[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 J9;fqQCt  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 'aV'Am+:  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of H}_R`S  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear cGm?F,/`  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 xR$T/]/  
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%fid=fopen('e21.dat','w'); sMVk]Mb  
N = 128;                       % Number of Fourier modes (Time domain sampling points) OqRRf  
M1 =3000;              % Total number of space steps -Op^3WWyY  
J =100;                % Steps between output of space +-),E.  
T =10;                  % length of time windows:T*T0 &N=vs  
T0=0.1;                 % input pulse width tBJ4lb  
MN1=0;                 % initial value for the space output location F#L1~\7  
dt = T/N;                      % time step o(DG 3qk  
n = [-N/2:1:N/2-1]';           % Index ,)dlL tUm  
t = n.*dt;   #Vmf 6  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 x%k@&d;z  
u20=u10.*0.0;                  % input to waveguide 2 NNr6~m)3v  
u1=u10; u2=u20;                 pl[@U<8aw  
U1 = u1;   6&;GC<].(y  
U2 = u2;                       % Compute initial condition; save it in U S,5>/'fy0  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. rZ n@i  
w=2*pi*n./T; 8oI|Z=  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T JvvN>bg  
L=4;                           % length of evoluation to compare with S. Trillo's paper S[7^#O.)  
dz=L/M1;                       % space step, make sure nonlinear<0.05 SWhzcqp  
for m1 = 1:1:M1                                    % Start space evolution $kN=45SR  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS <[ 2?~s  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; MCEHv}W  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 5oCg&aT  
   ca2 = fftshift(fft(u2)); }wp/,\_ >  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation
aaKf4}  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   jDQ?b\^  
   u2 = ifft(fftshift(c2));                        % Return to physical space KIv_ AMr  
   u1 = ifft(fftshift(c1)); ZCZ@ZN  
if rem(m1,J) == 0                                 % Save output every J steps. /W*Z.  
    U1 = [U1 u1];                                  % put solutions in U array k]$oir  
    U2=[U2 u2]; z7sDaZL?_  
    MN1=[MN1 m1]; VJTO:}Q  
    z1=dz*MN1';                                    % output location 7$g$p&,VX  
  end yZ[g2*1L  
end ^dk$6%0  
hg=abs(U1').*abs(U1');                             % for data write to excel h/|p`MP\1  
ha=[z1 hg];                                        % for data write to excel "9c=kqkX  
t1=[0 t']; 573,b7Yf  
hh=[t1' ha'];                                      % for data write to excel file #|,cy,v4  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format =9 )k:S(  
figure(1) R)*DkL!  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn N8Zz6{rp  
figure(2) GrJLQO0$N  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn [|c%<|d2  
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非线性超快脉冲耦合的数值方法的Matlab程序 a,S;JF)v  
M.s'~S7y  
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。   ti%RE:*  
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 +e2:?d@  
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%  This Matlab script file solves the nonlinear Schrodinger equations 8Vj'&UY  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Kw?3joy  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @>VVB{1@,]  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 >O24#!9XW  
/N_:npbJF  
C=1;                           UsFn!!+  
M1=120,                       % integer for amplitude }]mxKz  
M3=5000;                      % integer for length of coupler KfBT'6t  
N = 512;                      % Number of Fourier modes (Time domain sampling points) s^eiymP  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. /QyKXg6)l  
T =40;                        % length of time:T*T0. `q<W %'Tb$  
dt = T/N;                     % time step T#3@r0M  
n = [-N/2:1:N/2-1]';          % Index xR3$sA2  
t = n.*dt;   bz#]>RD  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. -c0ypz  
w=2*pi*n./T; hF0,{v  
g1=-i*ww./2; fM"*;LN!N  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 77)WNL/ x  
g3=-i*ww./2; +Z|3[#W  
P1=0; ]'(D*4  
P2=0; \|{/
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P3=1; m?<E >-bI  
P=0; =8?Kn@nMN  
for m1=1:M1                 S=mqxIo@m  
p=0.032*m1;                %input amplitude |0=UZK7%O  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 1\&j)3mC  
s1=s10; m:?"|.]  
s20=0.*s10;                %input in waveguide 2 kc^,V|Nbq6  
s30=0.*s10;                %input in waveguide 3 3)W zX  
s2=s20; K$M+"#./  
s3=s30; ={ms@/e/T  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   P7.b
n  
%energy in waveguide 1 [rT.k5_  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   OA[e}Vn  
%energy in waveguide 2 DpgTm&}-  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   nlNk  
%energy in waveguide 3 .N qXdari  
for m3 = 1:1:M3                                    % Start space evolution vNv!fkl  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Y"MHs0O5>  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ZKrLp8l\  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; a^p#M  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform  @;bBc  
   sca2 = fftshift(fft(s2)); A<X?1$  
   sca3 = fftshift(fft(s3)); 22CET9iCe  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   z~ C8JY:  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); \c:$eF  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); "ntP928  
   s3 = ifft(fftshift(sc3)); c;$4}U4  
   s2 = ifft(fftshift(sc2));                       % Return to physical space LWF,w7v[L  
   s1 = ifft(fftshift(sc1)); fu^W#
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end 1g{Pe`G,  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); \x}\)m_7M<  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 2]5{Xmmo9  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); h= sNj  
   P1=[P1 p1/p10]; E&P2E3P  
   P2=[P2 p2/p10]; v4n< G-  
   P3=[P3 p3/p10]; \EySKQ=  
   P=[P p*p]; PW5]+ |#  
end {rUg,y{v  
figure(1) W[\6h Zv  
plot(P,P1, P,P2, P,P3); VLez<Id9(  
pd|KIs%jl  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~