[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 u/k' ry=  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of g3s5ra[
 
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Q?hf2iw  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear bv41et+Kb  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 TlO=dLR7d  
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%fid=fopen('e21.dat','w'); ;7[DFlS\P  
N = 128;                       % Number of Fourier modes (Time domain sampling points) P:J|![  
M1 =3000;              % Total number of space steps pv4#`.m  
J =100;                % Steps between output of space rhYARr'  
T =10;                  % length of time windows:T*T0 ZT"vVX-)G  
T0=0.1;                 % input pulse width GRpwEfG  
MN1=0;                 % initial value for the space output location {Mo[C%  
dt = T/N;                      % time step `4ga~Ch  
n = [-N/2:1:N/2-1]';           % Index 5~>j98K  
t = n.*dt;   GQ85ykky  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 b4$g$()  
u20=u10.*0.0;                  % input to waveguide 2 9k4z__Ke  
u1=u10; u2=u20;                 ys)
  
U1 = u1;   1z; !)pG.  
U2 = u2;                       % Compute initial condition; save it in U ;Ym6ey0t  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. -5os0G80  
w=2*pi*n./T; +U'n|>t9  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T .R)Ho4CE  
L=4;                           % length of evoluation to compare with S. Trillo's paper /:-ig .YY  
dz=L/M1;                       % space step, make sure nonlinear<0.05 oGXcu?ft  
for m1 = 1:1:M1                                    % Start space evolution ui"`c%2n  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS { zL4dJw  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; JFu.o8[Q  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform "tbKbFn9  
   ca2 = fftshift(fft(u2)); Hl}m*9<9us  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation H[R6 ?H@$F  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   aA%x9\Y  
   u2 = ifft(fftshift(c2));                        % Return to physical space U_9|ED:  
   u1 = ifft(fftshift(c1)); XYV`[,^h&  
if rem(m1,J) == 0                                 % Save output every J steps. E-X02A  
    U1 = [U1 u1];                                  % put solutions in U array F)l1%FCm  
    U2=[U2 u2]; D41.$t
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    MN1=[MN1 m1]; >7?Lq<H  
    z1=dz*MN1';                                    % output location V[8!ymi0  
  end e*<pO@Uy  
end W;X:U.  
hg=abs(U1').*abs(U1');                             % for data write to excel g5nL7;`N  
ha=[z1 hg];                                        % for data write to excel 0p,_?3nX  
t1=[0 t']; 5a5JOl$8  
hh=[t1' ha'];                                      % for data write to excel file q@mZ0
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format #VZ-gy4$\B  
figure(1) .^- I<4.  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn X#W6;?Z\  
figure(2) -hK^*vJ  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn p:|7d\r  
ju.`c->k"  
非线性超快脉冲耦合的数值方法的Matlab程序 U~|)=+%O  
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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。   s2tNQtq0W  
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 j;_E0j#  
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%  This Matlab script file solves the nonlinear Schrodinger equations JFRbWQ0  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of C]zG@O!  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear uE#"wm'J  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 `'rvDa
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C=1;                           <UW-fI)X  
M1=120,                       % integer for amplitude L$]Y$yv  
M3=5000;                      % integer for length of coupler P?=}}DI  
N = 512;                      % Number of Fourier modes (Time domain sampling points) o3'Za'N.  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. j3o?B  
T =40;                        % length of time:T*T0. )C#>@W
  
dt = T/N;                     % time step 9]S;%:64  
n = [-N/2:1:N/2-1]';          % Index q) e*eN  
t = n.*dt;   oPxh+|0?  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ;%/}(&E2  
w=2*pi*n./T; Q-e(>=Gv_  
g1=-i*ww./2;
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g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; @ &GA0;q0t  
g3=-i*ww./2; cS",Bw\  
P1=0; . N5$s2t  
P2=0; 1mv8[^pF  
P3=1; <@c9S,@t  
P=0; tY`%vI [  
for m1=1:M1                 o3:h!(#G  
p=0.032*m1;                %input amplitude ?KFj=Yo  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 q$B|a5a?  
s1=s10; _]kw|[)  
s20=0.*s10;                %input in waveguide 2 g|
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s30=0.*s10;                %input in waveguide 3 W>$mU&ew[  
s2=s20; K!tM "`a  
s3=s30; ,/-DAo~O  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   \`?4PQ  
%energy in waveguide 1 a;G
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p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ?2S<D5MSb  
%energy in waveguide 2 &A&2z l %#  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Ye\&_w"  
%energy in waveguide 3 wEix8Ow*  
for m3 = 1:1:M3                                    % Start space evolution B5qlU4km&  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS {G-y7y+
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; LV]F?O[K=  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 9d+z?J:  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 1{CVd m<9  
   sca2 = fftshift(fft(s2)); jGn2QL  
   sca3 = fftshift(fft(s3)); V}/AQe2m&  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   U1pwk[  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); q!) nSD  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); f!}e*oX  
   s3 = ifft(fftshift(sc3)); Uclta  
   s2 = ifft(fftshift(sc2));                       % Return to physical space M
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   s1 = ifft(fftshift(sc1)); ^4 ~ V/  
end 6$5SS#  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); %xN91j["  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); $_u)~O4$  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); s,8g^aF4  
   P1=[P1 p1/p10]; MgQb"
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   P2=[P2 p2/p10]; . L]!*  
   P3=[P3 p3/p10]; kIH)>euZ  
   P=[P p*p]; 3Ebk
q[/*%  
end u[LsH  
figure(1) ]]V|]}<)m  
plot(P,P1, P,P2, P,P3); F t;[>o  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~