[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 f}%sO  
GBW 7Y  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Txu>/1N,  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Yx!n*+:J  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear m EFWo  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 FbuKZp+  
g4Bg6<;  
%fid=fopen('e21.dat','w');  X
tR`?  
N = 128;                       % Number of Fourier modes (Time domain sampling points) .jCk#@+  
M1 =3000;              % Total number of space steps h~ZNHSP:  
J =100;                % Steps between output of space GV=V^Fl .  
T =10;                  % length of time windows:T*T0 ;2BPPZ  
T0=0.1;                 % input pulse width @Ys
L*zw  
MN1=0;                 % initial value for the space output location g{]ej  
dt = T/N;                      % time step ;=#qHo9k1%  
n = [-N/2:1:N/2-1]';           % Index v3Eo@,-  
t = n.*dt;   Wz5d|b  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ]Px:d+wX:  
u20=u10.*0.0;                  % input to waveguide 2 x7Eeb!s0f,  
u1=u10; u2=u20;                 IG>>j}  
U1 = u1;   uQ-WTz|*  
U2 = u2;                       % Compute initial condition; save it in U >"i~ x  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Z"+(LO!  
w=2*pi*n./T; pc^E'h:  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 8`6 LMQ  
L=4;                           % length of evoluation to compare with S. Trillo's paper 1/!nV  
dz=L/M1;                       % space step, make sure nonlinear<0.05 lf}?!*V`+  
for m1 = 1:1:M1                                    % Start space evolution ;>sq_4_  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 2
e)  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Y/#:)(&@  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform cS+?s=d  
   ca2 = fftshift(fft(u2)); 3$;J0{&[i  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation O$YJku  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   I)qKS@  
   u2 = ifft(fftshift(c2));                        % Return to physical space /]P%b K6B  
   u1 = ifft(fftshift(c1)); 6CCZda@  
if rem(m1,J) == 0                                 % Save output every J steps. !:&2+%  
    U1 = [U1 u1];                                  % put solutions in U array zv>ZrFl*  
    U2=[U2 u2]; WReYF+Uen  
    MN1=[MN1 m1]; (gFQK[  
    z1=dz*MN1';                                    % output location A5`#Ot*3  
  end >I{4  
end f45x%tha%  
hg=abs(U1').*abs(U1');                             % for data write to excel i_'|:Uy*F  
ha=[z1 hg];                                        % for data write to excel rAtai}Lx  
t1=[0 t']; `>$gy/N  
hh=[t1' ha'];                                      % for data write to excel file ikeJDKSG  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format :+kg4v&r  
figure(1) <#:Ebofsn  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn @DRfNJ}  
figure(2) iLc)"L-i  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn a>#d=.  
-<u- +CbuT  
非线性超快脉冲耦合的数值方法的Matlab程序 "0p +SZ~D  
Q5T(;u6  
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。   Z:W')Nd(  
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 g9RzzE!  
sqgD?:@J  
9CgXc5  
=P@M&Yy'  
%  This Matlab script file solves the nonlinear Schrodinger equations ayB=|*Q"  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
dfYYyE  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear WMt&8W5  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]0at2  
&6=TtTp"9  
C=1;                           X
Y&]T'A  
M1=120,                       % integer for amplitude (Q*2dd>  
M3=5000;                      % integer for length of coupler yHV^a0e7EH  
N = 512;                      % Number of Fourier modes (Time domain sampling points) /1s9;'I  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 5pN08+  
T =40;                        % length of time:T*T0. eUGmns  
dt = T/N;                     % time step w yuJSB  
n = [-N/2:1:N/2-1]';          % Index *RUd!]bh  
t = n.*dt;   \rB/83[;u  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 4DG 9`5.  
w=2*pi*n./T; G~Q*:m  
g1=-i*ww./2; \{Ox@   
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 3"2<T^H]  
g3=-i*ww./2; g~i''lng  
P1=0; (9'G  
P2=0; a!S
R"3 k  
P3=1; +3~Gc<OO  
P=0; 59"Nn\}3gE  
for m1=1:M1                 VdjU2d  
p=0.032*m1;                %input amplitude O4'kS @  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 +w_MSj#P  
s1=s10; V@54k*V  
s20=0.*s10;                %input in waveguide 2 Xm0&U?dZB  
s30=0.*s10;                %input in waveguide 3 GSUOMy[M-  
s2=s20; wUZ(Tin  
s3=s30; iPtm@f,bI  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   !Ed<xG/  
%energy in waveguide 1 P"h,[{Y*>  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ^|a&%wxA  
%energy in waveguide 2 H8=vQy  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   qU /W
g  
%energy in waveguide 3 hz>yv@1  
for m3 = 1:1:M3                                    % Start space evolution \|b1s @c8  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 2=Vkjh-  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 0YsN82IDD  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; [4+a 1/^  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform s K$Sar  
   sca2 = fftshift(fft(s2)); eL]w' }\  
   sca3 = fftshift(fft(s3)); =":V WHf  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   k*UR#z(I  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ^0,&R\e+  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ;]O 7^s#v  
   s3 = ifft(fftshift(sc3)); !]jNVg  
   s2 = ifft(fftshift(sc2));                       % Return to physical space aS1P]&  
   s1 = ifft(fftshift(sc1)); (fLbg,  
end Hhce:E@K  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ko7-%+0|]  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Ow&'sR'CX  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ?-6x]l=]  
   P1=[P1 p1/p10]; 0I ND9h.%  
   P2=[P2 p2/p10]; BR0p0%  
   P3=[P3 p3/p10]; szM=U$jKq  
   P=[P p*p]; S92!jp/  
end 6u]OXPA|  
figure(1) UdM5R [  
plot(P,P1, P,P2, P,P3); [7Kj$PB3  
(/rIodHJO  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~