[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 T%
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of ?0 KiR?  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of dXf]G6  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear r_qncy,F  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 B;Q`vKY  
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%fid=fopen('e21.dat','w'); (1saof*p%  
N = 128;                       % Number of Fourier modes (Time domain sampling points) o>/uW8  
M1 =3000;              % Total number of space steps r_!{!i3B  
J =100;                % Steps between output of space e>ZbZy?  
T =10;                  % length of time windows:T*T0 *o:BoP=S  
T0=0.1;                 % input pulse width |IyM"UH  
MN1=0;                 % initial value for the space output location 8gu'dG=  
dt = T/N;                      % time step i{1)=_$Vt`  
n = [-N/2:1:N/2-1]';           % Index /h}wM6pg  
t = n.*dt;   bn<I#ZH2  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 )D6'k{6M  
u20=u10.*0.0;                  % input to waveguide 2 S20nk.x  
u1=u10; u2=u20;                 @M1yBN  
U1 = u1;   H`+]dXLB  
U2 = u2;                       % Compute initial condition; save it in U {Kq*5Aq8  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. L~?,6  
w=2*pi*n./T; ^^t]vojX  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T IxK 3,@d  
L=4;                           % length of evoluation to compare with S. Trillo's paper )n[`Z#  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ^6N3nkyZ  
for m1 = 1:1:M1                                    % Start space evolution ^-csi  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS kp#c:ym  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; [7SI<xkv  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ?h>%Ix  
   ca2 = fftshift(fft(u2)); ';fU.uy  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 4:
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   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   kcma/d  
   u2 = ifft(fftshift(c2));                        % Return to physical space fmZz
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   u1 = ifft(fftshift(c1)); 
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if rem(m1,J) == 0                                 % Save output every J steps. g#9*bF  
    U1 = [U1 u1];                                  % put solutions in U array y$r?t0
 
    U2=[U2 u2]; btB(n<G2#  
    MN1=[MN1 m1]; n'x`oI)-  
    z1=dz*MN1';                                    % output location g O\f:Pg  
  end VQG /g\  
end {8>_,z^P)  
hg=abs(U1').*abs(U1');                             % for data write to excel JJbM)B@-  
ha=[z1 hg];                                        % for data write to excel h!t2H6eyF  
t1=[0 t']; >m;|I/2@  
hh=[t1' ha'];                                      % for data write to excel file =`7)X\i@z  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format >FEQtD~F  
figure(1) !,-qn)b  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn u6bB5(s`&  
figure(2) [w#x5Xs
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn B 3,ig9  
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非线性超快脉冲耦合的数值方法的Matlab程序 ?[L0LL?ce  
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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 {*5;:QnT  
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%  This Matlab script file solves the nonlinear Schrodinger equations "#eNFCo7k  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Jj^<:t5{rN  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear w3]0 !)t1  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Ph7(JV{  
T$8$9D_u  
C=1;                           o`y*yucHI  
M1=120,                       % integer for amplitude +D{*L0$D"  
M3=5000;                      % integer for length of coupler M@LaD 5  
N = 512;                      % Number of Fourier modes (Time domain sampling points) WHD/s  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. [0,q7d?"  
T =40;                        % length of time:T*T0. #*;fQ&p  
dt = T/N;                     % time step `$x#_-Hn  
n = [-N/2:1:N/2-1]';          % Index o4I!VK(C#s  
t = n.*dt;   ;HLMU36q  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. k~s>8N:&G  
w=2*pi*n./T; 9|kE
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g1=-i*ww./2; Iy1XnS*  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; .5Z@5g`  
g3=-i*ww./2; {i7Fu+xZj  
P1=0; ;(iUY/ h[h  
P2=0; $nd-[xV  
P3=1; wGQhr="  
P=0; d=5}^v#4  
for m1=1:M1                 gJ[q {b  
p=0.032*m1;                %input amplitude }zfLm`vJ  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 I>4Tbwy.-  
s1=s10; a518N*]j  
s20=0.*s10;                %input in waveguide 2 ]zR;%p  
s30=0.*s10;                %input in waveguide 3 Z?!:=x>7m  
s2=s20; G>{:D'#  
s3=s30; Er+3S@sfq,  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ThqfZl=V  
%energy in waveguide 1 *$Wx*Jo  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   #/sE{jm  
%energy in waveguide 2 /dvnQW4}8  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   G|Yp<W%o  
%energy in waveguide 3 Vi-!E  
for m3 = 1:1:M3                                    % Start space evolution uc(yos  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS y8WXp_\  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; .gsu_
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   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; L!Zxc~  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform uB&I56  
   sca2 = fftshift(fft(s2)); ZzaW@6LJF  
   sca3 = fftshift(fft(s3)); {4jSj0W  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   PNxO\Rc  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); f!kdcr=/"  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); mt6uW+t/
 
   s3 = ifft(fftshift(sc3)); xA1pDrfC/  
   s2 = ifft(fftshift(sc2));                       % Return to physical space lG^nT  
   s1 = ifft(fftshift(sc1)); 7)It1i-  
end (a4y1k t-  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); %|6Q7'@p  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); uXW. (x7"f  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); }6{)Jv  
   P1=[P1 p1/p10]; )^2jsy -/  
   P2=[P2 p2/p10]; f%%En5e+  
   P3=[P3 p3/p10]; SE-, 1p  
   P=[P p*p]; %Bun@  
end yW,#&>]# |  
figure(1) [&}<!:9'  
plot(P,P1, P,P2, P,P3); kk./-G  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~