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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 sCAWrbOe>  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of R?kyJ4S  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of K~\Ocl  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @(e/Y/  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 #Ic-?2Gn4<  
^pvnUODW[  
%fid=fopen('e21.dat','w'); ?7aeY5p  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Qnv)\M1  
M1 =3000;              % Total number of space steps Ykj+D7rA:  
J =100;                % Steps between output of space )>^!X$`3  
T =10;                  % length of time windows:T*T0 V)Y#m/$`  
T0=0.1;                 % input pulse width i}LVBx"K(  
MN1=0;                 % initial value for the space output location 8<X; 8R  
dt = T/N;                      % time step ,S=ur%  
n = [-N/2:1:N/2-1]';           % Index n]WVT@  
t = n.*dt;   nTPq|=C  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 s\ YHT.O?  
u20=u10.*0.0;                  % input to waveguide 2 [`|gj  
u1=u10; u2=u20;                 ft 4(^|~  
U1 = u1;   *Ag,/Cm]  
U2 = u2;                       % Compute initial condition; save it in U A>J,Bi  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. [Xo[J?w],2  
w=2*pi*n./T; g,5Tr_  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T #?RT$L>n  
L=4;                           % length of evoluation to compare with S. Trillo's paper Zm/I&  
dz=L/M1;                       % space step, make sure nonlinear<0.05 |jTRIMj%,_  
for m1 = 1:1:M1                                    % Start space evolution [#C(^J*@c  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS @L5s.]vg=  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; HO9w"){d$  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform </jTWc'}  
   ca2 = fftshift(fft(u2)); Z(a,$__  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation j.7BoV  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   D1 f}g  
   u2 = ifft(fftshift(c2));                        % Return to physical space QNgfvy  
   u1 = ifft(fftshift(c1)); 5TS&NefM  
if rem(m1,J) == 0                                 % Save output every J steps. L+2<J,   
    U1 = [U1 u1];                                  % put solutions in U array y^hCO:`l3  
    U2=[U2 u2]; # Q61c  
    MN1=[MN1 m1]; 5Z*6,P0  
    z1=dz*MN1';                                    % output location Hn!13+fS  
  end 4,qhWe`/  
end FWDAG$K@0  
hg=abs(U1').*abs(U1');                             % for data write to excel #>dj!33  
ha=[z1 hg];                                        % for data write to excel Z+G/==%3#,  
t1=[0 t']; k^*S3#"  
hh=[t1' ha'];                                      % for data write to excel file f#b;s<G  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format MPD<MaW$  
figure(1) ,\=,,1_  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn L/2,r*LNx$  
figure(2) o==:e  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn jdAjCy;s!  
\d}>@@U&  
非线性超快脉冲耦合的数值方法的Matlab程序 I7e.p m  
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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。   X6SWcJtSw  
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 6_kv~`"tZ  
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M.?[Xpa  
%  This Matlab script file solves the nonlinear Schrodinger equations 6#(==}Sm+  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of }*s`R;B|,  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 2c1L[]h'  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 &Na,D7A:3I  
H[D<G9:  
C=1;                           yttaZhK^u  
M1=120,                       % integer for amplitude <S68UN(Ke  
M3=5000;                      % integer for length of coupler xSy`VuSl  
N = 512;                      % Number of Fourier modes (Time domain sampling points) :.aMhyh#*  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Bvsxn5z+:  
T =40;                        % length of time:T*T0. N`et]'_A}  
dt = T/N;                     % time step t4v@d  
n = [-N/2:1:N/2-1]';          % Index zy(NJ  
t = n.*dt;   2xK v;  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. #Ic)]0L  
w=2*pi*n./T; 85?;\ 5%-  
g1=-i*ww./2; fs\A(]`$  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; w;;9YFBdM  
g3=-i*ww./2; !QS j*)V#  
P1=0; 7BkY0_KK  
P2=0; |wINb~trz  
P3=1; #g=  
P=0; `Vl9/IEk  
for m1=1:M1                 1V.oR`&2E  
p=0.032*m1;                %input amplitude 5yk#(i 7C  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 o2~P vef  
s1=s10; c*.-mS~Z`  
s20=0.*s10;                %input in waveguide 2 LS]0p#  
s30=0.*s10;                %input in waveguide 3 %z~=Jz^  
s2=s20; -}(2}~{e(  
s3=s30; GRh430V [  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   6GA+xr=  
%energy in waveguide 1 [h63*&  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   5Mz:$5Tm  
%energy in waveguide 2 Q$(Fm a4a  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   rld8hFj  
%energy in waveguide 3 )M><09  
for m3 = 1:1:M3                                    % Start space evolution gCq'#G\Z  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS i&YWutG  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; U0Uy C  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; LwYWgT\e  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform `I.pwst8i-  
   sca2 = fftshift(fft(s2)); JED\"(d(  
   sca3 = fftshift(fft(s3)); Z@(KZ|  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   EpH_v`  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); $[UUf}7L   
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 6EeO\Qj{  
   s3 = ifft(fftshift(sc3)); GZ^Qt*5 {  
   s2 = ifft(fftshift(sc2));                       % Return to physical space -Xx4:S  
   s1 = ifft(fftshift(sc1)); 0X3yfrim  
end RqX^$C8M  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); tI)|y?q  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); gxx#<=`  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 5th?m>  
   P1=[P1 p1/p10]; hd6O+i Y4  
   P2=[P2 p2/p10]; !2h ZtX  
   P3=[P3 p3/p10]; MU%7'J :_  
   P=[P p*p]; 2+_a<5l~  
end Ol~M BQs  
figure(1) Q(36RX%@  
plot(P,P1, P,P2, P,P3); Wy%FF\D.Y  
*YSRZvD<\  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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