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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 uSn<]OrZo`  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 9A9yZlt  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of -JB~yO?0  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear a2`|6M;  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004  N'e3<  
@G>Q(a*,  
%fid=fopen('e21.dat','w'); !&8HA   
N = 128;                       % Number of Fourier modes (Time domain sampling points) i slg5  
M1 =3000;              % Total number of space steps j= Ebk;6p  
J =100;                % Steps between output of space !S}4b   
T =10;                  % length of time windows:T*T0 q8e34Ly7  
T0=0.1;                 % input pulse width |c5r&oM&m  
MN1=0;                 % initial value for the space output location 9)]asY  
dt = T/N;                      % time step b#z{["%Zp  
n = [-N/2:1:N/2-1]';           % Index -H(\[{3{V  
t = n.*dt;   ojQjx|Q}  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 dw e$, 9  
u20=u10.*0.0;                  % input to waveguide 2 u'Ua ++a\  
u1=u10; u2=u20;                 eZ[O:Wvk:  
U1 = u1;   f6-OR]R5  
U2 = u2;                       % Compute initial condition; save it in U y72=d?]W  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. HOrD20  
w=2*pi*n./T; auV<=1<zJ  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T F8%.-.l)  
L=4;                           % length of evoluation to compare with S. Trillo's paper 7Eett)4  
dz=L/M1;                       % space step, make sure nonlinear<0.05 f)/5%W7n}  
for m1 = 1:1:M1                                    % Start space evolution b63tjqk  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS #:n:3]t  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; b )mU9   
   ca1 = fftshift(fft(u1));                        % Take Fourier transform  W .t`  
   ca2 = fftshift(fft(u2)); ct#3*]  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation w-M,@[G  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   h1'j1uI  
   u2 = ifft(fftshift(c2));                        % Return to physical space }Kc03Ue`%e  
   u1 = ifft(fftshift(c1)); S>s{t=AY~  
if rem(m1,J) == 0                                 % Save output every J steps. %uWq)D4r  
    U1 = [U1 u1];                                  % put solutions in U array U4hFPK<  
    U2=[U2 u2]; hs  m%o\  
    MN1=[MN1 m1]; ZdjmZx%%  
    z1=dz*MN1';                                    % output location &6mXsx$  
  end ndU<,{r  
end 0pu=,  
hg=abs(U1').*abs(U1');                             % for data write to excel 0j )D[K  
ha=[z1 hg];                                        % for data write to excel chr^>%Q_  
t1=[0 t']; vw/L|b7G  
hh=[t1' ha'];                                      % for data write to excel file W<AxctId  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format vUU)zZB ~  
figure(1) } JePEmj  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn !.nyIA(  
figure(2) sF`ELrR \  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn p#eai  
Anu`F%OzB  
非线性超快脉冲耦合的数值方法的Matlab程序 .+ w#n<  
1:+f@#  
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。   %kRQ9I".  
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 O!7v&$]1  
,xeJf6es  
97%S{_2m/  
x&SG gl  
%  This Matlab script file solves the nonlinear Schrodinger equations .7|kxJq  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of  *Fe  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 3+j!{tJ z2  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ~T_4M  
Jbrjt/OG#I  
C=1;                           uGxh}'&  
M1=120,                       % integer for amplitude u\9t+wi}<  
M3=5000;                      % integer for length of coupler 6ofi8( n[  
N = 512;                      % Number of Fourier modes (Time domain sampling points) NQx`u"=  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. AD ,  
T =40;                        % length of time:T*T0. <lBY  
dt = T/N;                     % time step ?Thh7#7LM  
n = [-N/2:1:N/2-1]';          % Index ]N\J~Gm  
t = n.*dt;   )S;pYVVAl  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ah (lH5r  
w=2*pi*n./T; dP0%<Q|  
g1=-i*ww./2; ,a&&y0,  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; :Rq>a@Rp  
g3=-i*ww./2; C{r Sq  
P1=0; j6NK 7Li  
P2=0; 8 )W{&#C>  
P3=1; {O4y Y=G  
P=0; rk$$gXg9/  
for m1=1:M1                 .D~ZE94@  
p=0.032*m1;                %input amplitude aWe?n;  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 1I{^]]qw  
s1=s10; e95x,|.-_  
s20=0.*s10;                %input in waveguide 2 ,'KQFC   
s30=0.*s10;                %input in waveguide 3 |V 3AA   
s2=s20; V@QWJZ"  
s3=s30; am$-1+iX  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   'k?%39  
%energy in waveguide 1 \,b@^W6e>  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   COF_a%  
%energy in waveguide 2  t dl Y  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ]Ywj@-*q  
%energy in waveguide 3 U',9t  
for m3 = 1:1:M3                                    % Start space evolution /:YJ2AARY  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS nMniHB'  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; wcdD i[E>i  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; w A0 $d  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform >8pmClVvmR  
   sca2 = fftshift(fft(s2)); -W^jmwM   
   sca3 = fftshift(fft(s3)); jP]I>Tq  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   X/5\L.g2  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 3( Y#*f|  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); [%8t~zg  
   s3 = ifft(fftshift(sc3)); !yo/ F& 6  
   s2 = ifft(fftshift(sc2));                       % Return to physical space %,l+?fF  
   s1 = ifft(fftshift(sc1)); 8op,;Z7Y  
end ~s :M l  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); @dy<=bh~  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); zjzW;bo( d  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); y?t2@f]!XK  
   P1=[P1 p1/p10]; x"n!nT%Z  
   P2=[P2 p2/p10]; % |6t\[gn  
   P3=[P3 p3/p10]; yEaim~  
   P=[P p*p]; 63J_u-o  
end 5eZ8$-&([  
figure(1) |Ew~3-u!  
plot(P,P1, P,P2, P,P3); k,~I>qg  
M!{;:m28X!  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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