[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 |iO2,99i  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of rpDH>Hzq  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear mIl^  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 MEq ()}7P  
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%fid=fopen('e21.dat','w'); HYW+,ts'  
N = 128;                       % Number of Fourier modes (Time domain sampling points) %<I0-o  
M1 =3000;              % Total number of space steps .\*\bvyCw  
J =100;                % Steps between output of space 9Tjvc!4_b  
T =10;                  % length of time windows:T*T0 r&Za*TD^  
T0=0.1;                 % input pulse width pS0-<-\R  
MN1=0;                 % initial value for the space output location U:YT>U1Z  
dt = T/N;                      % time step ke)3*.Y%C  
n = [-N/2:1:N/2-1]';           % Index 3#0nus|=S  
t = n.*dt;   '<4OA!,^)  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 D@O'8  
u20=u10.*0.0;                  % input to waveguide 2 ~mmI] p
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u1=u10; u2=u20;                 WpSdukXY{  
U1 = u1;   36&7J{MU  
U2 = u2;                       % Compute initial condition; save it in U 7m@pdq5Ub  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. %# J8
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w=2*pi*n./T; .:_dS=ut  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T  :jB(!XH  
L=4;                           % length of evoluation to compare with S. Trillo's paper R
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dz=L/M1;                       % space step, make sure nonlinear<0.05 Xo{Ce%L  
for m1 = 1:1:M1                                    % Start space evolution \=,+weGw@  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS |MTgKEsn  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; N#]f?6*R  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform bpKMQrwd  
   ca2 = fftshift(fft(u2)); #r:J,D6*   
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation NoZz3*j=  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   l|j&w[c[Q0  
   u2 = ifft(fftshift(c2));                        % Return to physical space *"j_3vAx  
   u1 = ifft(fftshift(c1)); YgdoQBQ  
if rem(m1,J) == 0                                 % Save output every J steps. C=%go1! $  
    U1 = [U1 u1];                                  % put solutions in U array jVk|(  
    U2=[U2 u2]; +z("'Cv  
    MN1=[MN1 m1]; AvP*p{w
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    z1=dz*MN1';                                    % output location &&JI$x0;  
  end 'HW(RC0dR  
end ~g>15b
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hg=abs(U1').*abs(U1');                             % for data write to excel q w|M~vdm  
ha=[z1 hg];                                        % for data write to excel >\(Ma3S   
t1=[0 t']; bLSI\  
hh=[t1' ha'];                                      % for data write to excel file P]r"E  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format B:+}^=  
figure(1) >JCSOI  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ,MOB+i(3*u  
figure(2) JL;H:`x  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn >,hJ5-9  
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非线性超快脉冲耦合的数值方法的Matlab程序 e0>@Yp[Kd  
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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。   kDO6:sjR7  
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 8q_3*++D  
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%  This Matlab script file solves the nonlinear Schrodinger equations $`_(%tl  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of UkXc7D^jwm  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear y%ER51+  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 t6-c{ZX>A  
hO{@!H$l  
C=1;                           |[k6X=5  
M1=120,                       % integer for amplitude 9OT2yCT  
M3=5000;                      % integer for length of coupler V!"^6)  
N = 512;                      % Number of Fourier modes (Time domain sampling points) t$Irr*  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 4B (*{  
T =40;                        % length of time:T*T0. YF&SH)Y7  
dt = T/N;                     % time step #J^p,6  
n = [-N/2:1:N/2-1]';          % Index \UtUP#Y{t  
t = n.*dt;   +u25>pX  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. pok,`yW\  
w=2*pi*n./T; ufEt"P-X.  
g1=-i*ww./2; 8 _`Lx_R  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; rhNdXYY>  
g3=-i*ww./2; +".&A#wU  
P1=0; Ie4*#N_  
P2=0; JBb}{fo~  
P3=1; vbwEX6  
P=0; =bv8W <#  
for m1=1:M1                 r\=p.cw<  
p=0.032*m1;                %input amplitude %qja:'k  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 36Wuc@<H  
s1=s10; `yuD/-j  
s20=0.*s10;                %input in waveguide 2 #Kn7 xn[  
s30=0.*s10;                %input in waveguide 3 ?7a<V+V:  
s2=s20; xW"J@OiKL  
s3=s30; /_jApZz  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   /0SPRf}
p  
%energy in waveguide 1 V!FzVl=G  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   E8NIH!dI  
%energy in waveguide 2 O]{H2&k@  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   hih`:y  
%energy in waveguide 3 3t%uUkXl  
for m3 = 1:1:M3                                    % Start space evolution s/ZOA[Yux  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Txoc  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; @Cqg2  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; /!AdX0dx  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform `I m;@_J  
   sca2 = fftshift(fft(s2)); g08=D$P  
   sca3 = fftshift(fft(s3)); JZP2NB_xt  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   !lu$WJ{M  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); JanLJe)  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); +[~\\X  
   s3 = ifft(fftshift(sc3)); vO4 &ZQ>6  
   s2 = ifft(fftshift(sc2));                       % Return to physical space by8d18:it  
   s1 = ifft(fftshift(sc1)); B8a!"AQ~5  
end EidIi"sr  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); @ju-cv+  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); o_\b{<^I  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Y`(I};MO  
   P1=[P1 p1/p10]; Th,2gX9  
   P2=[P2 p2/p10]; @ZX{q~g!  
   P3=[P3 p3/p10]; 2ix_,yTO  
   P=[P p*p]; jl:O~UL6i  
end c#{<| .  
figure(1) d5zzQ]|L  
plot(P,P1, P,P2, P,P3); GD< Afni  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~