[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 n7{1m$/  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of -4GSGR'L&y  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of (S9"(\A  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear UDp"+nS  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 >E)UmO{S  
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%fid=fopen('e21.dat','w'); [nG/>Z]W  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 2.; OHQTE  
M1 =3000;              % Total number of space steps ncS^NH(&  
J =100;                % Steps between output of space ixfkMM,W  
T =10;                  % length of time windows:T*T0 R`s /^0  
T0=0.1;                 % input pulse width @6t3Us~/  
MN1=0;                 % initial value for the space output location X>*zA?:  
dt = T/N;                      % time step +cjNA2@  
n = [-N/2:1:N/2-1]';           % Index A.z~wu%(  
t = n.*dt;   }m0Lr:vq<r  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 @^;\(If2  
u20=u10.*0.0;                  % input to waveguide 2 Xwx;m/  
u1=u10; u2=u20;                 )Dq
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U1 = u1;   q8[Nr3.  
U2 = u2;                       % Compute initial condition; save it in U 'n>|jw)  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ` qt4~rD  
w=2*pi*n./T; u6B (f;  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 0*t
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L=4;                           % length of evoluation to compare with S. Trillo's paper ~r>WnI:vg  
dz=L/M1;                       % space step, make sure nonlinear<0.05 (<8T*Xo  
for m1 = 1:1:M1                                    % Start space evolution 4H\O&pSS
 
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS -B`;Sx  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; HjV^6oP  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform >n` OLHg;  
   ca2 = fftshift(fft(u2)); EaP#~x  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ODEy2).  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   X)nOY*  
   u2 = ifft(fftshift(c2));                        % Return to physical space WpmypkJA#  
   u1 = ifft(fftshift(c1)); ybYSz@7  
if rem(m1,J) == 0                                 % Save output every J steps. 1J<-P9 vk+  
    U1 = [U1 u1];                                  % put solutions in U array I s8|  
    U2=[U2 u2]; sav2.w  
    MN1=[MN1 m1]; 8<_WtDg
 
    z1=dz*MN1';                                    % output location Ulktd^A\  
  end [5m;L5  
end (:[><-h.  
hg=abs(U1').*abs(U1');                             % for data write to excel =8tduB  
ha=[z1 hg];                                        % for data write to excel 0udE\/4!^  
t1=[0 t']; 
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hh=[t1' ha'];                                      % for data write to excel file t^h>~o'\  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format }8r+&e  
figure(1) Oe;9[=
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waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn o'H$g%  
figure(2) MN1|k  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn kg !@i7  
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非线性超快脉冲耦合的数值方法的Matlab程序 4|XE f,  
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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。    OSSMIPr  
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 x80~j(uVf  
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%  This Matlab script file solves the nonlinear Schrodinger equations e7hPIG  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of y ruN5  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Q |l93Rb`  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 xQmk2S` y  
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C=1;                           _xmM~q[c7p  
M1=120,                       % integer for amplitude 8fDnDA.e  
M3=5000;                      % integer for length of coupler S++}kR);  
N = 512;                      % Number of Fourier modes (Time domain sampling points) (:hPT-1  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. q.g!WLiI  
T =40;                        % length of time:T*T0. 9Y/c<gbY  
dt = T/N;                     % time step f'#7i@Je  
n = [-N/2:1:N/2-1]';          % Index bAW;2 NB  
t = n.*dt;   z?yADYr9  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. !(o)*S  
w=2*pi*n./T; Ay2|@1e  
g1=-i*ww./2; B!8]\D  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; &Nec(q<  
g3=-i*ww./2; 2+Fq'!  
P1=0; mFo6f\DHr`  
P2=0; Q2tGe~H  
P3=1; WOg_Pn9HI  
P=0; AS8T!  
for m1=1:M1                 1x\%VtO>\b  
p=0.032*m1;                %input amplitude |Yk23\!  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ^K;,,s;0  
s1=s10; 0?sIod  
s20=0.*s10;                %input in waveguide 2 1nvs51?H  
s30=0.*s10;                %input in waveguide 3 =Qz8"rt#  
s2=s20; u`("x5sa  
s3=s30; >j
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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))));   <rCl  
%energy in waveguide 1 ff{ESFtD  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   i5)trSM|  
%energy in waveguide 2 ;vd%=vR  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   T!/$@]%\7  
%energy in waveguide 3 7R)"HfUh  
for m3 = 1:1:M3                                    % Start space evolution xeu] X|,  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; S'?XI@t[  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Fmsg*s7w  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform fTH?t_e  
   sca2 = fftshift(fft(s2)); qdcCX:Z<  
   sca3 = fftshift(fft(s3)); r3iNfY b  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Pp26UWW  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); `@`Q"J  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); d B?I(  
   s3 = ifft(fftshift(sc3)); 9{>m04888  
   s2 = ifft(fftshift(sc2));                       % Return to physical space dnN"  
   s1 = ifft(fftshift(sc1)); VF6@;5p  
end R;,&CQUl  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); OBj.-jL  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); X|8Yz3:o  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); b@5bN\"x$  
   P1=[P1 p1/p10]; W'6*$Ron  
   P2=[P2 p2/p10]; ){gOb  
   P3=[P3 p3/p10]; u/k#b2BqL  
   P=[P p*p]; Q}]Q0'X8  
end SYl:X  
figure(1) }F@`A?k  
plot(P,P1, P,P2, P,P3); &jg,8  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~