[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 vK`S!7x'&  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of *e,CDV  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of i/M+t~  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ,{TQ ~LP  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9 G((wiE  
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%fid=fopen('e21.dat','w'); ec`>KuY  
N = 128;                       % Number of Fourier modes (Time domain sampling points) l^BEFk;  
M1 =3000;              % Total number of space steps -|$*l Q  
J =100;                % Steps between output of space ev*c4^z:
s  
T =10;                  % length of time windows:T*T0 ;HT0w_,  
T0=0.1;                 % input pulse width o[2Y;kP3*P  
MN1=0;                 % initial value for the space output location [5-!d!a|st  
dt = T/N;                      % time step =yo=q)W  
n = [-N/2:1:N/2-1]';           % Index *\C}Ok=  
t = n.*dt;   yvS^2+jW  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 H7J`]nr6  
u20=u10.*0.0;                  % input to waveguide 2 % M+s{ l  
u1=u10; u2=u20;                 e8 v; D  
U1 = u1;   ;,FT&|3o  
U2 = u2;                       % Compute initial condition; save it in U Vzk cZK  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 8\P JSr  
w=2*pi*n./T; fyGCfM  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T I S.F
 
L=4;                           % length of evoluation to compare with S. Trillo's paper Ep,1}
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dz=L/M1;                       % space step, make sure nonlinear<0.05 .k p$oAL  
for m1 = 1:1:M1                                    % Start space evolution ]zX\8eHp!  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS %d ZM9I0  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Mn-<51.%  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform mMga"I9  
   ca2 = fftshift(fft(u2)); a_xQ~:H  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation %~ ;nlDw  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   jDFp31_X  
   u2 = ifft(fftshift(c2));                        % Return to physical space pFS F[9?e>  
   u1 = ifft(fftshift(c1)); Q1K"%  
if rem(m1,J) == 0                                 % Save output every J steps. D1"1MUSod  
    U1 = [U1 u1];                                  % put solutions in U array a\.//?  
    U2=[U2 u2]; 'et(:}i  
    MN1=[MN1 m1]; VvzPQk  
    z1=dz*MN1';                                    % output location (di
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  end (}VuiNY<3  
end 1w(<0Be  
hg=abs(U1').*abs(U1');                             % for data write to excel cF-Jc}h  
ha=[z1 hg];                                        % for data write to excel qT 5WaO)  
t1=[0 t']; X9p+a,  
hh=[t1' ha'];                                      % for data write to excel file gCjH%=s  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format K lPm=  
figure(1) ::kpl2r\c  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 27}.s0{D  
figure(2) wEZqkV  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ~:R4))qpg  
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非线性超快脉冲耦合的数值方法的Matlab程序 6(!,H<bON  
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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。   {\ A_%  
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 ADuZ}]  
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%  This Matlab script file solves the nonlinear Schrodinger equations hhN(;.  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 1uKD&k%q  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6nM rO$i0k  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 VGq{y{(  
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C=1;                           .N?|t$J  
M1=120,                       % integer for amplitude k
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M3=5000;                      % integer for length of coupler w@<<zItSo  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 9aW8wYL~b  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ;igEIGR  
T =40;                        % length of time:T*T0. !pE>O-| K  
dt = T/N;                     % time step }xpe  
n = [-N/2:1:N/2-1]';          % Index @B}&62T  
t = n.*dt;   |:`?A3^m#  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. PX+"" #  
w=2*pi*n./T; #JX|S'\x  
g1=-i*ww./2; D3,t6\m  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; q>Dr)x)  
g3=-i*ww./2; Vs2v j  
P1=0; pO-)x:Wg  
P2=0; !XG/,)A  
P3=1; BV_a-\Sa=  
P=0; ee__3>H"/  
for m1=1:M1                 b}"vIRz  
p=0.032*m1;                %input amplitude 0B#rqTEKu  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 LNsE7t  
s1=s10; T%z!+/=&^  
s20=0.*s10;                %input in waveguide 2 0  /D5  
s30=0.*s10;                %input in waveguide 3 1tuator  
s2=s20; [qc6Q:  
s3=s30; fb;hf:B:  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   x_>"Rnv:K  
%energy in waveguide 1 q[We][Nrzb  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   lcuH]z  
%energy in waveguide 2 ^@l5u=  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Au\=ypK  
%energy in waveguide 3 exa}dh/uC  
for m3 = 1:1:M3                                    % Start space evolution 0|f_C3  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS jHUz`.8B  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; A
=@V LU4%  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; w|3fioLs  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform GtGyY0  
   sca2 = fftshift(fft(s2)); "X!_37kQ  
   sca3 = fftshift(fft(s3)); ,sy/rV  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ^O,6(@>  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); g tSHy*3]  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); NR@SDW  
   s3 = ifft(fftshift(sc3)); ]"7El;2z  
   s2 = ifft(fftshift(sc2));                       % Return to physical space -qr:c9\px  
   s1 = ifft(fftshift(sc1)); U iPVZ@?  
end d<^6hF  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); )gm\e?^
 
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); cmC&s'/8`D  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); hPX2 Bp  
   P1=[P1 p1/p10]; x Ps&CyI  
   P2=[P2 p2/p10]; *jqPKK/  
   P3=[P3 p3/p10]; //@sktHsw(  
   P=[P p*p]; :5qqu{GL  
end 9EY_R&Yq%  
figure(1) [eTck73  
plot(P,P1, P,P2, P,P3); YP@?j  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~