[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 x%`YV):*  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of g%T
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of cY5;~lO  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Rd7U5MBEF  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 'k]~Q{K$  
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%fid=fopen('e21.dat','w'); h STcL:b   
N = 128;                       % Number of Fourier modes (Time domain sampling points) st
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M1 =3000;              % Total number of space steps ML'y`S  
J =100;                % Steps between output of space DzMg^
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T =10;                  % length of time windows:T*T0 UUDHknm"  
T0=0.1;                 % input pulse width C{$iuus0  
MN1=0;                 % initial value for the space output location K"VcPDK  
dt = T/N;                      % time step uvJHkAi  
n = [-N/2:1:N/2-1]';           % Index J*b Je"8  
t = n.*dt;   &xB*Shp,B  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 LI@BB:)[  
u20=u10.*0.0;                  % input to waveguide 2 sgP{A}4
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u1=u10; u2=u20;                 D'u7"^=  
U1 = u1;   $ c-O+~  
U2 = u2;                       % Compute initial condition; save it in U Z8Ig
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. O>+=cg  
w=2*pi*n./T; ,
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g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T pTi7Xy!Cw  
L=4;                           % length of evoluation to compare with S. Trillo's paper ^%zhj3#  
dz=L/M1;                       % space step, make sure nonlinear<0.05 L,.~V
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for m1 = 1:1:M1                                    % Start space evolution , d $"`W2  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS $365VTh"  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 8#JX#<HEo  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform pl3ap(/  
   ca2 = fftshift(fft(u2)); #S9J9k  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation UL}wGWaoG  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   O!nS3%De  
   u2 = ifft(fftshift(c2));                        % Return to physical space J;Z2<x/H  
   u1 = ifft(fftshift(c1)); ?ckV 2  
if rem(m1,J) == 0                                 % Save output every J steps. ;AJQ2  
    U1 = [U1 u1];                                  % put solutions in U array dq.U#Rhrx  
    U2=[U2 u2]; 17
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    MN1=[MN1 m1]; d/yF}%0QI  
    z1=dz*MN1';                                    % output location ~Z
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  end }R16WY_'  
end Jn=;gtD-*  
hg=abs(U1').*abs(U1');                             % for data write to excel 1|4,jm$  
ha=[z1 hg];                                        % for data write to excel v.<mrI#?  
t1=[0 t']; oDu6W9+  
hh=[t1' ha'];                                      % for data write to excel file P#!
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format 5C1EdQ4S0  
figure(1) 1UJrPM%  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn aR6F%7gvz  
figure(2) 5z0VMt  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn PlH~um[J  
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非线性超快脉冲耦合的数值方法的Matlab程序 T4wk$R L  
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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|pd[{ag  
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 ?110} [jw  
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%  This Matlab script file solves the nonlinear Schrodinger equations hm73Zy
 
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ~5&4
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ]87BP%G  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 xA(z/%  
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C=1;                           SC~k4&xy  
M1=120,                       % integer for amplitude an"~n`g  
M3=5000;                      % integer for length of coupler O_1[KiZ  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 3:nBl?G<  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. FiiDmhu  
T =40;                        % length of time:T*T0. HQm_ K0$  
dt = T/N;                     % time step A/<u>cCW  
n = [-N/2:1:N/2-1]';          % Index ;9OhK71}  
t = n.*dt;   -:ucp2  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. At:8+S<?A  
w=2*pi*n./T; ]w6Q?%'9  
g1=-i*ww./2; .c-a$39  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; U)bv,{-q  
g3=-i*ww./2; wUCxa>h'  
P1=0; \PE;R.v_:  
P2=0; IANSpWea?  
P3=1; T3P9  
P=0; fYUV[Gm  
for m1=1:M1                 (|^m9v0:  
p=0.032*m1;                %input amplitude sRD fA4/TF  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 O<cP1TF  
s1=s10; Gf\h7)T\  
s20=0.*s10;                %input in waveguide 2 hNN[djR  
s30=0.*s10;                %input in waveguide 3 bOj)Wu  
s2=s20; z;S-Q,  
s3=s30; DD$>3`  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   !}TsFa  
%energy in waveguide 1 d{4;qM#  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   AVpg  
%energy in waveguide 2 mcez3gH  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   e7U\gtZ.  
%energy in waveguide 3 v~Q'm1!O4\  
for m3 = 1:1:M3                                    % Start space evolution uAPVR  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 7l69SQo]?  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; vt#;j;liG  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; S\TXx79PhC  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform en< $.aY  
   sca2 = fftshift(fft(s2)); 06pvI}  
   sca3 = fftshift(fft(s3)); bGWfMu=n  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   l\s!A&L  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); X@`a_XAfd  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); p' >i3T(  
   s3 = ifft(fftshift(sc3)); W91yj:  
   s2 = ifft(fftshift(sc2));                       % Return to physical space GF ux?8A:%  
   s1 = ifft(fftshift(sc1)); lv 8EfN  
end B`}um;T#~,  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); f,HUr% @  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 5M
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   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); G
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   P1=[P1 p1/p10]; B'
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   P2=[P2 p2/p10]; ?mg@zq8  
   P3=[P3 p3/p10]; f4f2xe7\Q  
   P=[P p*p]; O_:l;D#i  
end lxhb)]c ^>  
figure(1) Z4VFfGCTL  
plot(P,P1, P,P2, P,P3); jn2=)KBa_  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~