[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 W#bOx0  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of WJ&a9]&C  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 7Eo;TNbb  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 1$S`>M%a  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 /cX%XZg  
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%fid=fopen('e21.dat','w'); Qn!KL0w  
N = 128;                       % Number of Fourier modes (Time domain sampling points) lc(}[Z/|V  
M1 =3000;              % Total number of space steps WNK)IC~c  
J =100;                % Steps between output of space haSC[[o=  
T =10;                  % length of time windows:T*T0 G_E \p%L>]  
T0=0.1;                 % input pulse width ra|Ku!  
MN1=0;                 % initial value for the space output location BCI[jfd7  
dt = T/N;                      % time step 4
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n = [-N/2:1:N/2-1]';           % Index Fzk%eHG=  
t = n.*dt;   e6i m_ Tk  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Vpe\Okt:  
u20=u10.*0.0;                  % input to waveguide 2 ws([bS2h  
u1=u10; u2=u20;                 m85Hx1!p.  
U1 = u1;   08qM?{zo^  
U2 = u2;                       % Compute initial condition; save it in U kKs}E| T  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. oIv\Xdc81  
w=2*pi*n./T; <i ";5+  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T #/ HQ?3h]  
L=4;                           % length of evoluation to compare with S. Trillo's paper j2`%sBo  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Fql|0Fq  
for m1 = 1:1:M1                                    % Start space evolution S7h?tR*u  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS uwc@~=;  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; fA"9eUu  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform &Vy.)0  
   ca2 = fftshift(fft(u2)); .H}#,pQ}l  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation .YlhK=d4  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   XR+  
   u2 = ifft(fftshift(c2));                        % Return to physical space @ruWnwb  
   u1 = ifft(fftshift(c1)); 7srq~;j3  
if rem(m1,J) == 0                                 % Save output every J steps. >zV  
    U1 = [U1 u1];                                  % put solutions in U array +GL[uxe"  
    U2=[U2 u2]; 1'!%$D  
    MN1=[MN1 m1]; ^D?{[L
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    z1=dz*MN1';                                    % output location D zdKBJT+  
  end ` 1vDp.  
end 7{Zs"d{s  
hg=abs(U1').*abs(U1');                             % for data write to excel Vs9
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ha=[z1 hg];                                        % for data write to excel EQVa8xt/C  
t1=[0 t']; &W{<Yf9  
hh=[t1' ha'];                                      % for data write to excel file Zq{TY)PI]  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 4Cp)!Bq?/  
figure(1) 4O7 {a  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 589P$2e1X  
figure(2) 
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn C#@-uo2  
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非线性超快脉冲耦合的数值方法的Matlab程序 '3iJq9  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   [8'^"  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 4l@aga  
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%  This Matlab script file solves the nonlinear Schrodinger equations V?- ]ZkI  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of SedVp cb+  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ot,=.%O  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Rnw v/)  
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C=1;                           g(l:>=g]?  
M1=120,                       % integer for amplitude S\sy] 1*?$  
M3=5000;                      % integer for length of coupler a,eEP43dn  
N = 512;                      % Number of Fourier modes (Time domain sampling points) vT#m 8Kg  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ?nwg.
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T =40;                        % length of time:T*T0.  ->'xjD  
dt = T/N;                     % time step J@qwz[d i  
n = [-N/2:1:N/2-1]';          % Index {
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t = n.*dt;   +&[X7r<  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. $pajE^d4V  
w=2*pi*n./T; p7Z/%~0v:  
g1=-i*ww./2; CcZM0  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; +8.1cDEH\  
g3=-i*ww./2; Pv\-D<&@m  
P1=0; NdB:2P  
P2=0; #]J"j]L  
P3=1; :'sMrf_EA  
P=0; ^qNZ!V4T  
for m1=1:M1                 y'_2|5!Qs  
p=0.032*m1;                %input amplitude .$xTX'  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 [Uw3.CVh  
s1=s10; .xe+cK  
s20=0.*s10;                %input in waveguide 2 YJ>P+e\o9  
s30=0.*s10;                %input in waveguide 3 vk<4P;
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s2=s20;  #zg"E<  
s3=s30; S$qpClXS,  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   .q'{3  
%energy in waveguide 1 SHQgI<D7  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   :Fi$-g  
%energy in waveguide 2 _.xicov  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   %JuT'7VB  
%energy in waveguide 3 [fg-"-+:M  
for m3 = 1:1:M3                                    % Start space evolution vP^V3  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS =QhK|C!$A  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Qb@i_SX(fs  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; V eLGxc  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform `%$+rbo~  
   sca2 = fftshift(fft(s2)); 1SG^X-(GM/  
   sca3 = fftshift(fft(s3)); hs<OzM  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   m{by
%  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); "]B%V!@  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); j# n  
   s3 = ifft(fftshift(sc3)); ft?c&h;At  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 0A F}wz>  
   s1 = ifft(fftshift(sc1)); c"pu"t@/Z  
end ddw^oU  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); g5t`YcL  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); }r|$\ms  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); |b+CXEzo  
   P1=[P1 p1/p10]; Y``]66\Fp  
   P2=[P2 p2/p10]; N^zFKDJG  
   P3=[P3 p3/p10]; 4E@_Fn_#  
   P=[P p*p]; MGsY3~!K  
end |D1TSv}rZD  
figure(1) Ly]J-BTe  
plot(P,P1, P,P2, P,P3); kNoS% ?1,  
#pk  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~