[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

计算脉冲在非线性耦合器中演化的Matlab 程序 "=9L7.E)  
69r<Z  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Gnj|y?'  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of @(Ou
;Uy  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear  5ah]E  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 #\
@*C=  
bNY_V;7Kw`  
%fid=fopen('e21.dat','w'); yWFDGk  
N = 128;                       % Number of Fourier modes (Time domain sampling points)
5
"^$3&)  
M1 =3000;              % Total number of space steps _hAp@? M  
J =100;                % Steps between output of space `dn|nI2  
T =10;                  % length of time windows:T*T0 JL`n12$m  
T0=0.1;                 % input pulse width hM/|k0YV  
MN1=0;                 % initial value for the space output location
o}7`SYn  
dt = T/N;                      % time step ~e ]83?  
n = [-N/2:1:N/2-1]';           % Index y!mjZR,&  
t = n.*dt;   MPT*[&\-  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 RBwI*~%g{  
u20=u10.*0.0;                  % input to waveguide 2 (6>8Dt 9[  
u1=u10; u2=u20;                 I r<5%  
U1 = u1;   !m'lOz  
U2 = u2;                       % Compute initial condition; save it in U vitmG'|WG  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. j5G8IP_Wx  
w=2*pi*n./T; { >bw:^F  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T K\5@yqy5  
L=4;                           % length of evoluation to compare with S. Trillo's paper K.",=\53  
dz=L/M1;                       % space step, make sure nonlinear<0.05 \;.\g6zX  
for m1 = 1:1:M1                                    % Start space evolution yWsNG;>  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS R4]t
D|  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; z6A
rSLlZ  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform |.)oV;9  
   ca2 = fftshift(fft(u2)); 2"c$#N  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 4nXS}bWf  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   D7olu29  
   u2 = ifft(fftshift(c2));                        % Return to physical space f,k'gM{K  
   u1 = ifft(fftshift(c1));
=UM30 P/  
if rem(m1,J) == 0                                 % Save output every J steps. op/HZa  
    U1 = [U1 u1];                                  % put solutions in U array :hwZz2Dhi  
    U2=[U2 u2]; l~!\<, !  
    MN1=[MN1 m1]; O!\P]W4r$  
    z1=dz*MN1';                                    % output location (w-z~#<  
  end tTLD6#  
end '_@Y  
hg=abs(U1').*abs(U1');                             % for data write to excel Jj8z~3XnJ  
ha=[z1 hg];                                        % for data write to excel .`)\GjDv  
t1=[0 t']; fJH09:@^%  
hh=[t1' ha'];                                      % for data write to excel file ~kD/dXt  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format c'vxT<8fWW  
figure(1) 7(QRG\G#  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn R/Mwq#xUb  
figure(2) "<Dn%r  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn e>#*$4tg  
\&NpVH,-  
非线性超快脉冲耦合的数值方法的Matlab程序 3qXOsa7  
zy"L%i  
在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   'u@
)F`  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 D}>pl8ke~g  
1j`-lD  
SsIy;l  
+%OINMo.A  
%  This Matlab script file solves the nonlinear Schrodinger equations IgI*mDS&b  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of |h\e(_G\  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +?w 7Nm`  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 &BY%<h0c  
rr>QG<i;G  
C=1;                          
X};m\Bz  
M1=120,                       % integer for amplitude =;W"Pi;*  
M3=5000;                      % integer for length of coupler w9rwuk  
N = 512;                      % Number of Fourier modes (Time domain sampling points) mSp-  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Hz
cy'  
T =40;                        % length of time:T*T0. 1XSA3;ZEc  
dt = T/N;                     % time step 9z$]hl  
n = [-N/2:1:N/2-1]';          % Index #v0"hFOH,  
t = n.*dt;   5x(`z   
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. o]t6u .L  
w=2*pi*n./T; Kfa7}f_  
g1=-i*ww./2; cv=nGFx6  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; %0fF
_OU  
g3=-i*ww./2; 1P. W 34  
P1=0; MUhC6s\F  
P2=0; d rnqX-E;  
P3=1; X^r5su?  
P=0; p(QB5at  
for m1=1:M1                 >6*"g{/  
p=0.032*m1;                %input amplitude MqGF~h|+  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ]( V+ qj
 
s1=s10; M#LQz~E  
s20=0.*s10;                %input in waveguide 2 3~z4#8=  
s30=0.*s10;                %input in waveguide 3 A{iI,IFe  
s2=s20; veFl0ILd  
s3=s30;
VUC  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   vA2@Db}  
%energy in waveguide 1 `zGK
$,[%  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   F1JSf&8  
%energy in waveguide 2 (#Z2  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   BIEc4k5(  
%energy in waveguide 3 M>D 3NY[,  
for m3 = 1:1:M3                                    % Start space evolution q>/# P5V  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS JZQkr  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; S(9Xbw)T  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; R $HIJM  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ?v-IN  
   sca2 = fftshift(fft(s2)); fu?5gzT+b  
   sca3 = fftshift(fft(s3)); /e1m1B  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   C7[ge&  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); %Fig`qX  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); X0O0Y>"  
   s3 = ifft(fftshift(sc3)); ;>QED  
   s2 = ifft(fftshift(sc2));                       % Return to physical space F,Y@  
   s1 = ifft(fftshift(sc1)); AFcsbw  
end *Dtwr  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); +(0Fab8g  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ]as_7  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); !4GGq  
   P1=[P1 p1/p10]; Ja>UcE29  
   P2=[P2 p2/p10]; T=35?   
   P3=[P3 p3/p10]; ["- pylhK  
   P=[P p*p]; j!q5Bc?  
end jY EB`&  
figure(1) EF=.L{  
plot(P,P1, P,P2, P,P3); ^
wPKqu)^  
'\\dh  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~