[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 P+$:(I  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of M|Rb&6O  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of |DsnNk0c
 
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 7.`fJf?   
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Phke`3tth  
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%fid=fopen('e21.dat','w'); y:6; LZ9[  
N = 128;                       % Number of Fourier modes (Time domain sampling points) KGg3 !jY  
M1 =3000;              % Total number of space steps J_;o|gqX  
J =100;                % Steps between output of space Dtj&W<NXo  
T =10;                  % length of time windows:T*T0
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T0=0.1;                 % input pulse width LGtIm7  
MN1=0;                 % initial value for the space output location Y0X-Zqk'  
dt = T/N;                      % time step ?Ec7" hK  
n = [-N/2:1:N/2-1]';           % Index G["c\Xux  
t = n.*dt;   Bi{$@n&?f  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 YD7Oao4:o  
u20=u10.*0.0;                  % input to waveguide 2 ' MxrQ;|S  
u1=u10; u2=u20;                 Q@HopiC  
U1 = u1;   ->V<DZK  
U2 = u2;                       % Compute initial condition; save it in U 1@-Ns  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. k`N^Vdr  
w=2*pi*n./T; ?5{>;#0Z  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T G nG>7f[v  
L=4;                           % length of evoluation to compare with S. Trillo's paper OE-gC2&Bm  
dz=L/M1;                       % space step, make sure nonlinear<0.05 jB(|";G  
for m1 = 1:1:M1                                    % Start space evolution a0#J9O_  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS zOiu5  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; {lc\,F*$  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform V=*wKuB  
   ca2 = fftshift(fft(u2)); 1{JV}O  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation &e!7Z40w@&  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   N}t 2Nu-  
   u2 = ifft(fftshift(c2));                        % Return to physical space hr
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   u1 = ifft(fftshift(c1)); 1|jt"Hz  
if rem(m1,J) == 0                                 % Save output every J steps. ruld B,n  
    U1 = [U1 u1];                                  % put solutions in U array 9c("x%nLpB  
    U2=[U2 u2]; eYvWZJa4  
    MN1=[MN1 m1]; NN?`"Fww  
    z1=dz*MN1';                                    % output location 5wDg'X]>V  
  end K9up:.{QQ  
end 2_Z ? #Y  
hg=abs(U1').*abs(U1');                             % for data write to excel <Pi|J-Y  
ha=[z1 hg];                                        % for data write to excel :w^Ed%>y7  
t1=[0 t']; )z28=
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hh=[t1' ha'];                                      % for data write to excel file m*kl  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 2V#>)R#k  
figure(1) Zo~  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn m+T;O/lG0{  
figure(2) =7m)sxj]w  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn "9Q40w\  
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非线性超快脉冲耦合的数值方法的Matlab程序 c$yk s  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   _y} T/I9  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 }WH&iES@P  
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%  This Matlab script file solves the nonlinear Schrodinger equations #;2n;.a  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of t,+nQ9  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear |$ lM#Ua  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 z)r=+ -  
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C=1;                           7Bd-!$j+  
M1=120,                       % integer for amplitude [rV>57`YD  
M3=5000;                      % integer for length of coupler waj0"u^#  
N = 512;                      % Number of Fourier modes (Time domain sampling points) fy@<&U5rg  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 3!|;iJRH  
T =40;                        % length of time:T*T0. ?q{,R"  
dt = T/N;                     % time step hRD=Y<>A  
n = [-N/2:1:N/2-1]';          % Index heC/\@B  
t = n.*dt;   (Fhs"  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. #PH~1`vl  
w=2*pi*n./T; [QoK5Yw{  
g1=-i*ww./2; q%"VYt4  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; NRIG1v>  
g3=-i*ww./2; .ufTQ?Fe  
P1=0; _n50C"X=&(  
P2=0; `n@*{J8  
P3=1; |8l<$J  
P=0; 8y.wSu  
for m1=1:M1                 V8C:"UZ;  
p=0.032*m1;                %input amplitude S79;^X  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 O @j} K4  
s1=s10; TE7nJ gm  
s20=0.*s10;                %input in waveguide 2 VyXhl;  
s30=0.*s10;                %input in waveguide 3 iW%I|

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s2=s20; DpvI[r//'*  
s3=s30; OuID%p"O  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   bU2Z[sn.  
%energy in waveguide 1 y[)>yq y  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   PGhY>$q>b  
%energy in waveguide 2 CR"|^{G  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   /-_h1.!   
%energy in waveguide 3 8m\7*l^D:  
for m3 = 1:1:M3                                    % Start space evolution 4gz H8sF  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ( u\._Gwsx  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
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   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; .*Ct bGw  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform C.Kh[V\Ut  
   sca2 = fftshift(fft(s2)); T?tgdJ  
   sca3 = fftshift(fft(s3)); e478U$  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   >,$_| C  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); NV72  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); "$+Jnc!!  
   s3 = ifft(fftshift(sc3)); /v1Q4mq  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ff,pvk8N5  
   s1 = ifft(fftshift(sc1)); ;o2$ Q  
end 1{ ~#H<K  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 0ghGBuv1s  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); |,gc_G  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); mS$j?>m  
   P1=[P1 p1/p10]; S1Wj8P-  
   P2=[P2 p2/p10]; K1"*.\?F  
   P3=[P3 p3/p10]; Z<1FSk,[  
   P=[P p*p]; {JZZZY!n2  
end (2J: #  
figure(1) 8dZSi  
plot(P,P1, P,P2, P,P3); la0BiLzb]  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~