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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 _ p%=RIR  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of OSreS5bg  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 4eH:eCZze  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 0z&]imU  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]!CMo+  
oGt,^!V1  
%fid=fopen('e21.dat','w'); mq 0d ea  
N = 128;                       % Number of Fourier modes (Time domain sampling points) *\Z9=8yK  
M1 =3000;              % Total number of space steps $eHYy,,  
J =100;                % Steps between output of space T_iX1blrgh  
T =10;                  % length of time windows:T*T0 QS7<7+  
T0=0.1;                 % input pulse width dRj2% Q f  
MN1=0;                 % initial value for the space output location OlRtVp1  
dt = T/N;                      % time step )Y4;@pEU  
n = [-N/2:1:N/2-1]';           % Index 4JQd/;  
t = n.*dt;   (;\" K?  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 pmda9V4  
u20=u10.*0.0;                  % input to waveguide 2 \Lu aI  
u1=u10; u2=u20;                 B xAyjA6  
U1 = u1;   R !&9RvNw  
U2 = u2;                       % Compute initial condition; save it in U |wbXu:  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 0O>T{<  
w=2*pi*n./T; "&Q sv-9t  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 7R5m|h`M  
L=4;                           % length of evoluation to compare with S. Trillo's paper |"]#jx*8KC  
dz=L/M1;                       % space step, make sure nonlinear<0.05 F8xz^UQO  
for m1 = 1:1:M1                                    % Start space evolution gq%U5J"x;J  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS df\^uyD;  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; W%ml/ 4  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform UHyGW$B  
   ca2 = fftshift(fft(u2)); V.w L  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation mD5Vsy{Pb  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   t@X{qm:%Z  
   u2 = ifft(fftshift(c2));                        % Return to physical space :m]KVcF.  
   u1 = ifft(fftshift(c1)); {L'uuG\9U  
if rem(m1,J) == 0                                 % Save output every J steps. ?)NgODU  
    U1 = [U1 u1];                                  % put solutions in U array zv .#9^/y  
    U2=[U2 u2]; {Jbouj?V!  
    MN1=[MN1 m1]; @LSfP  
    z1=dz*MN1';                                    % output location "+XF'ZO  
  end _tlr8vL  
end , wXixf2  
hg=abs(U1').*abs(U1');                             % for data write to excel +MR]h [  
ha=[z1 hg];                                        % for data write to excel `. i #3P  
t1=[0 t']; J]W? V vv  
hh=[t1' ha'];                                      % for data write to excel file [_T6  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 8u%rh[g'  
figure(1) ~"J7=u1o  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn >//yvkZ9,  
figure(2) = }ELu@\V[  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn rS>@>8k2,  
nt:ZO,C:R  
非线性超快脉冲耦合的数值方法的Matlab程序 [L>mrHqG  
y$Fk0s*>  
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。   KzZfpdI92  
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 %y)]Q|  
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%  This Matlab script file solves the nonlinear Schrodinger equations uK%0,!q  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of XqLR2 d  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear &8;Fi2}(L  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 uS<og P  
'7<^x>D|  
C=1;                           ;fYJ]5>  
M1=120,                       % integer for amplitude QVF561Yz  
M3=5000;                      % integer for length of coupler %0 p9\I  
N = 512;                      % Number of Fourier modes (Time domain sampling points) RD6>\9  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. vYybQ&E/  
T =40;                        % length of time:T*T0. ,\ -4X  
dt = T/N;                     % time step '/s/o]'sUd  
n = [-N/2:1:N/2-1]';          % Index dUQ )&Hv  
t = n.*dt;   =}" P;4:  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. /hur6yI8  
w=2*pi*n./T; sa}.o ZpQ  
g1=-i*ww./2; ]`q]\EH  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; tUksIUYD\  
g3=-i*ww./2; |H(i)yu"5'  
P1=0; lDL(,ZZS`  
P2=0; C1#f/o->  
P3=1; *:% I|5  
P=0; ! o?E.  
for m1=1:M1                 HBNX a  
p=0.032*m1;                %input amplitude IL,iu  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 [{0/'+;9  
s1=s10; wE -y4V e  
s20=0.*s10;                %input in waveguide 2 4~AY: ib|  
s30=0.*s10;                %input in waveguide 3 F0wW3+G  
s2=s20; l1.eAs5U  
s3=s30; _}gfec4o  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   (QdLz5\  
%energy in waveguide 1 .E 9$j<SP-  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   WOeG3jMz?  
%energy in waveguide 2 E#A}2|7,g  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   iL<FF N~{  
%energy in waveguide 3 B~E>=85z  
for m3 = 1:1:M3                                    % Start space evolution (tF/2cZk  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS -UWyBM3c@  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; cJ>^@pd{  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; yjOZed;M  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform pJ x H  
   sca2 = fftshift(fft(s2)); /uPMzl  
   sca3 = fftshift(fft(s3)); Ld'3uM/  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   \'X-><1  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); sHPlNwyy  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); /IG3>|R  
   s3 = ifft(fftshift(sc3)); E*yot[kj  
   s2 = ifft(fftshift(sc2));                       % Return to physical space _ t.E_K  
   s1 = ifft(fftshift(sc1));  wH\ K'/  
end a *bc#!e  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); /GO((v+J  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); H? %I((+  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); W6)XMl}n  
   P1=[P1 p1/p10]; 5! ]T%.rM  
   P2=[P2 p2/p10]; Va4AE)[/*  
   P3=[P3 p3/p10]; .G}$jO}  
   P=[P p*p]; -aDBdZ;y  
end w uhL r(  
figure(1) OTEx9  
plot(P,P1, P,P2, P,P3); 'N&s$XB,  
BA9;=orx  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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