[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 v"O5u%P  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of \>Zvev!s  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of zfI}Q
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear H9 tXSh  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 WF2-$`x  
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%fid=fopen('e21.dat','w'); ^{yk[tHpS  
N = 128;                       % Number of Fourier modes (Time domain sampling points) EqB)sK/3  
M1 =3000;              % Total number of space steps L 3XB"A#  
J =100;                % Steps between output of space L}k/9F.5  
T =10;                  % length of time windows:T*T0 ;;U:Jtn2  
T0=0.1;                 % input pulse width 1KE:[YQ1  
MN1=0;                 % initial value for the space output location m`A% p  
dt = T/N;                      % time step aX6}6zubr  
n = [-N/2:1:N/2-1]';           % Index +9A\HQ|22  
t = n.*dt;   []pN$]+c  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 $j
zFc!rs  
u20=u10.*0.0;                  % input to waveguide 2 ~$,qgf  
u1=u10; u2=u20;                 ,!QV>=  
U1 = u1;   j<yiNHC  
U2 = u2;                       % Compute initial condition; save it in U F5
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. gzn^#3b  
w=2*pi*n./T; ^QXbJJ  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T lS5ny  
L=4;                           % length of evoluation to compare with S. Trillo's paper !cX[-}Q  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ~/#1G.H  
for m1 = 1:1:M1                                    % Start space evolution D-p.kA3MJ  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Ctu?o+^;z  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 7<\C?`q"  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform
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   ca2 = fftshift(fft(u2)); nHXX\i  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation +0$/y]k  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   FY3IUG  
   u2 = ifft(fftshift(c2));                        % Return to physical space chI.{R
j  
   u1 = ifft(fftshift(c1)); :l u5Uu~  
if rem(m1,J) == 0                                 % Save output every J steps. TLa]O1=Bf.  
    U1 = [U1 u1];                                  % put solutions in U array 0Q9T3X  
    U2=[U2 u2]; -G|a*^  
    MN1=[MN1 m1]; OjE`1h\  
    z1=dz*MN1';                                    % output location sy5 Fn~\R  
  end
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end z?]G3$i(  
hg=abs(U1').*abs(U1');                             % for data write to excel ro~+j}*  
ha=[z1 hg];                                        % for data write to excel _.)eL3OF  
t1=[0 t']; rRFAD{5)  
hh=[t1' ha'];                                      % for data write to excel file =6nD sibf  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format dl]#
 
figure(1) n~IVNB*  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ed!>)Cb  
figure(2) 9)dfL?x8V{  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn UK[v6".^h  
aptY6lGv-|  
非线性超快脉冲耦合的数值方法的Matlab程序 G=9d&
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gXFWxT8S  
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。   }?@5W,  
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 ^eq</5q D  
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%  This Matlab script file solves the nonlinear Schrodinger equations ~p1EF;4#  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of f:
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear /B3R1kNf|  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 \E1U@6a  
je,}_:7  
C=1;                           %q3$|>  
M1=120,                       % integer for amplitude +C]&2zc.  
M3=5000;                      % integer for length of coupler Av J4\  
N = 512;                      % Number of Fourier modes (Time domain sampling points) r),PtI0X  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. uq3{hB#  
T =40;                        % length of time:T*T0. mB'3N;~  
dt = T/N;                     % time step %:v`EjRD0  
n = [-N/2:1:N/2-1]';          % Index *~XA'Vw!  
t = n.*dt;   uzOYVN$t  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. LaFZ?7@|}  
w=2*pi*n./T; g2cVZ!GIj  
g1=-i*ww./2; W~n.Xeu{C  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; R[tC^]ai  
g3=-i*ww./2; -NGK@Yk22  
P1=0; k`KGB  
P2=0; OR6ML-|  
P3=1; w
*7|dZk{  
P=0; ZfAzc6J?\  
for m1=1:M1                 vsB*rP=  
p=0.032*m1;                %input amplitude #Il_J\#  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Xf'=+f2p  
s1=s10; "Y:/= Gx  
s20=0.*s10;                %input in waveguide 2 q6#<[ 4?  
s30=0.*s10;                %input in waveguide 3 6rti '  
s2=s20; \/`?  
s3=s30; ={2!c0s  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   R9vT[{!i  
%energy in waveguide 1 =HDI \LD<  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   imB#Eo4eY  
%energy in waveguide 2 ^?"\?M1  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   RrrK*Fk8=  
%energy in waveguide 3 j-@kW'K  
for m3 = 1:1:M3                                    % Start space evolution kK>Xrj6  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 5X.ebd;PT  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; -F/st  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; +ZsX*/TOn  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform F'8T;J7  
   sca2 = fftshift(fft(s2)); 5FKBv e@  
   sca3 = fftshift(fft(s3)); b}!3;:iD  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   5E\#%K[  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); od<b!4k~s  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); MZv]s  
   s3 = ifft(fftshift(sc3)); b}9[s  
   s2 = ifft(fftshift(sc2));                       % Return to physical space vE, 37  
   s1 = ifft(fftshift(sc1)); 2/P"7A=<  
end z$lF)r:Bc  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); >QE{O.Z  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ihe(F7\U  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); . v)mZp  
   P1=[P1 p1/p10]; f|EUqu%E  
   P2=[P2 p2/p10]; 
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   P3=[P3 p3/p10]; M
hEw _{?  
   P=[P p*p]; t G.(flW,  
end ,<,:8B  
figure(1) {QaNAR
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plot(P,P1, P,P2, P,P3); -cF'2Sfr  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~