[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 0nBDF79  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of a;Pn.@NVq  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of E`xpZ>$mPx  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear T12Zak4.=  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 SXe1Q8;  
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%fid=fopen('e21.dat','w'); L%3Bp/`S  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Y^DGnx("m  
M1 =3000;              % Total number of space steps hi(e%da  
J =100;                % Steps between output of space eB_r.R{  
T =10;                  % length of time windows:T*T0 v>nBdpjXh  
T0=0.1;                 % input pulse width 0;)Q  
MN1=0;                 % initial value for the space output location .x] pJ9  
dt = T/N;                      % time step :.=j)ljTx  
n = [-N/2:1:N/2-1]';           % Index \ntUxPox.  
t = n.*dt;   Qc!3y>Y=_  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 $;$vcV9*  
u20=u10.*0.0;                  % input to waveguide 2 _iDVd2X"H  
u1=u10; u2=u20;                 oa=TlBk<  
U1 = u1;   HCkfw+gaV  
U2 = u2;                       % Compute initial condition; save it in U /ece
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 3G<4rH]  
w=2*pi*n./T; 4Z=`;  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T oC} u  
L=4;                           % length of evoluation to compare with S. Trillo's paper }CZw'fhVWO  
dz=L/M1;                       % space step, make sure nonlinear<0.05 4^YE*6z  
for m1 = 1:1:M1                                    % Start space evolution G;W2Z,  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS TF!v,cX  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; G9am}qr  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform O^6anUV0  
   ca2 = fftshift(fft(u2)); [MKG5=kaE  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation F#)bGi  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   d-m.aP)y:  
   u2 = ifft(fftshift(c2));                        % Return to physical space $%M]2_W(
 
   u1 = ifft(fftshift(c1)); hosY`"X  
if rem(m1,J) == 0                                 % Save output every J steps. 1tI=Dwx  
    U1 = [U1 u1];                                  % put solutions in U array u)r:0;5  
    U2=[U2 u2]; 
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    MN1=[MN1 m1]; B/;'D7i|S  
    z1=dz*MN1';                                    % output location %K=_  
  end @x743}Y\  
end dS <*DP  
hg=abs(U1').*abs(U1');                             % for data write to excel a]%sks
 
ha=[z1 hg];                                        % for data write to excel olL? 6)gC  
t1=[0 t']; d:^B2~j  
hh=[t1' ha'];                                      % for data write to excel file Z^'\()3t  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ZvT>A#R;l~  
figure(1) "lt5gu!`u  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn b5 NlL`g  
figure(2) xYW&Mfka  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 'DpJ#w\81  
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非线性超快脉冲耦合的数值方法的Matlab程序 T*=*$%  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   y:Of~ ]9@  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 96#]P  
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%  This Matlab script file solves the nonlinear Schrodinger equations 1 JIU5u)  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of +w?R4Sxjn  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear tk=S4/VWv  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 :Y1;= W  
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dp($L9r  
C=1;                           ZE_  
M1=120,                       % integer for amplitude v3XM-+Z4  
M3=5000;                      % integer for length of coupler 0x]?rd+q8Q  
N = 512;                      % Number of Fourier modes (Time domain sampling points)  O&|<2Qr  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ]cmX f
 
T =40;                        % length of time:T*T0. bJD$!*r\%!  
dt = T/N;                     % time step  |Nj6RB7  
n = [-N/2:1:N/2-1]';          % Index Za3}:7`Gu  
t = n.*dt;   k1zK3I&c_  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. a@qc?  
w=2*pi*n./T; 2u!&Te(!9  
g1=-i*ww./2; v0E6i!D/  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; DC-d@N+  
g3=-i*ww./2; #C?M-  
P1=0; 66" 6>  
P2=0; $8HiX6r  
P3=1; %Pt){9b  
P=0; SUUN_w~  
for m1=1:M1                 9:VUtx#}2  
p=0.032*m1;                %input amplitude 650qG$  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 :N$-SV  
s1=s10; >-<iY4|[d  
s20=0.*s10;                %input in waveguide 2 1
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s30=0.*s10;                %input in waveguide 3 cY_ke  
s2=s20; p:Lmf8EI  
s3=s30; N8#j|yf  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   aVc{ aP  
%energy in waveguide 1 L*A-&9.p3  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Z 
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%energy in waveguide 2 *`
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   hdrsa}{g  
%energy in waveguide 3 }58MDpOF1  
for m3 = 1:1:M3                                    % Start space evolution [x>Ju&))$  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS }AJoF41X  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; s:"Sbml  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; DHw)]WB M  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform bSX/)')jU  
   sca2 = fftshift(fft(s2)); @&WHX#  
   sca3 = fftshift(fft(s3)); g""GQeR  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   B#SVN Lv  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); }shxEsq  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); l&qCgw  
   s3 = ifft(fftshift(sc3)); ZCPUNtOl  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Dpw*m.f  
   s1 = ifft(fftshift(sc1)); Cg]),S  
end }P fAf  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); _J W|3q  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); I

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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)))); Y6sX|~Zy  
   P1=[P1 p1/p10]; #m{*]mY@  
   P2=[P2 p2/p10]; HRDpFMA/~  
   P3=[P3 p3/p10]; y3s+.5;  
   P=[P p*p]; o1$u;}^|  
end &gY) x{  
figure(1) <c p
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plot(P,P1, P,P2, P,P3); /]xa}{^B  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~