physical space +yH~G9u(  
   s1 = ifft(fftshift(sc1)); QJM!W
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end z44~5J]  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); -$t,}3  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); <SZO- -+lB  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); p\;)^O4  
   P1=[P1 p1/p10]; 3og$'#6P  
   P2=[P2 p2/p10]; X$iJ|=vW  
   P3=[P3 p3/p10]; UiZp-Y%ki  
   P=[P p*p]; wP0+Xv,  
end "|*Kf#  
figure(1) >1G*ya)  
plot(P,P1, P,P2, P,P3); jY+S,lD  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~