[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 BD [<>Wm  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Y+gNi_dE  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of A#gy[.Bb  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6('CB|ga  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 /k KVIlO  
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%fid=fopen('e21.dat','w'); @xr}(.  
N = 128;                       % Number of Fourier modes (Time domain sampling points) @[#)zO  
M1 =3000;              % Total number of space steps C8y[B1Y  
J =100;                % Steps between output of space 2p
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T =10;                  % length of time windows:T*T0 7 b{y  
T0=0.1;                 % input pulse width nnTiu,2R  
MN1=0;                 % initial value for the space output location ;Q<2Y#  
dt = T/N;                      % time step t\O#5mo  
n = [-N/2:1:N/2-1]';           % Index f%yNq6l  
t = n.*dt;   QwLSL<.  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Ej<`HbJ'Q  
u20=u10.*0.0;                  % input to waveguide 2 s
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u1=u10; u2=u20;                 MADt$_  
U1 = u1;   dB8 e  
U2 = u2;                       % Compute initial condition; save it in U (Ft#6oK"  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. NYeL1h)l  
w=2*pi*n./T; _pkmHj(  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T } a!HbH  
L=4;                           % length of evoluation to compare with S. Trillo's paper ITZ}$=   
dz=L/M1;                       % space step, make sure nonlinear<0.05 EME}G42KN  
for m1 = 1:1:M1                                    % Start space evolution 2>)::9e4  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS <1<0odB  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; db.~^][k  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform yY!@FGsA  
   ca2 = fftshift(fft(u2)); :/6u*HwZh  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation vV>=
Uvm  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   q*}$1 zb  
   u2 = ifft(fftshift(c2));                        % Return to physical space awSi0*d~  
   u1 = ifft(fftshift(c1)); b<BkI""b  
if rem(m1,J) == 0                                 % Save output every J steps. cK75Chsu  
    U1 = [U1 u1];                                  % put solutions in U array $Zj3#l:rK  
    U2=[U2 u2]; o`nJJ:Cxq-  
    MN1=[MN1 m1]; G*g*+D[HM  
    z1=dz*MN1';                                    % output location 1~S''[  
  end rEjEz+wu  
end HFX,EE  
hg=abs(U1').*abs(U1');                             % for data write to excel 58]t iP"  
ha=[z1 hg];                                        % for data write to excel Mlo:\ST
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t1=[0 t']; ooj^Z%9P  
hh=[t1' ha'];                                      % for data write to excel file E0eZal],  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 1n#{c5T  
figure(1) mzcxq:uZ5  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Y r8gKhv W  
figure(2) 8O0]h
z  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn c#a>> V  
2,p= %  
非线性超快脉冲耦合的数值方法的Matlab程序 |9mGX9q  
@1V?94T1  
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。   LG=_>:~t>  
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 oP:/%  
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%  This Matlab script file solves the nonlinear Schrodinger equations tY60~@YO&  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of I9YMxf>nI  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear d
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 o:@A%*jg  
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C=1;                           J74kK#uF=  
M1=120,                       % integer for amplitude T/q*k)IoR  
M3=5000;                      % integer for length of coupler C+0BV~7J<<  
N = 512;                      % Number of Fourier modes (Time domain sampling points) #^w8Y'{?  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. JiGS[tR  
T =40;                        % length of time:T*T0. UC!"1)~mt`  
dt = T/N;                     % time step 
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n = [-N/2:1:N/2-1]';          % Index qR^+K@*|  
t = n.*dt;   u9{Z*w3L7  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. (n2=.9k!  
w=2*pi*n./T; 1(/rg  
g1=-i*ww./2; I}\`l+  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; u4Z Accj  
g3=-i*ww./2; YGZa##i  
P1=0; C{YTHNn  
P2=0; S>R40T=e  
P3=1; muKjeg'b  
P=0; $ 3R5p  
for m1=1:M1                 6g"qwWZp  
p=0.032*m1;                %input amplitude 2l+t-  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 U-#vssJhk  
s1=s10; v#9Uy}NJ9  
s20=0.*s10;                %input in waveguide 2 1fV\84m^  
s30=0.*s10;                %input in waveguide 3 `12Y2W 9  
s2=s20; =l%|W[OO  
s3=s30; t=n
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p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   #$JY&!M  
%energy in waveguide 1 -V:7j8  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   8VMD304  
%energy in waveguide 2 |w.5*]?H  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   8-)@q|  
%energy in waveguide 3 $lF\FC  
for m3 = 1:1:M3                                    % Start space evolution !8o;~PPVl  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 8b $e)  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; $wqi^q*)  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; t8Giv89{  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 0;" >.  
   sca2 = fftshift(fft(s2)); K}Lu1:~  
   sca3 = fftshift(fft(s3)); }1YQ?:@  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   @&2#kO~=  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); NJ(H$tB@  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ]Waa7)}DM  
   s3 = ifft(fftshift(sc3)); zC!Pb{IaH  
   s2 = ifft(fftshift(sc2));                       % Return to physical space }?Tz=hP  
   s1 = ifft(fftshift(sc1)); zmU>  
end `YK#m4gc  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); O_&Km[  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); um$L;-2:  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); fUB+9G(Bx  
   P1=[P1 p1/p10]; 9S{0vc/2@  
   P2=[P2 p2/p10]; b+THn'2  
   P3=[P3 p3/p10]; 0vcFX)]yW  
   P=[P p*p]; zG~nRt{4  
end kDWvjT  
figure(1) :SVWi}:Co1  
plot(P,P1, P,P2, P,P3); =T|m#*{.L  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~