[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 C ?aa)H  
%u*H
No  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of O _^Y*!  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of AXPdgo6  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear XlxM
.;i0H  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Xcci)",!  
zQsW*)L  
%fid=fopen('e21.dat','w'); ce1U}">11
 
N = 128;                       % Number of Fourier modes (Time domain sampling points) H:`H4S}  
M1 =3000;              % Total number of space steps xc1-($Q,  
J =100;                % Steps between output of space b'(Hwc\ t  
T =10;                  % length of time windows:T*T0 f.ws\^v%  
T0=0.1;                 % input pulse width 1,pPLc(  
MN1=0;                 % initial value for the space output location 8MBvp*  
dt = T/N;                      % time step }?,Eb~q  
n = [-N/2:1:N/2-1]';           % Index Lz`_&&6  
t = n.*dt;   B3&ETi5NTU  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 (iu IeJ^Z  
u20=u10.*0.0;                  % input to waveguide 2 ,TQ;DxB}=E  
u1=u10; u2=u20;                 A=BT2j'l)  
U1 = u1;   0 TOw4pC  
U2 = u2;                       % Compute initial condition; save it in U }_9yemP  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. x UTlM  
w=2*pi*n./T; VI8/@A1Gv  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T .;%`I  
L=4;                           % length of evoluation to compare with S. Trillo's paper E5t /-
4  
dz=L/M1;                       % space step, make sure nonlinear<0.05 *30T$_PiX|  
for m1 = 1:1:M1                                    % Start space evolution Eyg F,>.4  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS kntULI$`  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; UZ7ukn-  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform OBnvY2)Ri  
   ca2 = fftshift(fft(u2));  cjf_,x  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ~p\r( B7G  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   n<DZb`/uHZ  
   u2 = ifft(fftshift(c2));                        % Return to physical space +S
g+% 8T  
   u1 = ifft(fftshift(c1)); W%<z|  
if rem(m1,J) == 0                                 % Save output every J steps. }n?D#Pk,  
    U1 = [U1 u1];                                  % put solutions in U array >ToI$~84  
    U2=[U2 u2]; wo\O0?d3{  
    MN1=[MN1 m1]; 3Hhu]5  
    z1=dz*MN1';                                    % output location  lLNI5C  
  end 2mfG:^^c  
end GT-ONwVDq  
hg=abs(U1').*abs(U1');                             % for data write to excel hGU 3DKHT  
ha=[z1 hg];                                        % for data write to excel NdM \RD_R  
t1=[0 t']; FdS'0#$  
hh=[t1' ha'];                                      % for data write to excel file (iY2d_FQ[  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ]1|OQYG  
figure(1) B1z7r0Rm,  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn eY3<LVAX  
figure(2) %H=^U
8WB  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn C@9K`N[*  
!>6`+$=U  
非线性超快脉冲耦合的数值方法的Matlab程序 !s[
gv1  
km6O3>p5r  
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。   qDjH^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 Bh()?{q  
I\('b9"*  
|uM(A~?  
Ba9"IXKH  
%  This Matlab script file solves the nonlinear Schrodinger equations %=i/MFGX  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of |5\: E}1  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear WM GiV  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ~!'T!g%C  
@g1T??h   
C=1;                           ;tfGhHpQn  
M1=120,                       % integer for amplitude hGo/Ve+@  
M3=5000;                      % integer for length of coupler `i6q\-12n  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ~?KbpB|  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. b:x*H
jf  
T =40;                        % length of time:T*T0. _`xhP-,`S  
dt = T/N;                     % time step )H%RwV#  
n = [-N/2:1:N/2-1]';          % Index `k3s
l 0z%  
t = n.*dt;   -8&P1jrI  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. gg$:U  
w=2*pi*n./T; OQ4rJ#b  
g1=-i*ww./2; 2Kw i4R  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; /B5rWJ2AS  
g3=-i*ww./2; +A2}@k  
P1=0; phy:G
}F6%  
P2=0; z#+Sf.  
P3=1; EP6@5PNZ  
P=0; k(_^Lq f-  
for m1=1:M1                 aa\?k\h'7X  
p=0.032*m1;                %input amplitude ab*O7v  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 |S3w
CG  
s1=s10; 6x@4gPy[  
s20=0.*s10;                %input in waveguide 2 \|$GBU  
s30=0.*s10;                %input in waveguide 3 slV]CXW)t  
s2=s20; LEY k  
s3=s30; U6~79Hnt  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   x6 h53R  
%energy in waveguide 1 O,0j+1?  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   C59H| S  
%energy in waveguide 2
S,RC;D7  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   -nnAe F  
%energy in waveguide 3 +xBM\Dz8  
for m3 = 1:1:M3                                    % Start space evolution /mnV$+BE  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS pYX!l:hk  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; gHVD,Jr  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 6jz~q~I  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 8lF:70wia  
   sca2 = fftshift(fft(s2)); r1.OLn?C  
   sca3 = fftshift(fft(s3)); MG74,D.f  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ='<*mT<  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); je=XZ's,i~  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Q$~_'I7~Mz  
   s3 = ifft(fftshift(sc3)); }dG>_/3  
   s2 = ifft(fftshift(sc2));                       % Return to physical space $H1igYc  
   s1 = ifft(fftshift(sc1)); Tnb5tHjnh  
end i/F].Sag  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); &u~%5
;  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); xWKUti i  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
>@q4Uez  
   P1=[P1 p1/p10]; :bz;_DZP  
   P2=[P2 p2/p10]; }*56DX  
   P3=[P3 p3/p10]; ~0Mw\p%}  
   P=[P p*p]; JO\KTWtjO  
end ilFS9A3P  
figure(1) T_~xDQ`v  
plot(P,P1, P,P2, P,P3); ;ZR^9%+y9  
H;RgYu2J  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~