[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 F7&Oc)f"B  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of +![\7  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 4"et4Y7  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear F*_ytL  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 \Lz4ZZjSY  
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%fid=fopen('e21.dat','w'); #eY?6Kjn  
N = 128;                       % Number of Fourier modes (Time domain sampling points) }&Ul(HR  
M1 =3000;              % Total number of space steps -&0HAtc  
J =100;                % Steps between output of space 55V&[>|K5  
T =10;                  % length of time windows:T*T0 !=p^@N7  
T0=0.1;                 % input pulse width 28,g'k!  
MN1=0;                 % initial value for the space output location ."h>I @MH  
dt = T/N;                      % time step i{MzQE+_^  
n = [-N/2:1:N/2-1]';           % Index I,7n-G_'  
t = n.*dt;   E
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u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Stk'|-z  
u20=u10.*0.0;                  % input to waveguide 2 9;L50q>s  
u1=u10; u2=u20;                 osPrr QoH  
U1 = u1;   /9<62F@zJ"  
U2 = u2;                       % Compute initial condition; save it in U 9V?:!%J  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. nD!5I@D  
w=2*pi*n./T; Lb0BmR%0  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T *GC9o/  
L=4;                           % length of evoluation to compare with S. Trillo's paper OcZ8:`=%  
dz=L/M1;                       % space step, make sure nonlinear<0.05 K)nn;j=  
for m1 = 1:1:M1                                    % Start space evolution m ol|E={si  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ~Aoo\fN_U  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 9~6~[z  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform Sz0CP1WB  
   ca2 = fftshift(fft(u2)); lk%W2N5  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation GU]_Z!3  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   VN >X/  
   u2 = ifft(fftshift(c2));                        % Return to physical space ]oE:p  
   u1 = ifft(fftshift(c1)); 5tcJTz  
if rem(m1,J) == 0                                 % Save output every J steps. i1-wzI  
    U1 = [U1 u1];                                  % put solutions in U array l
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    U2=[U2 u2]; oWcBQ|   
    MN1=[MN1 m1]; Y5\=5r/  
    z1=dz*MN1';                                    % output location )kt,E}609  
  end l3;MjNB^V  
end }NF7"tOL  
hg=abs(U1').*abs(U1');                             % for data write to excel {PQ!o^7y  
ha=[z1 hg];                                        % for data write to excel >@i{8AD  
t1=[0 t']; "V:E BR  
hh=[t1' ha'];                                      % for data write to excel file |s{[<;  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format g/jlG%kI}  
figure(1) r|JZU  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn +HfZs"x  
figure(2) yUlYf#`H  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn +I_p\/J?w/  
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非线性超快脉冲耦合的数值方法的Matlab程序 D",~?  
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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。   JB(P-Y#yyA  
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 Vv~:^6il  
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%  This Matlab script file solves the nonlinear Schrodinger equations +,A7XBn  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of jLgx(bM
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear [cvtF(,  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 :Tn1]a)f6  
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C=1;                           >TQnCG=  
M1=120,                       % integer for amplitude ,]8$QFf  
M3=5000;                      % integer for length of coupler E@D}Sqt  
N = 512;                      % Number of Fourier modes (Time domain sampling points) .80L>0  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. h;Se.{  
T =40;                        % length of time:T*T0. H/BU2sa  
dt = T/N;                     % time step 4Q5c'  
n = [-N/2:1:N/2-1]';          % Index O*y@4AR"S  
t = n.*dt;   DTp|he  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. nk-V{']  
w=2*pi*n./T; E-XFW]I  
g1=-i*ww./2; \ws^L,h  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; iJem9XXb  
g3=-i*ww./2; 1)N{!w`  
P1=0; {wyf>L0j  
P2=0; /8tF7Mmr  
P3=1; Fmu
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P=0; $H2H
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for m1=1:M1                 *m9,_~t  
p=0.032*m1;                %input amplitude Nw|m"VLb  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 xXm:S{I  
s1=s10; R8YA"(j!L  
s20=0.*s10;                %input in waveguide 2 L!V6Rfy  
s30=0.*s10;                %input in waveguide 3 [t}$W*hY  
s2=s20; a<ztA:xt|1  
s3=s30; 7n*[r*$  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   7d"gRM;  
%energy in waveguide 1 ~Y /55uC  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   E#A}J:  
%energy in waveguide 2 ^lCQHz  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Bq)aA)gF  
%energy in waveguide 3 1X$hwkof  
for m3 = 1:1:M3                                    % Start space evolution c DO<z  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS X__>r ?oJ  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; H&3i[D!p  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; k6PHyt`3'  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ~[d|:]  
   sca2 = fftshift(fft(s2)); t:<dirw,o  
   sca3 = fftshift(fft(s3)); /vG)n9Rc  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   XP'7+/A  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 9Di@r!Db  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); g4fe(.?c,  
   s3 = ifft(fftshift(sc3)); 5\|u] ~b  
   s2 = ifft(fftshift(sc2));                       % Return to physical space XexslzI  
   s1 = ifft(fftshift(sc1)); {Y#
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end nax(V  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); jQLiqi`  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); x&PVsXdt5m  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); -F+dmI,1$  
   P1=[P1 p1/p10]; Wu9))Ir  
   P2=[P2 p2/p10]; fR6.:7&  
   P3=[P3 p3/p10]; 5$C]$o}  
   P=[P p*p]; 5,n{-V  
end @g~hYc  
figure(1) IU*w'a  
plot(P,P1, P,P2, P,P3); GDMg.w4Yk  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~