[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 V7}5Zw1  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of T=6fZ;7  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of W`HO Q  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +X
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 :<$B o  
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%fid=fopen('e21.dat','w'); !QK~l  
N = 128;                       % Number of Fourier modes (Time domain sampling points) ~Pq(Ta  
M1 =3000;              % Total number of space steps X2>qx^jT  
J =100;                % Steps between output of space T~B'- >O  
T =10;                  % length of time windows:T*T0 Hgs=qH  
T0=0.1;                 % input pulse width M{#  
MN1=0;                 % initial value for the space output location K:Mm?28s  
dt = T/N;                      % time step qI-q%]l  
n = [-N/2:1:N/2-1]';           % Index nO{@p_3mi  
t = n.*dt;   :2#8\7IU^'  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 2n}nRv/'  
u20=u10.*0.0;                  % input to waveguide 2 W\xM$#
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u1=u10; u2=u20;                 $6\-8zNk  
U1 = u1;   +3B^e%`NPm  
U2 = u2;                       % Compute initial condition; save it in U 0Y7b$~n'Y  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Y{yN*9a79  
w=2*pi*n./T; r,^}/<*  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T uYW9kw>$  
L=4;                           % length of evoluation to compare with S. Trillo's paper #$trC)?~q  
dz=L/M1;                       % space step, make sure nonlinear<0.05 @@$%+XNY  
for m1 = 1:1:M1                                    % Start space evolution a o_A%?Ld  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS -&87nR(eW  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; *Jd,8B/hC  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform -cW`qWbd  
   ca2 = fftshift(fft(u2)); WU oGIT'  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation {4u8~whLp  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   X ?p_O2#k  
   u2 = ifft(fftshift(c2));                        % Return to physical space hVQ TW[  
   u1 = ifft(fftshift(c1)); 6L--FY>.-  
if rem(m1,J) == 0                                 % Save output every J steps. &%YFO'>>}  
    U1 = [U1 u1];                                  % put solutions in U array XRU^7@Ylks  
    U2=[U2 u2]; v/%q*6@  
    MN1=[MN1 m1]; E8]PV,#xY  
    z1=dz*MN1';                                    % output location UPtWj8h  
  end y?BzZ16\bL  
end Jz(!eTVs  
hg=abs(U1').*abs(U1');                             % for data write to excel Mv9q-SIc[  
ha=[z1 hg];                                        % for data write to excel `V N $ S  
t1=[0 t']; (GnwK1f  
hh=[t1' ha'];                                      % for data write to excel file -!]Ie4"  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format DwTqj=l  
figure(1) pPztUz/.  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn FS.z lk\D=  
figure(2) j!c[$;  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn \L14rQ t  
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非线性超快脉冲耦合的数值方法的Matlab程序 ~i)O^CKq  
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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。   7Gb(&'n  
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 l@}BWSx&ms  
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%  This Matlab script file solves the nonlinear Schrodinger equations |.D_[QI  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
 .*H0{  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear yK"OZ2Mv  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 M,YlhL  
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C=1;                           g*9jPwdG  
M1=120,                       % integer for amplitude QC:/xP  
M3=5000;                      % integer for length of coupler \Fhk>  
N = 512;                      % Number of Fourier modes (Time domain sampling points)  )]2yTG[  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. wEK@B&DV  
T =40;                        % length of time:T*T0. %9|=\# G  
dt = T/N;                     % time step {b@rQCre7  
n = [-N/2:1:N/2-1]';          % Index C7=Q!UK`\  
t = n.*dt;   jjgY4<n  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 7#Qa/[? D  
w=2*pi*n./T; 1m-"v:fT5D  
g1=-i*ww./2; _`!@  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; zT}Qrf~  
g3=-i*ww./2; 9E{Bn#  
P1=0; \mZ\1wzn'{  
P2=0; ?i4}[q  
P3=1; hA`>SkO  
P=0; ZyqTtA!A  
for m1=1:M1                 `~( P  
p=0.032*m1;                %input amplitude \K 01F  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 @URLFMFi  
s1=s10; OwGl&  
s20=0.*s10;                %input in waveguide 2 nLq7J:  
s30=0.*s10;                %input in waveguide 3 C]UBu-]#S  
s2=s20; T6f{'.w  
s3=s30; uh`@qmu)  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   hoASrj{s  
%energy in waveguide 1 JWG7QH  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   #)%N+Odnr  
%energy in waveguide 2 $1(u.Ud  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   RM53B  
%energy in waveguide 3 F2yM2Ldx  
for m3 = 1:1:M3                                    % Start space evolution YgaJ*%\  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS N$ZThZqqv  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ?,r bD1  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ' U(v  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 5|1&s3/f  
   sca2 = fftshift(fft(s2)); z)5n&w S  
   sca3 = fftshift(fft(s3)); [Dq7mqr$  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   #&">x7?5  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); A"Rzn1/  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); I=hgfo  
   s3 = ifft(fftshift(sc3)); ovCk:Vz  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Kq`Luf  
   s1 = ifft(fftshift(sc1)); 7|6tH@4Ub  
end uqZLlP#&#  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); *MkhRLw\,  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); t Zj6=#  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); |aN0|O2  
   P1=[P1 p1/p10]; !mL,Ue3/  
   P2=[P2 p2/p10]; C5Q|3d  
   P3=[P3 p3/p10]; e%G-+6  
   P=[P p*p]; ]^gD@]
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end p)tac*US  
figure(1) &F\J%#{  
plot(P,P1, P,P2, P,P3); nvD"_.KrJ  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~