[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 an0@EkZ  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of ;2#HM^Mu  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of d=N5cCqq  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear kX5v!pm[  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 yd#4b`8U`  
P8z++h  
%fid=fopen('e21.dat','w'); x\I9J4Q  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 0`,a@Q4  
M1 =3000;              % Total number of space steps oV,>u5:B  
J =100;                % Steps between output of space pd>EUdbrp&  
T =10;                  % length of time windows:T*T0 h#;fBQ]   
T0=0.1;                 % input pulse width n3~xiQ'  
MN1=0;                 % initial value for the space output location ~A>3k2N/e  
dt = T/N;                      % time step Vu;tU.  
n = [-N/2:1:N/2-1]';           % Index ~cU,3g  
t = n.*dt;   Gd:fWz(  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 /`:5#O  
u20=u10.*0.0;                  % input to waveguide 2 F RS@-P  
u1=u10; u2=u20;                 k<8:  
U1 = u1;   #HM0s~^w&  
U2 = u2;                       % Compute initial condition; save it in U 9~Q.[ A  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. qhLe[[>  
w=2*pi*n./T; EDL<J1%  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ,i,f1XJ|  
L=4;                           % length of evoluation to compare with S. Trillo's paper yd`.Rb&V  
dz=L/M1;                       % space step, make sure nonlinear<0.05 evu@uq  
for m1 = 1:1:M1                                    % Start space evolution <Pg.N  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS \HTXl]  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; GMB%
A  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform CNfeHMT  
   ca2 = fftshift(fft(u2)); G)'cd D1  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation {Qlvj.Xw  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   HO&#Lv  
   u2 = ifft(fftshift(c2));                        % Return to physical space vseuk@>  
   u1 = ifft(fftshift(c1)); A%%WPBk{O  
if rem(m1,J) == 0                                 % Save output every J steps.  7&l  
    U1 = [U1 u1];                                  % put solutions in U array _oe2pL&  
    U2=[U2 u2]; !oM1  
    MN1=[MN1 m1]; *gVRMSrx4  
    z1=dz*MN1';                                    % output location 3 T&m  
  end Jw"'ZW#W  
end vIz~B2%x  
hg=abs(U1').*abs(U1');                             % for data write to excel YujhpJ<  
ha=[z1 hg];                                        % for data write to excel tw\/1wa.  
t1=[0 t']; "d%":F(  
hh=[t1' ha'];                                      % for data write to excel file o`hF1*yp  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format %UgyGQeo  
figure(1) g%[lUxL  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn spd>.Cm`  
figure(2) YadyRUE  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn m|=/|Hm  
]7c715@  
非线性超快脉冲耦合的数值方法的Matlab程序 NWb,$/7T  
=,,!a/U  
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。   v=9:N/sW  
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 Sf lHSMFw  
bBC3% H^  
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%  This Matlab script file solves the nonlinear Schrodinger equations [ V/*{Z  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Ko2{[%  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear VY Va8[}  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 e"[o2=v;5  
SP5/K3t-*  
C=1;                           A2*
z  
M1=120,                       % integer for amplitude N[E t  
M3=5000;                      % integer for length of coupler PL%_V ?z  
N = 512;                      % Number of Fourier modes (Time domain sampling points) >k kuw?O@  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. umSbxEZU@  
T =40;                        % length of time:T*T0. NC@OmSR\0  
dt = T/N;                     % time step G|IO~o0+  
n = [-N/2:1:N/2-1]';          % Index vMj"%  
t = n.*dt;   V.\do"m  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. !W .ooy5(  
w=2*pi*n./T; 3%!d&j>v  
g1=-i*ww./2; |brl<*:  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; PgxD?Oi8  
g3=-i*ww./2; 97'*Xq  
P1=0; /< h~d  
P2=0; $(.[b][S  
P3=1; yH@W6'.  
P=0; "P"~/<:)  
for m1=1:M1                 |f?tyQ  
p=0.032*m1;                %input amplitude 0rjx
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 1+.(N:) +  
s1=s10; &37QUdp+p  
s20=0.*s10;                %input in waveguide 2 ![{>f6{J  
s30=0.*s10;                %input in waveguide 3 %R-"5?eTtu  
s2=s20; |*i0h`a  
s3=s30; .KXpB7:  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   '-S^z"ZrI  
%energy in waveguide 1 yA \C3r'
 
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   YPFjAQ  
%energy in waveguide 2 @/E5$mX`  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   u])N^AY"sj  
%energy in waveguide 3 aQ46e
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for m3 = 1:1:M3                                    % Start space evolution Ef:.)!;jy  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 8;-a_VjA)  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; !T#~.QP4  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ?b:l.0m  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 11Pm lzy  
   sca2 = fftshift(fft(s2)); 4}gqtw:  
   sca3 = fftshift(fft(s3)); .@gv}`>  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   w=e~ M  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Qpe&_.&RE  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Ca0~K42~  
   s3 = ifft(fftshift(sc3)); K p~x  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ~OAST  
   s1 = ifft(fftshift(sc1)); 1|q$Wn:*  
end NYm2fFPc  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
E,>/6AU  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); TmvI+AY/  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); \%K< S  
   P1=[P1 p1/p10]; 4b,N"w{v  
   P2=[P2 p2/p10]; zdlysr#  
   P3=[P3 p3/p10]; w|OMT>.  
   P=[P p*p]; AQDT6E:  
end :1PT`:Y  
figure(1) ^Z$%OM,  
plot(P,P1, P,P2, P,P3); )k.;.7dXe  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~