[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|7Qw|I7  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of {!1n5a3" 1  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Ccr+SR2  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Qf-
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 a\69,%!:  
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%fid=fopen('e21.dat','w'); //M4Sq(  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Gr"7w[|+  
M1 =3000;              % Total number of space steps NhoS7 y(  
J =100;                % Steps between output of space 3y=<w|4F  
T =10;                  % length of time windows:T*T0 Q^Z<RA(C  
T0=0.1;                 % input pulse width [du>ff  
MN1=0;                 % initial value for the space output location >3`ctbe  
dt = T/N;                      % time step |5IY`;+9  
n = [-N/2:1:N/2-1]';           % Index gQh Ccv  
t = n.*dt;   sIRrEea  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 :.S41S   
u20=u10.*0.0;                  % input to waveguide 2 H'0*CiHes  
u1=u10; u2=u20;                 ]X: rby$  
U1 = u1;   oiv2rOFu  
U2 = u2;                       % Compute initial condition; save it in U %wjB)Mae  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. S`c]Fc  
w=2*pi*n./T; ?gR\A8:8  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 22/?JWL>  
L=4;                           % length of evoluation to compare with S. Trillo's paper }1]!#yMfq  
dz=L/M1;                       % space step, make sure nonlinear<0.05 `,-
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for m1 = 1:1:M1                                    % Start space evolution UiK+c30FU  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS -hVv  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; c,+(FQ9  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform c_z/At;4  
   ca2 = fftshift(fft(u2)); KBr5bcm4u  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Kcw1uLb  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   e.}3OK  
   u2 = ifft(fftshift(c2));                        % Return to physical space R)d99j^"  
   u1 = ifft(fftshift(c1)); K_&c5(-
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if rem(m1,J) == 0                                 % Save output every J steps. ^?6 W<  
    U1 = [U1 u1];                                  % put solutions in U array XW~ BEa  
    U2=[U2 u2]; zK>'tFU  
    MN1=[MN1 m1]; XJJ[F|k~  
    z1=dz*MN1';                                    % output location l<aqiZSY  
  end HhWwc#B  
end 2-6.r_  
hg=abs(U1').*abs(U1');                             % for data write to excel XY!{g(  
ha=[z1 hg];                                        % for data write to excel #U$YZ#B  
t1=[0 t']; /+4^.Q*  
hh=[t1' ha'];                                      % for data write to excel file %%as>}.  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 2%5^Fi  
figure(1) KO-Zz&2f  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ^/%o%J&Hz  
figure(2) 8tV=fSHd  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn yul<n>X|  
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非线性超快脉冲耦合的数值方法的Matlab程序 )
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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。   L,L~ .E  
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 (RDa,
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%  This Matlab script file solves the nonlinear Schrodinger equations V4`:Vci Aw  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of &?/N}g@K  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ]^
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 _'!N q  
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C=1;                           +p9LE4g7Q  
M1=120,                       % integer for amplitude IW1GhZ41'  
M3=5000;                      % integer for length of coupler `P^u:  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 24H^hN9  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ~j/bCMEf!  
T =40;                        % length of time:T*T0. Q? <-`7  
dt = T/N;                     % time step zj~nnfoys  
n = [-N/2:1:N/2-1]';          % Index $f<eq7rRe  
t = n.*dt;   "ibK1}-  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. s6uF5]M;2  
w=2*pi*n./T; g[#k.CuP  
g1=-i*ww./2; zB#_:(1qK  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; .)iO Du  
g3=-i*ww./2; iUeV5c
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P1=0; WZ^
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P2=0; }mKGuCoH>  
P3=1; U8-Q'1IT&  
P=0; d9
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for m1=1:M1                 yxaT7Oqh%  
p=0.032*m1;                %input amplitude ZR!cQ oV=  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 |MTpU@`p5  
s1=s10; F^.om2V|9  
s20=0.*s10;                %input in waveguide 2 F5FNhuC  
s30=0.*s10;                %input in waveguide 3 V*6l6-y~Ih  
s2=s20; aL8p"iSG9  
s3=s30; Np.no$_  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   /hm84La  
%energy in waveguide 1 1YJ_1VJ  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ~
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%energy in waveguide 2 d{QMST2&  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   vC{h2A  
%energy in waveguide 3 0n4g$JK7  
for m3 = 1:1:M3                                    % Start space evolution FX%t  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Pv< QjY  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; B3y?.  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; +<S9E'gT3V  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform -Nsk}Rnk*  
   sca2 = fftshift(fft(s2)); =LlLE<X"%x  
   sca3 = fftshift(fft(s3)); CTl(_g  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   qq OxTG]  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ooTc/QEYi  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); `+roQX.p  
   s3 = ifft(fftshift(sc3));
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   s2 = ifft(fftshift(sc2));                       % Return to physical space Yuwc$Qp)  
   s1 = ifft(fftshift(sc1)); #$LH2?)  
end ctp?y  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); )D:9R)m  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); z'7#"D  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); n4^~gT%b5]  
   P1=[P1 p1/p10]; Ee{`Y0  
   P2=[P2 p2/p10]; Wu4ot0SZ  
   P3=[P3 p3/p10]; tS?a){^:c  
   P=[P p*p]; j*tk(o}qG  
end 8V6=i'GK  
figure(1) rVUUH!  
plot(P,P1, P,P2, P,P3); inYM+o!Ub  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~