[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 QJ&]4*>a  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Z`_x|cU?J  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of s"@}^ )*}  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ku4Gc6f#gG  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 qt
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%fid=fopen('e21.dat','w'); +BeA4d8b  
N = 128;                       % Number of Fourier modes (Time domain sampling points) -T}r$A  
M1 =3000;              % Total number of space steps /qKA1-R}4  
J =100;                % Steps between output of space Wv|CJN
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T =10;                  % length of time windows:T*T0 mqHcD8X  
T0=0.1;                 % input pulse width {#st>%i  
MN1=0;                 % initial value for the space output location -AD@wn!wCJ  
dt = T/N;                      % time step  svx7  
n = [-N/2:1:N/2-1]';           % Index c2t`i  
t = n.*dt;   ~s-bA#0S  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ^&D5J\][  
u20=u10.*0.0;                  % input to waveguide 2 A!,c@Kv 3  
u1=u10; u2=u20;                 0BNH~,0u  
U1 = u1;   x <a}*8"  
U2 = u2;                       % Compute initial condition; save it in U ,4S[<(T"  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. h/oun2C  
w=2*pi*n./T; j,Mbl"P  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T k-H6c  
L=4;                           % length of evoluation to compare with S. Trillo's paper *^%+PQ  
dz=L/M1;                       % space step, make sure nonlinear<0.05 (/2rj[F&  
for m1 = 1:1:M1                                    % Start space evolution cRH(@b Xr  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS B`.aQ  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; DXG`%<ZMn  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform X{Fr  
   ca2 = fftshift(fft(u2)); ~n8UN<  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation whYk"N  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   xT+#K5  
   u2 = ifft(fftshift(c2));                        % Return to physical space v-N4&9)%9  
   u1 = ifft(fftshift(c1)); /lbj!\~  
if rem(m1,J) == 0                                 % Save output every J steps. e`co:HO`#  
    U1 = [U1 u1];                                  % put solutions in U array 8o[gzW:Q)U  
    U2=[U2 u2]; V@]SKbK}wN  
    MN1=[MN1 m1]; TFG? EO  
    z1=dz*MN1';                                    % output location "f8,9@  
  end Fm=jgt3wv8  
end !zt
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hg=abs(U1').*abs(U1');                             % for data write to excel ;e*okYM  
ha=[z1 hg];                                        % for data write to excel i9Beap/t$  
t1=[0 t']; e,{k!BXU#'  
hh=[t1' ha'];                                      % for data write to excel file Dt<MEpbur  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format '%4fQ%ID}  
figure(1) VH4wsEH]  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn L*dGo,oN  
figure(2) KB
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn %f'=9pit  
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非线性超快脉冲耦合的数值方法的Matlab程序 tH&eKM4
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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。   FAL#p$y}  
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 
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%  This Matlab script file solves the nonlinear Schrodinger equations >]anTF`d  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of p2Gd6v.t  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear NC!B-3?x  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 qLN\>Z,3;  
H>D sAHS  
C=1;                           ;~DrsQb  
M1=120,                       % integer for amplitude eI:x4K,#  
M3=5000;                      % integer for length of coupler %TRJ  
N = 512;                      % Number of Fourier modes (Time domain sampling points) [T4{K&  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. WMnSkO  
T =40;                        % length of time:T*T0. x1Y/^ks@2  
dt = T/N;                     % time step @GD $KR9  
n = [-N/2:1:N/2-1]';          % Index 9(qoME}>=  
t = n.*dt;   ZQym8iV/  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. OM^`P  
w=2*pi*n./T; p#Po?  
g1=-i*ww./2; X.>~DT%0Lm  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; %z.V$2  
g3=-i*ww./2; y`8U0TE3R  
P1=0; *z6A ~U  
P2=0; $[b}r#P  
P3=1; Z2@e~&L  
P=0; *;McX  
for m1=1:M1                 FWU>WHX  
p=0.032*m1;                %input amplitude Gh.?6kuh  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ^7ID |uMr  
s1=s10; kCEo*/,  
s20=0.*s10;                %input in waveguide 2
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s30=0.*s10;                %input in waveguide 3 }"nm3\Df  
s2=s20; ?/1LueC:  
s3=s30; V1
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p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   F'>yBDm*OM  
%energy in waveguide 1 bf=\ED^  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   H"A@Q.'  
%energy in waveguide 2 ~3Pp}eO~V  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   6iXV  
%energy in waveguide 3 '5*&  
for m3 = 1:1:M3                                    % Start space evolution O"|d~VQ  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 9015PEO  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; R\X;`ptT  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; >);M\,1\I  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform p5OoDo  
   sca2 = fftshift(fft(s2)); ns~bz-n  
   sca3 = fftshift(fft(s3)); )g?jHm-p\  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   zt9A-% \R  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ~N}Zr$D  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); v!DK.PZbi  
   s3 = ifft(fftshift(sc3)); =bP<cC=3b  
   s2 = ifft(fftshift(sc2));                       % Return to physical space A'uaR?  
   s1 = ifft(fftshift(sc1)); mJd8?d  
end THX% z `  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 5M9o(Z\AF  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); YahW%mv`d  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); h+!R)q8M  
   P1=[P1 p1/p10]; M6quPj  
   P2=[P2 p2/p10]; 6 <`e]PT  
   P3=[P3 p3/p10]; k,'MmAz  
   P=[P p*p]; yxT}hMa  
end p ^TCr<=  
figure(1) J#j3?qrxu  
plot(P,P1, P,P2, P,P3); ^V9|uHOJoq  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~