[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 e
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of o-SRSu  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Y*Y&)k6t  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear tCWJSi`IJ  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 RRx`}E9,  
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%fid=fopen('e21.dat','w'); `aO.=:O_  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 7'_nc!ME  
M1 =3000;              % Total number of space steps G$cxDGo  
J =100;                % Steps between output of space X,>(Y8  
T =10;                  % length of time windows:T*T0 qPsyqn?Y|  
T0=0.1;                 % input pulse width X!T|07#c  
MN1=0;                 % initial value for the space output location |.j^
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dt = T/N;                      % time step  ;e&
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n = [-N/2:1:N/2-1]';           % Index M$,Jg5Dc  
t = n.*dt;   C0zrXhY_v  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 5\VxXiy0  
u20=u10.*0.0;                  % input to waveguide 2 mYX56,b}5  
u1=u10; u2=u20;                 M|U';2hZN:  
U1 = u1;   c`-YIz)W  
U2 = u2;                       % Compute initial condition; save it in U b![t6-f^z  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Tv`_n2J`2  
w=2*pi*n./T; [/?c@N,  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Ip>^O/}$1  
L=4;                           % length of evoluation to compare with S. Trillo's paper PT mf  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Y.E?;iS
  
for m1 = 1:1:M1                                    % Start space evolution 3nwz<P  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS BpH|/7  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; {U(Bfe^a,  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform yHl@_rN sC  
   ca2 = fftshift(fft(u2)); ?LM:RADCm  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation y0;,dv]  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Y\.DQ  
   u2 = ifft(fftshift(c2));                        % Return to physical space LxB&7  
   u1 = ifft(fftshift(c1)); DK)u)?!  
if rem(m1,J) == 0                                 % Save output every J steps. HH7[tGF  
    U1 = [U1 u1];                                  % put solutions in U array yP x\ltG3  
    U2=[U2 u2]; pXssh  
    MN1=[MN1 m1]; MM7"a?y)  
    z1=dz*MN1';                                    % output location
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  end w.tW=z5  
end Pow|:Lau!  
hg=abs(U1').*abs(U1');                             % for data write to excel n-d:O\]  
ha=[z1 hg];                                        % for data write to excel XHy?  
t1=[0 t']; Ga.0Io&}C  
hh=[t1' ha'];                                      % for data write to excel file Cgo9
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format S:#e8H_7m]  
figure(1) M]1;  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn C]/&vh7ta  
figure(2) N50fL  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn HQl~Dh0DJ  

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非线性超快脉冲耦合的数值方法的Matlab程序 uw_H:-J  
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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。   ]s_@n!  
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 vuZf#\zh}  
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%  This Matlab script file solves the nonlinear Schrodinger equations YN/u9[=`  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of )XpVu  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Y5n>r@)m  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 %w$mSG  
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C=1;                           
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M1=120,                       % integer for amplitude of=ql  
M3=5000;                      % integer for length of coupler |e:rYLxm:  
N = 512;                      % Number of Fourier modes (Time domain sampling points) h<)yJh  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. bTiBmS  
T =40;                        % length of time:T*T0. 5\&]J7(  
dt = T/N;                     % time step O)`Gzx*ShU  
n = [-N/2:1:N/2-1]';          % Index l**3%cTb  
t = n.*dt;   l:)S 3  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. zXjwnep  
w=2*pi*n./T; 7u|%^Ao6  
g1=-i*ww./2; ,aWCiu}  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; -n-Z/5~ X  
g3=-i*ww./2; ?T <rt  
P1=0; hox< vr4  
P2=0; 1)'Iu`k/  
P3=1; l77'Lne  
P=0; IhfZLE.,  
for m1=1:M1                 TVYz3~m  
p=0.032*m1;                %input amplitude ]hL:33  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 .+HcAx{/2  
s1=s10; **n y!  
s20=0.*s10;                %input in waveguide 2 1U'ZVJ5bpK  
s30=0.*s10;                %input in waveguide 3 xvB8YW"  
s2=s20; *t]v}ZV*  
s3=s30; zC#%6@P\  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   6m@0;Ht  
%energy in waveguide 1 bLco:-G1E1  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   EWO /u.z  
%energy in waveguide 2 c@9##DPn  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   oBC]UL;8xJ  
%energy in waveguide 3 >9MS"t  
for m3 = 1:1:M3                                    % Start space evolution 9OfU7_m  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS zQ_z7FJCB  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; UhdqY]  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 3Soy3Xp  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform *{4 ETr7  
   sca2 = fftshift(fft(s2)); /S[?{QA  
   sca3 = fftshift(fft(s3)); 6uqUiRs()  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ~2(]ZfO?>H  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); }2=hd..  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); c})wD+1  
   s3 = ifft(fftshift(sc3)); op.d;lO@  
   s2 = ifft(fftshift(sc2));                       % Return to physical space F<gMUDB  
   s1 = ifft(fftshift(sc1)); T0Q51Q  
end \C7q4p?8  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ) $J7sa  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 0#^Bf[Dn  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); gvlFumg
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   P1=[P1 p1/p10]; 7 OWsHlU  
   P2=[P2 p2/p10]; TaWaHf  
   P3=[P3 p3/p10]; =+\$e1Mb*  
   P=[P p*p]; qX?[mdCHZ  
end !=y Q)l2  
figure(1) {Xv3:"E"O  
plot(P,P1, P,P2, P,P3); fM2^MUp[=1  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~