[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 2bLc57j{`9  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of p>\[[Md  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of A^6z.MdYZ  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear {d'B._#i  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ;<[!;8  
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%fid=fopen('e21.dat','w'); )quQI)Ym  
N = 128;                       % Number of Fourier modes (Time domain sampling points) r}e(MT:R'  
M1 =3000;              % Total number of space steps \Gk}Fer  
J =100;                % Steps between output of space N#jUqm  
T =10;                  % length of time windows:T*T0 "Dk@-Ac  
T0=0.1;                 % input pulse width :|S[i('  
MN1=0;                 % initial value for the space output location 1|-C(UW>  
dt = T/N;                      % time step frm[<-~w0  
n = [-N/2:1:N/2-1]';           % Index bZgo}`o%  
t = n.*dt;   lul  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ^`dMjeF  
u20=u10.*0.0;                  % input to waveguide 2 .pe.K3G&  
u1=u10; u2=u20;                 
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U1 = u1;   tj00xYY  
U2 = u2;                       % Compute initial condition; save it in U ;
nbEV2Y<  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 7Dl^5q.|  
w=2*pi*n./T; %rnRy<9  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ~H?v L c;>  
L=4;                           % length of evoluation to compare with S. Trillo's paper n#WOIweInf  
dz=L/M1;                       % space step, make sure nonlinear<0.05 9;vES^  
for m1 = 1:1:M1                                    % Start space evolution :jkPV%!~  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS |B$JX'_  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; >wb*kyO7(#  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform il{x?#Wrb  
   ca2 = fftshift(fft(u2)); rfQs 7S;G  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 5N6R%2,A  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   d^$cx(2$D  
   u2 = ifft(fftshift(c2));                        % Return to physical space Q2]7|C  
   u1 = ifft(fftshift(c1)); rk&oKd_&i  
if rem(m1,J) == 0                                 % Save output every J steps. $^ir3f+  
    U1 = [U1 u1];                                  % put solutions in U array J32{#\By  
    U2=[U2 u2]; w""u]b%:r  
    MN1=[MN1 m1]; XAF]B,h=  
    z1=dz*MN1';                                    % output location -gC%*S5&  
  end H3d|eO4+W  
end SJj_e-  
hg=abs(U1').*abs(U1');                             % for data write to excel d3?gh[$  
ha=[z1 hg];                                        % for data write to excel d/3&3>/  
t1=[0 t']; 2fc+PE  
hh=[t1' ha'];                                      % for data write to excel file _f "I%QTL  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format v[x 5@$  
figure(1) n31nORx50  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn F{7 BY~d  
figure(2) e*( _Cvxp  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn d3T7$'l$  
1uA-!T*e>  
非线性超快脉冲耦合的数值方法的Matlab程序 CnY dj~  
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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。   Kb5}M/8  
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#AHfKF  
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%  This Matlab script file solves the nonlinear Schrodinger equations SFsT^f<  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ^H<VH  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 5y0LkuRR:  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 6
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C=1;                           [ CU8%%7  
M1=120,                       % integer for amplitude c No)LF  
M3=5000;                      % integer for length of coupler N;m62N  
N = 512;                      % Number of Fourier modes (Time domain sampling points) b_~KtMO  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ={190=\9  
T =40;                        % length of time:T*T0. 5KYR"-jY  
dt = T/N;                     % time step =<=[E:B  
n = [-N/2:1:N/2-1]';          % Index zCwb>v  
t = n.*dt;   -M[BC~!0;  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. j=>WWlZ  
w=2*pi*n./T; &.0wPyw  
g1=-i*ww./2; a5@lWpQsV  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; SnO,-Rg  
g3=-i*ww./2; _@|_`5W  
P1=0; 0b,{4DOD  
P2=0; Z>@\!$Mc  
P3=1; 1BzU-Ma  
P=0; Gh'{O/F4*  
for m1=1:M1                 zq#gf  
p=0.032*m1;                %input amplitude 2fUz}w (  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 H{d/%}7[v  
s1=s10; a9nXh6  
s20=0.*s10;                %input in waveguide 2 d k|X&)xTJ  
s30=0.*s10;                %input in waveguide 3 5hiuBf<  
s2=s20; h&{>4{  
s3=s30; 3_ =:^Z  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   JlH5 <:#PN  
%energy in waveguide 1 rf&nTDaWI  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   a>nV!b\n5  
%energy in waveguide 2 MP8s}  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   V3\}]5  
%energy in waveguide 3 =1F F2#zS  
for m3 = 1:1:M3                                    % Start space evolution q]*:RI?wGT  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ><;.vP
 
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; gi\UNT9x  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; EmcwX4|  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform zhwajc  
   sca2 = fftshift(fft(s2)); X@B,w
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   sca3 = fftshift(fft(s3)); MWc{7,  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   @/?$ZX/e[  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); UC9w T  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 0`e- ;  
   s3 = ifft(fftshift(sc3)); ';x5 $5k'  
   s2 = ifft(fftshift(sc2));                       % Return to physical space W&a<Q)o*I  
   s1 = ifft(fftshift(sc1)); s|8_R;  
end &$NVEmW-J  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 9hs7B!3pc>  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 7Rom#Kl:  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ~E7=c3:"  
   P1=[P1 p1/p10]; `\S~;O  
   P2=[P2 p2/p10]; F(:]lM|  
   P3=[P3 p3/p10]; UBy:W^\g  
   P=[P p*p]; o"A%dC_  
end /F @a@m|  
figure(1) D&&11Iz&  
plot(P,P1, P,P2, P,P3); R:DW>LB  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~