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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 a9Zq{Ysj  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of am6L8N  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of uW %#  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear F*ylnB3z  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 67FWa   
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%fid=fopen('e21.dat','w'); 8zW2zkv2|#  
N = 128;                       % Number of Fourier modes (Time domain sampling points)  o-B$J?  
M1 =3000;              % Total number of space steps &mS^ZyG  
J =100;                % Steps between output of space  N4TV  
T =10;                  % length of time windows:T*T0 5*u+q2\F  
T0=0.1;                 % input pulse width \1M4Dl5!  
MN1=0;                 % initial value for the space output location 'PW5ux@`<  
dt = T/N;                      % time step W ]8 QM1$  
n = [-N/2:1:N/2-1]';           % Index ('+d.F[109  
t = n.*dt;   >uEzw4w  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ((%? `y  
u20=u10.*0.0;                  % input to waveguide 2 EQSQFRk;  
u1=u10; u2=u20;                 ) Hr`M B  
U1 = u1;   ^E>3|du]O  
U2 = u2;                       % Compute initial condition; save it in U 5L}/&^E#p  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Y"$xX8o  
w=2*pi*n./T;  uHRsFlw  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T qwAT>4  
L=4;                           % length of evoluation to compare with S. Trillo's paper jT;;/Fd3/  
dz=L/M1;                       % space step, make sure nonlinear<0.05 lNO;O}8  
for m1 = 1:1:M1                                    % Start space evolution ,64 -1!  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS -jm Y)(\  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; +R75v)  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform TIg3` Fon  
   ca2 = fftshift(fft(u2)); |-~Y#]  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation * kh tJ]=  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   XW92gI<O  
   u2 = ifft(fftshift(c2));                        % Return to physical space @BMx!r5kn  
   u1 = ifft(fftshift(c1)); 4E}Yt$|  
if rem(m1,J) == 0                                 % Save output every J steps. ;5( UzQU  
    U1 = [U1 u1];                                  % put solutions in U array P16~Qj  
    U2=[U2 u2]; SSzIih@u  
    MN1=[MN1 m1]; b*lkBqs$  
    z1=dz*MN1';                                    % output location yEy6]f+>+  
  end Q22 GIr  
end Y8t8!{ytg  
hg=abs(U1').*abs(U1');                             % for data write to excel t"I77aZ$A  
ha=[z1 hg];                                        % for data write to excel +jgSV.N  
t1=[0 t']; $<[79al#  
hh=[t1' ha'];                                      % for data write to excel file }c:M^Ff  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format _DEjF)S  
figure(1) ?+8\.a!  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 3=V &K-  
figure(2) ql~J8G9  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn +1!ia]  
cso8xq|b7  
非线性超快脉冲耦合的数值方法的Matlab程序 9+!hg'9Qn  
p5*jzQ  
在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   ML p9y#  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 xN'I/@ kb  
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:b!s2n!u  
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%  This Matlab script file solves the nonlinear Schrodinger equations M)(DZ}  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of +aAc9'k   
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear a$fnh3j[  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 /BL4<T f  
/dIzY0<aO  
C=1;                           HjwE+:w  
M1=120,                       % integer for amplitude B`sAk %  
M3=5000;                      % integer for length of coupler 62NsJ<#>  
N = 512;                      % Number of Fourier modes (Time domain sampling points) N6TH}~62}  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. JlJ a #  
T =40;                        % length of time:T*T0. PZzMHK?hP  
dt = T/N;                     % time step f%8C!W]Dm  
n = [-N/2:1:N/2-1]';          % Index $<OD31T  
t = n.*dt;   o{[qZc_%  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. l%=;  
w=2*pi*n./T; ^=*;X;7  
g1=-i*ww./2; 5~S5F3  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; |1Z)E+q*:  
g3=-i*ww./2; @PIp* [7oC  
P1=0; NX&_p!_V  
P2=0; wdoR%b{M  
P3=1; EhBKj |y  
P=0; gI`m.EH}}N  
for m1=1:M1                 *=xr-!MEk  
p=0.032*m1;                %input amplitude $Y gue5{c  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Qv ?"b  
s1=s10; FC4wwzb  
s20=0.*s10;                %input in waveguide 2 x|29L7i  
s30=0.*s10;                %input in waveguide 3 BL4-7  
s2=s20; A/?7w   
s3=s30; |&4/n6;P$0  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   .eC1qWZJpd  
%energy in waveguide 1 [.}oyz; }N  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   VG~Vs@c(  
%energy in waveguide 2 oD@7 SF  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ]JR +ayk7  
%energy in waveguide 3 EBmt9S  
for m3 = 1:1:M3                                    % Start space evolution d0 /#nz  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Ht&Y C<X  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; LXCx~;{\  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; kvj#c  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 9Gz=lc[!7  
   sca2 = fftshift(fft(s2)); W!(LF7_!  
   sca3 = fftshift(fft(s3)); (4-CF3D  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Yoll?_k+  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); uvS)8-o&F  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); q" 5(H5  
   s3 = ifft(fftshift(sc3)); 6d~'$<5on  
   s2 = ifft(fftshift(sc2));                       % Return to physical space [a<SDMR  
   s1 = ifft(fftshift(sc1)); -D~%|).'  
end Z$? #  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); L{Vqh0QD&  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); -H-~;EzU  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); +qdEq_ m  
   P1=[P1 p1/p10]; PTV:IzoW  
   P2=[P2 p2/p10]; Ef{Vp;]  
   P3=[P3 p3/p10]; '/%H3A#L  
   P=[P p*p]; YZJyk:H\  
end [opGZ`>)j"  
figure(1) ,"79P/C  
plot(P,P1, P,P2, P,P3); _h1mF<\ X^  
ygl0k \  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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