[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 j@u]( nf  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of G nPrwDB  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 8yDe{  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear c4V%
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 yQ!I`T>a  
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%fid=fopen('e21.dat','w'); E< Y!BT[X  
N = 128;                       % Number of Fourier modes (Time domain sampling points) `F`{s`E)  
M1 =3000;              % Total number of space steps oH='\M%+  
J =100;                % Steps between output of space |}><)}  
T =10;                  % length of time windows:T*T0 rt0_[i  
T0=0.1;                 % input pulse width  <BiSx  
MN1=0;                 % initial value for the space output location ?>s[B7wMp  
dt = T/N;                      % time step U!i1~)s  
n = [-N/2:1:N/2-1]';           % Index WCD)yTg:ES  
t = n.*dt;   e);`hNLih  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10  35%\"Y?  
u20=u10.*0.0;                  % input to waveguide 2 K1$
   
u1=u10; u2=u20;                 +3F%soum95  
U1 = u1;   $W]}m"l  
U2 = u2;                       % Compute initial condition; save it in U Jo''yrJpB  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. RJ1@a  
w=2*pi*n./T; Dv"HFQuF  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 43?uTnX/  
L=4;                           % length of evoluation to compare with S. Trillo's paper +L|x^B3  
dz=L/M1;                       % space step, make sure nonlinear<0.05 46##(4RF  
for m1 = 1:1:M1                                    % Start space evolution FrC)2wX  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS v>0I=ut  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; C2{*m{ D  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform oy-y QYX  
   ca2 = fftshift(fft(u2)); MfZamu5+F  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 0bG#'.-  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   C#LTF-$])  
   u2 = ifft(fftshift(c2));                        % Return to physical space '*B%&QC-  
   u1 = ifft(fftshift(c1)); OcLahz6  
if rem(m1,J) == 0                                 % Save output every J steps. ;,/4Ry22j-  
    U1 = [U1 u1];                                  % put solutions in U array 5=#2@qp  
    U2=[U2 u2]; +rJDDIb  
    MN1=[MN1 m1]; " GY3sam  
    z1=dz*MN1';                                    % output location Ihp Ea,v)  
  end I0*N "07n  
end B$M4f7  
hg=abs(U1').*abs(U1');                             % for data write to excel E7q,6f3@r  
ha=[z1 hg];                                        % for data write to excel *ze,
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t1=[0 t']; y$+=>p|d.^  
hh=[t1' ha'];                                      % for data write to excel file ,T*\9'Q  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 6 2#@Y-5  
figure(1) {53|X=D64  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn nC(Lr,(  
figure(2) =~
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ;nrkC\SYh:  
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非线性超快脉冲耦合的数值方法的Matlab程序 /dO*t4$@?  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   {n&GZG"f  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 x_t$*  
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%  This Matlab script file solves the nonlinear Schrodinger equations zm8k,e +5-  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of {#~A `crO  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear V-3;7  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 AZf69z  
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C=1;                           A'$>~Ev  
M1=120,                       % integer for amplitude <Sr:pm  
M3=5000;                      % integer for length of coupler $4*gi&  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Ii#+JY0k  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. -(7oFOtg  
T =40;                        % length of time:T*T0. `n@;%*6/  
dt = T/N;                     % time step * =*\w\ te  
n = [-N/2:1:N/2-1]';          % Index gF`hlYD  
t = n.*dt;   Vju/+  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. X"vDFE`?  
w=2*pi*n./T; ~k%XW$cV  
g1=-i*ww./2; VCVKh  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; !Na@T]J  
g3=-i*ww./2; X,c`,B03  
P1=0; r9*6=*J|  
P2=0; 'y5H%I
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P3=1; >6Jz=N,  
P=0; 7nB
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for m1=1:M1                 &bGf{P*Da  
p=0.032*m1;                %input amplitude 'Fc$?$c\  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 p"7[heExw  
s1=s10; P,b&

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s20=0.*s10;                %input in waveguide 2 !@*= b1  
s30=0.*s10;                %input in waveguide 3 jcjl q-x  
s2=s20; Q+/P>5O/  
s3=s30; R T~oJ~t;  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   rxs:)# ?A  
%energy in waveguide 1 R\Ckk;<$  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   9Fw NX  
%energy in waveguide 2 #2lvRJB  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   8C?E1f
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%energy in waveguide 3 OG_v[  C5  
for m3 = 1:1:M3                                    % Start space evolution _k;HhLj`  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS )||CU]"b?  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; J qmL|
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   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; .;S1HOHz4  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform yu
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   sca2 = fftshift(fft(s2)); x<OVtAUB  
   sca3 = fftshift(fft(s3)); j/F('r~L  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   m>3\1`ZF~<  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); fW[RCd
 
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); =diGuIB  
   s3 = ifft(fftshift(sc3)); }$sTnea  
   s2 = ifft(fftshift(sc2));                       % Return to physical space xJnN95`R@  
   s1 = ifft(fftshift(sc1)); NTO.;S|2%  
end W`P>vK@=  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); MttFB;Tp  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); uRYq.`v,  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 2[j`bYNe  
   P1=[P1 p1/p10]; Dd,i^,4Gj  
   P2=[P2 p2/p10]; t@a&&  
   P3=[P3 p3/p10]; /"8|26  
   P=[P p*p]; '1fyBU  
end T\ukJ25!  
figure(1) kBnb9'.A1  
plot(P,P1, P,P2, P,P3); w~jm0jK]  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~