[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 U:n~S  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of iQ8{N:58DN  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of %7aJSuQN%  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear <3@nv%  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9"+MZ$  
%N~c9B  
%fid=fopen('e21.dat','w'); @-\=`#C**  
N = 128;                       % Number of Fourier modes (Time domain sampling points) +pYwc0~  
M1 =3000;              % Total number of space steps rA B=H*|6  
J =100;                % Steps between output of space {nUmlP=mS  
T =10;                  % length of time windows:T*T0 YjTr49Af0  
T0=0.1;                 % input pulse width %H"  
MN1=0;                 % initial value for the space output location Fs $FR-x  
dt = T/N;                      % time step fx(8 o+  
n = [-N/2:1:N/2-1]';           % Index 2#lpIj  
t = n.*dt;   ]w;t0Bk  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 3!gz^[!?EN  
u20=u10.*0.0;                  % input to waveguide 2 m[2[9bQ0  
u1=u10; u2=u20;                 ||pOiR5  
U1 = u1;   qp6'n&^&  
U2 = u2;                       % Compute initial condition; save it in U uKM` umE  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Ea<\a1Tl43  
w=2*pi*n./T;  =5B5  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T $3>Rw/,  
L=4;                           % length of evoluation to compare with S. Trillo's paper \:1$E[3v  
dz=L/M1;                       % space step, make sure nonlinear<0.05 bF_0',W
 
for m1 = 1:1:M1                                    % Start space evolution IO"P /
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS T5ky:{Y(  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; m)pHCS  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform h~Z &L2V  
   ca2 = fftshift(fft(u2)); JcmMbd&B  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 3I( n];  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ^$O(oE(D  
   u2 = ifft(fftshift(c2));                        % Return to physical space 5Wa)_@qI)`  
   u1 = ifft(fftshift(c1)); *f;$5B#^  
if rem(m1,J) == 0                                 % Save output every J steps. ">t^jt{  
    U1 = [U1 u1];                                  % put solutions in U array w/(T  
    U2=[U2 u2]; L3wj vq^  
    MN1=[MN1 m1]; ';Nc;9  
    z1=dz*MN1';                                    % output location
HP[B%  
  end  wk8fa  
end R"O%##Ws  
hg=abs(U1').*abs(U1');                             % for data write to excel 4To$!=  
ha=[z1 hg];                                        % for data write to excel T?!SEblP]  
t1=[0 t']; WR#h~N 9c  
hh=[t1' ha'];                                      % for data write to excel file OQ_<Vxz  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format Y#V(CIDe  
figure(1) H#hpaP;  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn iz/CC V L  
figure(2) #'%ii,;wQ  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn AU`z.Isf  
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非线性超快脉冲耦合的数值方法的Matlab程序 ~Uv#)  
2'M5+[8y8  
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。   i7h^L)M  
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 !\%JOf}  
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%  This Matlab script file solves the nonlinear Schrodinger equations *lL
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%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of =#9#unvE!  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear RbxQTM_:M  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 <HRPloVKo  
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C=1;                           ]Bf1p  
M1=120,                       % integer for amplitude 2RNee@!JJP  
M3=5000;                      % integer for length of coupler 2Q@na@s  
N = 512;                      % Number of Fourier modes (Time domain sampling points) [O_5`X9|  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 6<S-o|Xw  
T =40;                        % length of time:T*T0. 6q>iPK Jt  
dt = T/N;                     % time step ]SU)L5Dt;
 
n = [-N/2:1:N/2-1]';          % Index 2@Nd02v|  
t = n.*dt;   ~gZ1*8s`  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. <$A/ ('  
w=2*pi*n./T; vS5}OV  
g1=-i*ww./2; aDX&j2/  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; h~ _i::vg  
g3=-i*ww./2; zB+e;x f|  
P1=0; [
|*7"Q(  
P2=0; l
W#2ox  
P3=1; ceks~[rP  
P=0; ~1*37w~  
for m1=1:M1                 RE4#a2  
p=0.032*m1;                %input amplitude H'!OEZ  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ) aMiT  
s1=s10; k^K76mB  
s20=0.*s10;                %input in waveguide 2 [>p!*%m  
s30=0.*s10;                %input in waveguide 3 z0ufLxq  
s2=s20; \^y~w~g?  
s3=s30; xh#_K@8  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   C "@>NC_  
%energy in waveguide 1 OMjPC_  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   b+whZtNk7  
%energy in waveguide 2 _IU5HT}2  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   TeZu*c  
%energy in waveguide 3 ^hZ0"c  
for m3 = 1:1:M3                                    % Start space evolution .
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   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS }I}GA:~$%  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; +[n#{;]<  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; =m (u=|N3  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform rf+}J_  
   sca2 = fftshift(fft(s2)); 'M?ptu?f  
   sca3 = fftshift(fft(s3)); `:r-&QdU o  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   lAA6tlc#C  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Iy*Q{H3[
 
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); j&S.k  
   s3 = ifft(fftshift(sc3)); *HV_$^)=  
   s2 = ifft(fftshift(sc2));                       % Return to physical space &*O'qOO<2  
   s1 = ifft(fftshift(sc1)); M9Sj@ww  
end mz<,nR\  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 8_`C&vx  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); =$#5Ge]b  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); N&k\X]U  
   P1=[P1 p1/p10]; SufM~9Ll  
   P2=[P2 p2/p10]; #;8VBbc\^  
   P3=[P3 p3/p10]; B!)9 >  
   P=[P p*p]; mhU=^/X  
end ;IPk+,hpmi  
figure(1) .@;5"  
plot(P,P1, P,P2, P,P3); T&S=/cRBK}  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~