[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 Fo|xzLm9*|  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of *@S@x{{s  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of uzU{z;  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 4na
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 L^0v\  
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%fid=fopen('e21.dat','w'); B$a-og(  
N = 128;                       % Number of Fourier modes (Time domain sampling points) ,/2LY4` 5  
M1 =3000;              % Total number of space steps lK(Fg  
J =100;                % Steps between output of space H3KTir"on  
T =10;                  % length of time windows:T*T0 lj[,|[X7`  
T0=0.1;                 % input pulse width c:hK$C)T  
MN1=0;                 % initial value for the space output location ]k%PG-9  
dt = T/N;                      % time step M]rO;^;6?  
n = [-N/2:1:N/2-1]';           % Index M {a #  
t = n.*dt;   _GA$6#]  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 j,-C{ K  
u20=u10.*0.0;                  % input to waveguide 2 tw K^I6@  
u1=u10; u2=u20;                 `DW2spd  
U1 = u1;   3YL l;TP_  
U2 = u2;                       % Compute initial condition; save it in U 1y5Ex:JVZT  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Te
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w=2*pi*n./T; %w}gzxN^  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T uh3)0.nR  
L=4;                           % length of evoluation to compare with S. Trillo's paper b>=_*nw9  
dz=L/M1;                       % space step, make sure nonlinear<0.05 [c&B|h=>  
for m1 = 1:1:M1                                    % Start space evolution
%JL]; 4'  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS `:|@Zln  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; tY/vL^mi  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform "VUY
h$=[  
   ca2 = fftshift(fft(u2)); )b4$A:  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 4,P bg|  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   IApT'QNM  
   u2 = ifft(fftshift(c2));                        % Return to physical space ql{_%x?  
   u1 = ifft(fftshift(c1)); -K%5(Eg  
if rem(m1,J) == 0                                 % Save output every J steps. }VCI=?-  
    U1 = [U1 u1];                                  % put solutions in U array %V_-%/3Z  
    U2=[U2 u2]; 2KJ1V+g@a6  
    MN1=[MN1 m1]; DVp5hR_$  
    z1=dz*MN1';                                    % output location VG@};dwbz*  
  end ERMa# L  
end l]LxL  
hg=abs(U1').*abs(U1');                             % for data write to excel P,xwSvO#M  
ha=[z1 hg];                                        % for data write to excel 0D&>Gyc*0  
t1=[0 t']; |Ul,6K@f"5  
hh=[t1' ha'];                                      % for data write to excel file G=/k>@Di  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format v! hY  
figure(1) l?
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waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn |zsbW9 W*m  
figure(2) LF<wt2?*  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn #2p#VQh  
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非线性超快脉冲耦合的数值方法的Matlab程序 [AzO:A  
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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。   m@G i6  
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 RrV>r<Z"Q  
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%  This Matlab script file solves the nonlinear Schrodinger equations +%*&.@z_  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of D56<fg$  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear YV'pVO'_+  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |`rJJFA  
/Ft:ffR|R  
C=1;                          
OYL]j{  
M1=120,                       % integer for amplitude S/A1RUt  
M3=5000;                      % integer for length of coupler
n{5NNV6  
N = 512;                      % Number of Fourier modes (Time domain sampling points) W[''Cc.  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. @r7:NU}  
T =40;                        % length of time:T*T0. :3ZYJW1  
dt = T/N;                     % time step #=c`of6  
n = [-N/2:1:N/2-1]';          % Index s4LO&STh{  
t = n.*dt;   l$Gl'R>>*  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. kyYLP"oB=  
w=2*pi*n./T; Yc Q=v
t{  
g1=-i*ww./2; 5p"BD'^:  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; uXZg1F)  
g3=-i*ww./2; X"asfA[6K  
P1=0; KM,|} .@:  
P2=0; Q
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P3=1; $hrIO+  
P=0; r`'y?Bra;  
for m1=1:M1                 |}&RXD  
p=0.032*m1;                %input amplitude ~eh0[mF^]  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 <O~WB  
s1=s10; x34f9! 't  
s20=0.*s10;                %input in waveguide 2 K|S:{9Q  
s30=0.*s10;                %input in waveguide 3 VU.@R,  
s2=s20; y*b3&%.ml  
s3=s30; 9i$NhfOe  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   K!z
`  
%energy in waveguide 1 ^-)txC5{T  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   %8.J=B  
%energy in waveguide 2 ]2SF9p_  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   AG6K daJ  
%energy in waveguide 3 {d3<W N  
for m3 = 1:1:M3                                    % Start space evolution )Di \_/G  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 3)Ac"nuyqH  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; dE`-\J
 
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; yx{3J  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform dR^"X3$  
   sca2 = fftshift(fft(s2)); D1s4`V -  
   sca3 = fftshift(fft(s3)); *Ust[u  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   BHFY%6J!  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); i{c@S:&@^  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); xG2+(f#C1  
   s3 = ifft(fftshift(sc3)); d' >>E  
   s2 = ifft(fftshift(sc2));                       % Return to physical space &K+0xnUH  
   s1 = ifft(fftshift(sc1)); _~'+Qe_o$5  
end <W)u{KS#TY  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); '_P\#7$!MV  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); U/{6%
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   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); eet Q}]  
   P1=[P1 p1/p10]; w(d>HHg  
   P2=[P2 p2/p10]; "`Ge~N[$A  
   P3=[P3 p3/p10]; ,FzeOSy'p  
   P=[P p*p]; `YBkF  
end 4-GXmC  
figure(1) o(kM9G|  
plot(P,P1, P,P2, P,P3); E ]9\R  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~