[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 x;bA\b  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of v%2Dz  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of e&T-GL  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ,\&r\!=  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 jLMy27Cn  
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%fid=fopen('e21.dat','w'); ??.aLeF&  
N = 128;                       % Number of Fourier modes (Time domain sampling points) |X XO0  
M1 =3000;              % Total number of space steps J| wk})?  
J =100;                % Steps between output of space hPz=Ec<zW  
T =10;                  % length of time windows:T*T0 .IY@Q  
T0=0.1;                 % input pulse width ,66(*\xT  
MN1=0;                 % initial value for the space output location p&<n_b  
dt = T/N;                      % time step d(RMD  
n = [-N/2:1:N/2-1]';           % Index NV(jp'i~  
t = n.*dt;   V*2*5hx  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 u]O}Ub`  
u20=u10.*0.0;                  % input to waveguide 2 E24}?t^|  
u1=u10; u2=u20;                 >m!Z$m([J  
U1 = u1;   n=~!x  
U2 = u2;                       % Compute initial condition; save it in U }m^^6h  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. /!t:MK;  
w=2*pi*n./T; [ypE[   
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T M,ybj5:6  
L=4;                           % length of evoluation to compare with S. Trillo's paper +I
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dz=L/M1;                       % space step, make sure nonlinear<0.05 b5]<!~Fv:`  
for m1 = 1:1:M1                                    % Start space evolution "0 %fR"  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS }dMX1e1h8  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; jP}Ry=V/  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform <zTz/Hk`  
   ca2 = fftshift(fft(u2)); HRbv%  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation toD!RE  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   [Rq|;p  
   u2 = ifft(fftshift(c2));                        % Return to physical space `DSFaBj,  
   u1 = ifft(fftshift(c1)); {%k[Z9*tO  
if rem(m1,J) == 0                                 % Save output every J steps. `~lG5|  
    U1 = [U1 u1];                                  % put solutions in U array adri02C/  
    U2=[U2 u2]; 4:O.x#p  
    MN1=[MN1 m1]; kRwY#  
    z1=dz*MN1';                                    % output location  %rlqq*  
  end $'d,X@}8  
end '?.']U,: $  
hg=abs(U1').*abs(U1');                             % for data write to excel $39TP@?:Z)  
ha=[z1 hg];                                        % for data write to excel v)|a}5={  
t1=[0 t']; r
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hh=[t1' ha'];                                      % for data write to excel file <Pe'&u  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 6?.S-.Mr  
figure(1) ?G!p4u?C  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn n.NWS/v_{  
figure(2) l]t^MEoc8  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn nB :iG  
q2`mu4B  
非线性超快脉冲耦合的数值方法的Matlab程序 (yuOY/~k/  
L">jSZW[[  
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。   z.)*/HGJm  
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 @Ss W  
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%  This Matlab script file solves the nonlinear Schrodinger equations O#J7GbrHO  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ';.y`{/  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear !J{[XT  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ,d.5K*?aI  
Ji=`XsV  
C=1;                           s{X+0_@Q  
M1=120,                       % integer for amplitude OaoHN& "  
M3=5000;                      % integer for length of coupler ~@<o-|#  
N = 512;                      % Number of Fourier modes (Time domain sampling points) %)dp a  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. pV:44  
T =40;                        % length of time:T*T0. wM;=^br  
dt = T/N;                     % time step MZX@Gi<S[  
n = [-N/2:1:N/2-1]';          % Index &E!m(|6?+  
t = n.*dt;   B2_fCSlg  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ,.=7{y~  
w=2*pi*n./T; gth_Sz5!#  
g1=-i*ww./2; "5N$u(: b  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; l`X?C~JhJ  
g3=-i*ww./2; ;Tq4!w'rH  
P1=0; 0/z$W.!  
P2=0; n >E1\($  
P3=1; } 21!b :a  
P=0; SjA'<ZX>TM  
for m1=1:M1                 UF89gG4  
p=0.032*m1;                %input amplitude &FZ~n?;hQ  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 \>j@!W  
s1=s10; ,*x/L?.Z!  
s20=0.*s10;                %input in waveguide 2 Aq'~'hS`1  
s30=0.*s10;                %input in waveguide 3 &i`(y>\  
s2=s20; #!yX2lR  
s3=s30; n1R{[\ >1  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   :y{@=E=XSC  
%energy in waveguide 1 0R]'HA>  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   y6G6wk;  
%energy in waveguide 2 c5KciTD^  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ,]9p&xu  
%energy in waveguide 3 ^foCcO  
for m3 = 1:1:M3                                    % Start space evolution $|!3ks  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS rT4qx2u  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; pf yJL?_%  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; w; f LnEz_  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform CA$|3m9)NM  
   sca2 = fftshift(fft(s2)); EQHCw<e  
   sca3 = fftshift(fft(s3)); 2`FDY3n  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   o9]!*Y!RA  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Ne1W!0YLK  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); r=RiuxxTq  
   s3 = ifft(fftshift(sc3)); #&K}w0}k  
   s2 = ifft(fftshift(sc2));                       % Return to physical space dg0WH_#  
   s1 = ifft(fftshift(sc1)); 8f'r_,"  
end v806f8  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); CzDg?wb  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); n5fc_N/8O=  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 7s0y.i~  
   P1=[P1 p1/p10]; ] J|#WtS  
   P2=[P2 p2/p10]; K)n058PO  
   P3=[P3 p3/p10]; dg(sRTi{  
   P=[P p*p]; 1dy"  
end .NF3dC\  
figure(1) J/Ch /Sa  
plot(P,P1, P,P2, P,P3); Jep/%cT$w  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~