[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 jn+NX)9  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of )3O0:]<H  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of { bjK(|  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear NXhQdf  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 C^Jf&a  
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%fid=fopen('e21.dat','w'); $,+'|_0yM  
N = 128;                       % Number of Fourier modes (Time domain sampling points) /($!("b  
M1 =3000;              % Total number of space steps o* qF"xG  
J =100;                % Steps between output of space \VW&z:/*pZ  
T =10;                  % length of time windows:T*T0 p)M\q fZ  
T0=0.1;                 % input pulse width VKa-  
MN1=0;                 % initial value for the space output location {4\hxyw  
dt = T/N;                      % time step H]:z:AAvX  
n = [-N/2:1:N/2-1]';           % Index TF %8pIg>Z  
t = n.*dt;   m#[tY>Q[b  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 z?~W]PWiZ  
u20=u10.*0.0;                  % input to waveguide 2 s(yVE  
u1=u10; u2=u20;                 !6:q#B*  
U1 = u1;   %\=oy=f  
U2 = u2;                       % Compute initial condition; save it in U p_hljgOV  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. s }P-4Sg  
w=2*pi*n./T; %y
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g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 1
c=Roiq  
L=4;                           % length of evoluation to compare with S. Trillo's paper I0\}S [+H  
dz=L/M1;                       % space step, make sure nonlinear<0.05 'TPRGX~&  
for m1 = 1:1:M1                                    % Start space evolution j[
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Q>gU(  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; {Kp<T  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform iR-MuDM  
   ca2 = fftshift(fft(u2)); !x9j~D'C`  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation %]9
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   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   y%T5"p$,  
   u2 = ifft(fftshift(c2));                        % Return to physical space :j/PtNT@  
   u1 = ifft(fftshift(c1)); yV
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if rem(m1,J) == 0                                 % Save output every J steps. 7#Qa/[? D  
    U1 = [U1 u1];                                  % put solutions in U array 1m-"v:fT5D  
    U2=[U2 u2]; _`!@  
    MN1=[MN1 m1]; zT}Qrf~  
    z1=dz*MN1';                                    % output location UV>^[/^O  
  end C~M~2@Iori  
end A%u@xL,_  
hg=abs(U1').*abs(U1');                             % for data write to excel ]y6`9p  
ha=[z1 hg];                                        % for data write to excel M%7H-^{  
t1=[0 t']; mY9u/;dK  
hh=[t1' ha'];                                      % for data write to excel file t`{^gt  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format |Iy55~hK`  
figure(1) R6 wK'  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Y^gK^?K  
figure(2) =+gp~RR,  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn zO>N3pMv  
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非线性超快脉冲耦合的数值方法的Matlab程序 vx=I3o  
P[{w23`4  
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。   ^o'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 +P6#7.p`Z  
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%  This Matlab script file solves the nonlinear Schrodinger equations :=04_5 z  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of U'LO;s04m  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear A"Rzn1/  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 I=hgfo  
kP%W:4l0  
C=1;                           @6GM)N\{[  
M1=120,                       % integer for amplitude *Kt7"J  
M3=5000;                      % integer for length of coupler *Rshzv[  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 6__@?XzJ  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 0c1}?$f[?%  
T =40;                        % length of time:T*T0. )iy>sa{  
dt = T/N;                     % time step 'O`jV0aa'  
n = [-N/2:1:N/2-1]';          % Index ]^gD@]
.  
t = n.*dt;   p)tac*US  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. &F\J%#{  
w=2*pi*n./T; nvD"_.KrJ  
g1=-i*ww./2; ;JFE7\-mC  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ,@!8jar@w}  
g3=-i*ww./2; nx=#QLi  
P1=0; S^)r,cC  
P2=0; *D<S \6=  
P3=1; UVu"meZX  
P=0; <X
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for m1=1:M1                 s~/]nz]"J  
p=0.032*m1;                %input amplitude p%IR4f  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 .mDqZOpf=4  
s1=s10; &7Ixf?e!K  
s20=0.*s10;                %input in waveguide 2 ~N[hY1}X[  
s30=0.*s10;                %input in waveguide 3 O( h
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s2=s20; TFxb\  
s3=s30; q22cp&gmX  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   R)cns7oW  
%energy in waveguide 1 '! 1ts@  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   -f9M*7O<gf  
%energy in waveguide 2 'n:Ft  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   RW(AjDM  
%energy in waveguide 3 Q77
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for m3 = 1:1:M3                                    % Start space evolution kTiQO2H  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS xOT'4v&.  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; *, *"G?  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 42p6l  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform (dMFYL>YP  
   sca2 = fftshift(fft(s2)); 0*3 <}  
   sca3 = fftshift(fft(s3)); --.j&w  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   3jS=  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); IU$bP#<  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); C2<y(GU[Bh  
   s3 = ifft(fftshift(sc3)); f=K1ZD  
   s2 = ifft(fftshift(sc2));                       % Return to physical space +crAkb}i  
   s1 = ifft(fftshift(sc1)); IJ4"X#Q/  
end MCh8Q|Yx4  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); a+{g~/z;,Q  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); WP]<\_r2  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); =AD/5E,3  
   P1=[P1 p1/p10]; )sV# b  
   P2=[P2 p2/p10]; T@yH.4D  
   P3=[P3 p3/p10]; (la<X<w  
   P=[P p*p]; \=N tbBL$[  
end ~Y'e1w$`  
figure(1) 2jhVmK  
plot(P,P1, P,P2, P,P3); $,aU"'D  
p1?}"bHk  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~