[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 Z}6^ve  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of :$3oFN*g  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of LRb,VD:/Y  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ~.g3ukt  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 B9dt=j3j2  
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%fid=fopen('e21.dat','w'); clO,}Ph>  
N = 128;                       % Number of Fourier modes (Time domain sampling points) MjL)IgT  
M1 =3000;              % Total number of space steps c,\i"=!$  
J =100;                % Steps between output of space &"Ux6mF-"  
T =10;                  % length of time windows:T*T0 bCv{1]RC2  
T0=0.1;                 % input pulse width 2h=%K/hhY  
MN1=0;                 % initial value for the space output location oA-:zz>wL  
dt = T/N;                      % time step !0VfbY9C  
n = [-N/2:1:N/2-1]';           % Index ]2SI!Ai7  
t = n.*dt;   S::=85[>z  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 QCOo  
u20=u10.*0.0;                  % input to waveguide 2 +a@GHx4-  
u1=u10; u2=u20;                 i^`9syD  
U1 = u1;   A#wEuX=[  
U2 = u2;                       % Compute initial condition; save it in U sYSLmUZ{  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 7E$&2U^Js  
w=2*pi*n./T; K,ej%Vtz  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T #s-iy+/1oN  
L=4;                           % length of evoluation to compare with S. Trillo's paper )$%Z:  
dz=L/M1;                       % space step, make sure nonlinear<0.05 _u0$,Y?&|  
for m1 = 1:1:M1                                    % Start space evolution Ka!I`Yf  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS cR7wx 0Aj  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; El_Qk[X|A  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform c
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   ca2 = fftshift(fft(u2)); X@N$Z{  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation IIFMYl gF  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   j V3)2C}  
   u2 = ifft(fftshift(c2));                        % Return to physical space -Yi,_#3{  
   u1 = ifft(fftshift(c1)); zt24qTKL  
if rem(m1,J) == 0                                 % Save output every J steps. g\fhp{gWB  
    U1 = [U1 u1];                                  % put solutions in U array $
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    U2=[U2 u2]; Z3KO90O!8  
    MN1=[MN1 m1]; +FG$x/\*0  
    z1=dz*MN1';                                    % output location :fcM:w&  
  end .1 )RW5|c  
end Rg&-0b  
hg=abs(U1').*abs(U1');                             % for data write to excel LwqC~N  
ha=[z1 hg];                                        % for data write to excel B:TR2G9UT  
t1=[0 t']; +!t}  
hh=[t1' ha'];                                      % for data write to excel file IE~%=/|  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format <~U4*  
figure(1) l(W[_ D  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn K]oM8H1  
figure(2) q}|U4MJm  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn #U7_a{cn"M  
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非线性超快脉冲耦合的数值方法的Matlab程序 6(&Y(/  

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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。   l*aj#%ha  
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 Z [Xa%~5>5  
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%  This Matlab script file solves the nonlinear Schrodinger equations }l0&a!C  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of \kIMDg3}  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Et2JxbD  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 w?vVVA  
9-1#( Y6S  
C=1;                           8kL4~(hY  
M1=120,                       % integer for amplitude *V^ #ga#A  
M3=5000;                      % integer for length of coupler 7v}x?I  
N = 512;                      % Number of Fourier modes (Time domain sampling points) \{\MxXW  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. !eR3@%4  
T =40;                        % length of time:T*T0. m4w')r~  
dt = T/N;                     % time step &a)eJF]:!  
n = [-N/2:1:N/2-1]';          % Index P,pnga3Wu  
t = n.*dt;   ~,6b_W p/  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. u0)7i.!M  
w=2*pi*n./T; [dX`K`k  
g1=-i*ww./2; *4Fr&^M\  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; mABe'"8  
g3=-i*ww./2;
l]!9$  
P1=0; EpPf_ \o  
P2=0; `s#Hq\C  
P3=1; /?-7Fg+,  
P=0; \,UZX&ip  
for m1=1:M1                 zdun,`6  
p=0.032*m1;                %input amplitude (P|~>k  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 !<@J6??a}s  
s1=s10; hqSJ(gs{  
s20=0.*s10;                %input in waveguide 2 |aToUi.Q%  
s30=0.*s10;                %input in waveguide 3 Y$8JM  
s2=s20; R>@uY(>dJ  
s3=s30; U!5)5c}G  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   dj6*6qX0'^  
%energy in waveguide 1 S]3Ev#
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p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   )U<Y0bZA!
 
%energy in waveguide 2 a?5[k}\  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   u'
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%energy in waveguide 3 ._:nw=Y0<}  
for m3 = 1:1:M3                                    % Start space evolution OK|qv[  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS `em9T oJV  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; .3pbu
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   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; \a^,sV  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform hv$yV%.`  
   sca2 = fftshift(fft(s2)); YA(@5CZ  
   sca3 = fftshift(fft(s3)); #<7O08:
 
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   AF,BwLN  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); n";02?@F  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ;(6g\'m  
   s3 = ifft(fftshift(sc3)); {Z;t ^:s#  
   s2 = ifft(fftshift(sc2));                       % Return to physical space #1-xw~_  
   s1 = ifft(fftshift(sc1)); BfTcI)  
end [|`U6 8}u  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); &:*q_$]Oz  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 3*S{;p  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); _1Z=q.sC  
   P1=[P1 p1/p10]; ]LPQYL  
   P2=[P2 p2/p10]; v0*N)eqDGd  
   P3=[P3 p3/p10]; O!1Tth
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   P=[P p*p]; (LAXM x  
end bBxw#_3A?E  
figure(1) a)-FGP^  
plot(P,P1, P,P2, P,P3); 2Nc>6  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~