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tianmen 2011-06-12 18:33

求解光孤子或超短脉冲耦合方程的Matlab程序

计算脉冲在非线性耦合器中演化的Matlab 程序 X ak~He  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of J|>P,x#G  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of @!Pq"/  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g_q{3PW.  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 {4Isz-P  
Z<wg`  
%fid=fopen('e21.dat','w'); 'J\%JAR@  
N = 128;                       % Number of Fourier modes (Time domain sampling points) abF_i#  
M1 =3000;              % Total number of space steps 4ASc`w*0  
J =100;                % Steps between output of space ND`~|6yb  
T =10;                  % length of time windows:T*T0 rUuM__;d  
T0=0.1;                 % input pulse width LPXwfEHOm  
MN1=0;                 % initial value for the space output location ;^xku%u  
dt = T/N;                      % time step UR\*KR;yM  
n = [-N/2:1:N/2-1]';           % Index 4f>Vg$4  
t = n.*dt;   2 o.Mh/D0  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 dW=]|t&  
u20=u10.*0.0;                  % input to waveguide 2 AvwX 2?tc  
u1=u10; u2=u20;                 E;X'.7[c  
U1 = u1;   QM$?}>:  
U2 = u2;                       % Compute initial condition; save it in U +[>m`XTq  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1.  mbd@4u  
w=2*pi*n./T; w ggl,+7  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T >97V2W  
L=4;                           % length of evoluation to compare with S. Trillo's paper +Oxl1fDf  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Hu;#uAnxQ  
for m1 = 1:1:M1                                    % Start space evolution @Pa ;h  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS =A,i9Z&  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; {>~|xW  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform .NPai4V'  
   ca2 = fftshift(fft(u2)); jKtbGVZ 7r  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation !]"T`^5,Y  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   9iv!+(ni  
   u2 = ifft(fftshift(c2));                        % Return to physical space k muF*0Bjk  
   u1 = ifft(fftshift(c1)); %II |;<  
if rem(m1,J) == 0                                 % Save output every J steps. t n}9(Oa)  
    U1 = [U1 u1];                                  % put solutions in U array K}* s^*X  
    U2=[U2 u2]; /6f$%:q  
    MN1=[MN1 m1]; }96^OQPE  
    z1=dz*MN1';                                    % output location h-6kf:XP%  
  end =XqmFr;h  
end \oaO7w,:"  
hg=abs(U1').*abs(U1');                             % for data write to excel <8'}H`w%  
ha=[z1 hg];                                        % for data write to excel n0cqM}P@;!  
t1=[0 t']; w 5,-+&;  
hh=[t1' ha'];                                      % for data write to excel file WyO10yvR  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format `M|fwlAJQ  
figure(1) VkUMMq{  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn **oN/5  
figure(2) @Gl=1  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn n}YRE`>D  
b2ZKhS8  
非线性超快脉冲耦合的数值方法的Matlab程序 cm-! 6'`  
O>}aK.H  
在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   vQ 5 p  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8?ZK^+]y  
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k|&@xEbS  
%  This Matlab script file solves the nonlinear Schrodinger equations 7=}`"7i~  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of V+DN<F-  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear l].dOso$`  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Q xKC5`1  
2y,f  
C=1;                           \|Us/_h  
M1=120,                       % integer for amplitude Z}WMpp^r  
M3=5000;                      % integer for length of coupler EdLbVrN,  
N = 512;                      % Number of Fourier modes (Time domain sampling points) *Z<`TB)<X  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. "*<9)vQ6|  
T =40;                        % length of time:T*T0. 3g)pLW  
dt = T/N;                     % time step j^>J*gLM}W  
n = [-N/2:1:N/2-1]';          % Index 6 fL=2a  
t = n.*dt;    \&"gCv#  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 4OC ^IS  
w=2*pi*n./T; `cCsJm$V"  
g1=-i*ww./2; w8c71C  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; vDqmD{%4N  
g3=-i*ww./2; +A O(e  
P1=0; [Jwo,?w  
P2=0; REli`"bR  
P3=1; >]s|'HTxF  
P=0; 3D(/k%;)  
for m1=1:M1                 1o V\QK&  
p=0.032*m1;                %input amplitude %?^IS&]Z  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 IyOb0WiEj  
s1=s10; }f/ 1  
s20=0.*s10;                %input in waveguide 2 t[Qf|#g  
s30=0.*s10;                %input in waveguide 3 S&q@M  
s2=s20; +7.\>Ucq`  
s3=s30; lmf vT}$B  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   w9G (^jS6  
%energy in waveguide 1 jEo)#j];`<  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   WRe9ki=R  
%energy in waveguide 2 `O5w M\Z  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   scT,yNV  
%energy in waveguide 3 xk7 MMRb  
for m3 = 1:1:M3                                    % Start space evolution fp^{612O?  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS TgoaEufS<  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 3rBSwgRl  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 0Q`Dp;a5&  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 5<^ $9('  
   sca2 = fftshift(fft(s2)); ~=67#&(R  
   sca3 = fftshift(fft(s3)); F0(P 2j  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   H,u{zU')  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); x-1RmL_%  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); #ueWU  
   s3 = ifft(fftshift(sc3)); g 0O~5.f  
   s2 = ifft(fftshift(sc2));                       % Return to physical space g(& huS  
   s1 = ifft(fftshift(sc1)); XYj!nx{k,  
end LDc?/ Z1  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); C9OEB6  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Ve)P/Zz}^  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); iI.pxo s  
   P1=[P1 p1/p10]; xq$(=WPI  
   P2=[P2 p2/p10]; tpPP5C{  
   P3=[P3 p3/p10]; & 6 wD  
   P=[P p*p]; w`KqB(36  
end 4&N#d;ErC  
figure(1) +-2o b90_m  
plot(P,P1, P,P2, P,P3); ,Pi!%an w  
}:+SA  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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