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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 #1oyRD-  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of -oR P ZtW  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 7@uhw">mX  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear }*9mNE  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 N-:.z]j#_  
@UCr`>  
%fid=fopen('e21.dat','w'); X/' t1  
N = 128;                       % Number of Fourier modes (Time domain sampling points) dcbE<W#ss  
M1 =3000;              % Total number of space steps ].r~?9'/  
J =100;                % Steps between output of space N(=Z4Nk5  
T =10;                  % length of time windows:T*T0 R7ze~[oF  
T0=0.1;                 % input pulse width e'0BP,\f_}  
MN1=0;                 % initial value for the space output location H4"'&A7$  
dt = T/N;                      % time step @K=C`N_22  
n = [-N/2:1:N/2-1]';           % Index  -#<AbT  
t = n.*dt;   [h[@? 8vB  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 NY3.?@Z  
u20=u10.*0.0;                  % input to waveguide 2 {7Q)2NC  
u1=u10; u2=u20;                 {k8R6l1  
U1 = u1;   I)wc&>Lc  
U2 = u2;                       % Compute initial condition; save it in U @Tz}y"VG  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 5~GH*!h%;  
w=2*pi*n./T; BOdd~f%&tn  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Z b}U 4  
L=4;                           % length of evoluation to compare with S. Trillo's paper VtnVl`/]  
dz=L/M1;                       % space step, make sure nonlinear<0.05 33z^Q`MTC  
for m1 = 1:1:M1                                    % Start space evolution !M@jW[s  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS [2\jQv\Y  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; )wyC8`&-  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform @ q:S]YB   
   ca2 = fftshift(fft(u2)); ~KP@wD~  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation HP2J`>oo  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   X([p0W 9V(  
   u2 = ifft(fftshift(c2));                        % Return to physical space L~|_CRw  
   u1 = ifft(fftshift(c1)); IC6r?  
if rem(m1,J) == 0                                 % Save output every J steps. oFL7dL  
    U1 = [U1 u1];                                  % put solutions in U array t5RV-$  
    U2=[U2 u2]; </]a`h]  
    MN1=[MN1 m1]; eY\w ?pT2  
    z1=dz*MN1';                                    % output location ]@{l<ExP  
  end zw[ #B #  
end =M9;`EmC  
hg=abs(U1').*abs(U1');                             % for data write to excel >0E3Em<(}l  
ha=[z1 hg];                                        % for data write to excel H[2W(q6  
t1=[0 t']; i[/`9 AK  
hh=[t1' ha'];                                      % for data write to excel file $|m'~AmI  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format P"f4`q  
figure(1) .s-*aoj  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn q1pB~eg5  
figure(2) l/-qVAd!q  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn pS+hE4D  
QWwdtk  
非线性超快脉冲耦合的数值方法的Matlab程序 TpcJ1*t  
~@mNR^W-W  
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。   9";qR,  
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 N"8'=wB  
oy\U\#k   
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L<k(stx~  
%  This Matlab script file solves the nonlinear Schrodinger equations EGVS8YP>h  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of >u+%H vzc  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear QjOY1Xze  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 bF'Jm*f  
)F+wk"`+6  
C=1;                           u0F{.fe  
M1=120,                       % integer for amplitude KAg-M#  
M3=5000;                      % integer for length of coupler \+j:d9?  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 'U-8w@\Z  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. =[,EFkU?B  
T =40;                        % length of time:T*T0. .iYp9?t  
dt = T/N;                     % time step "0LSy x  
n = [-N/2:1:N/2-1]';          % Index $Y M(NC  
t = n.*dt;   GT,1t=|&V  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. L)c]i'WZ  
w=2*pi*n./T; *Hz]<b?  
g1=-i*ww./2; B#r"|x#[  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; XtqhK"f%  
g3=-i*ww./2; +GncQs y  
P1=0; G=er0(7<  
P2=0; {r%T_BfY  
P3=1; %bS1$ v\n  
P=0; *!pn6OJ"Q}  
for m1=1:M1                 Clb7=@f  
p=0.032*m1;                %input amplitude m- bu{  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ^l<!:SS  
s1=s10; -S#jOr  
s20=0.*s10;                %input in waveguide 2 ?&!e f {  
s30=0.*s10;                %input in waveguide 3 Pkv+^[(4  
s2=s20; "B>8on8O  
s3=s30; "U/yq  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   | {Q}:_/q  
%energy in waveguide 1 qu&p)*M5  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   a7!{`fR5  
%energy in waveguide 2 a"l\_D'.K8  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   \-SC-c  
%energy in waveguide 3 ZW4$Ks2]Y  
for m3 = 1:1:M3                                    % Start space evolution qh+&Zx~  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS nk;^sq4M:  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ;iW>i8  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 1Tr%lO5?6  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform Xck`"RU<xA  
   sca2 = fftshift(fft(s2)); WL?qulC}h1  
   sca3 = fftshift(fft(s3)); NFF!g]QN  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ^7a@?|,q8  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Ww"]3  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); uPxJwWXO  
   s3 = ifft(fftshift(sc3)); 'uF75C  
   s2 = ifft(fftshift(sc2));                       % Return to physical space SLRF\mh!L  
   s1 = ifft(fftshift(sc1)); eV~"T2!Sb  
end >.I9S{7  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); f[ KI T  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); U }AIOtUw  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); zI\+]U'  
   P1=[P1 p1/p10]; [] el4.J,  
   P2=[P2 p2/p10]; mZG n:f}=  
   P3=[P3 p3/p10]; 8/T,{J\  
   P=[P p*p]; `X)A$lLr  
end E]}_hZU  
figure(1) :5BCW68le  
plot(P,P1, P,P2, P,P3); &;~?\>?I  
|o+*Iy)  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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