[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 {fI"p;|  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of >e^^YR^  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of I&9Itn p$  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear dvu8V_U  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 FaLc*CU  
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%fid=fopen('e21.dat','w'); Q#5~"C  
N = 128;                       % Number of Fourier modes (Time domain sampling points) c->.eL%   
M1 =3000;              % Total number of space steps eL_Il.:  
J =100;                % Steps between output of space }0}=-g&  
T =10;                  % length of time windows:T*T0 Dnp><%  
T0=0.1;                 % input pulse width a7}O.NDf  
MN1=0;                 % initial value for the space output location mu{\_JX.A  
dt = T/N;                      % time step VZ$^:.I0
  
n = [-N/2:1:N/2-1]';           % Index c<ORmg6  
t = n.*dt;   %+iAL<S  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 2&zklXuo:  
u20=u10.*0.0;                  % input to waveguide 2 1<;VD0XX  
u1=u10; u2=u20;                 D@)L?AB1f  
U1 = u1;   * /^}  
U2 = u2;                       % Compute initial condition; save it in U yVe<+Z\7  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Om(Ir&0  
w=2*pi*n./T; qH(HcsgD  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ZkryoIQ%=  
L=4;                           % length of evoluation to compare with S. Trillo's paper $kBcnk  
dz=L/M1;                       % space step, make sure nonlinear<0.05 J^-a@'`+  
for m1 = 1:1:M1                                    % Start space evolution 8osP$"/o  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS v Q51-.g  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; o]DYS,v  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 5><T#0W?  
   ca2 = fftshift(fft(u2)); bTMgEY  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation TPn#cIPG  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   7$mB.\|  
   u2 = ifft(fftshift(c2));                        % Return to physical space \U>|^$4 #5  
   u1 = ifft(fftshift(c1)); (SMk!b]}  
if rem(m1,J) == 0                                 % Save output every J steps. H.< F6  
    U1 = [U1 u1];                                  % put solutions in U array Zi}jf25  
    U2=[U2 u2]; ue*o>iohB  
    MN1=[MN1 m1]; "fC>]iA8I  
    z1=dz*MN1';                                    % output location LKBh{X0%(  
  end c{j)beaS  
end u\(>a  
hg=abs(U1').*abs(U1');                             % for data write to excel <
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ha=[z1 hg];                                        % for data write to excel F#^/=AR'  
t1=[0 t']; 1&RB=7.h
 
hh=[t1' ha'];                                      % for data write to excel file S3s6  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format M'VJE
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figure(1) DWS#q|j`"  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn =fJ
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figure(2) W5/|.}  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ?)H:.]7-x  
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非线性超快脉冲耦合的数值方法的Matlab程序 LqLhZBU9  
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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。   <}G/x*N  
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 yL
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%  This Matlab script file solves the nonlinear Schrodinger equations b94+GLU8b  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of $Gcj
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ~])Q[/=p  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 &eb8k2S  
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C=1;                           %,S{9q  
M1=120,                       % integer for amplitude vSR5F9  
M3=5000;                      % integer for length of coupler {Ve3EYYm  
N = 512;                      % Number of Fourier modes (Time domain sampling points) yqH9*&KH{  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. UW1i%u k  
T =40;                        % length of time:T*T0. 7\N }QP0"u  
dt = T/N;                     % time step u$FL(m4  
n = [-N/2:1:N/2-1]';          % Index y&/bp<Z  
t = n.*dt;   <zm:J4&>T  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. qHvU4v  
w=2*pi*n./T; cG&@PO]+.  
g1=-i*ww./2; z<%dWz  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; G#ELQ/Q  
g3=-i*ww./2;
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P1=0; (*kKfg4Wj  
P2=0; G'`^U}9V\  
P3=1; 7yjun|Lt}X  
P=0; Sk-Q 4D^  
for m1=1:M1                 {yB0JL}n  
p=0.032*m1;                %input amplitude ~NB|BwAh  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ttls.~DG  
s1=s10; @urZ  
s20=0.*s10;                %input in waveguide 2 ky&wv+7  
s30=0.*s10;                %input in waveguide 3 6&QOC9JW+7  
s2=s20; ^j2ve's:  
s3=s30; ^rd%{6m  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   @R<z=n"  
%energy in waveguide 1 8llXpe  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   1CR\!?  
%energy in waveguide 2 xel|,|*Yq  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   +Jm vB6s  
%energy in waveguide 3 L2_[M'  
for m3 = 1:1:M3                                    % Start space evolution _BONN6=*y  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 7w]3D  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; |!/+T^u  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; vvs2:87zvJ  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform $j8CF3d.6  
   sca2 = fftshift(fft(s2)); 5<e{)$C  
   sca3 = fftshift(fft(s3)); YWJ$Pp  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   @^DVA}*b)  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); a47e  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 22;B:  
   s3 = ifft(fftshift(sc3)); io(!z-$  
   s2 = ifft(fftshift(sc2));                       % Return to physical space m#R"~ >  
   s1 = ifft(fftshift(sc1)); .R#-u/6g(  
end _q}Cnp5  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 'p78^4'PL  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ^>>9?  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); F|VKrH.  
   P1=[P1 p1/p10]; )wXE\$  
   P2=[P2 p2/p10]; ]*gf$D  
   P3=[P3 p3/p10]; >ts}\.(]  
   P=[P p*p]; oRJ!TAbD  
end 'Z:wEt!  
figure(1) o4OB xHKy  
plot(P,P1, P,P2, P,P3); 2(x| %  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~