[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 x^]1m%  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of +0O^!o  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of #oD*H:%*  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 5VPP 2;J  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 a0x/?)DO  
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%fid=fopen('e21.dat','w'); ;u: }rA)  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Fh$Xcz~i  
M1 =3000;              % Total number of space steps cX/["AM  
J =100;                % Steps between output of space ^a
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T =10;                  % length of time windows:T*T0 WD5ulm?91|  
T0=0.1;                 % input pulse width :S |)  
MN1=0;                 % initial value for the space output location >|So`C3:e  
dt = T/N;                      % time step @VcSK`  
n = [-N/2:1:N/2-1]';           % Index p![CH  
t = n.*dt;   [-Dl,P=  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 $:MO/Suz{  
u20=u10.*0.0;                  % input to waveguide 2 goV[C]|  
u1=u10; u2=u20;                 y|@=j~}Zq  
U1 = u1;   - '5OX/Szq  
U2 = u2;                       % Compute initial condition; save it in U Bx32pY  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 675x/0}GO  
w=2*pi*n./T; bbU{ />yW  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T L3-tD67oa  
L=4;                           % length of evoluation to compare with S. Trillo's paper oLp:Z=  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Ka\%kB>*`  
for m1 = 1:1:M1                                    % Start space evolution  !(<Yc5  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ` 
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; OVm $  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform eqze7EY  
   ca2 = fftshift(fft(u2)); *xOrt)D=  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation L?n*b  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Pc4FEH/  
   u2 = ifft(fftshift(c2));                        % Return to physical space [UHDN:y  
   u1 = ifft(fftshift(c1)); JOIbxU{U_  
if rem(m1,J) == 0                                 % Save output every J steps. T+[N-"N  
    U1 = [U1 u1];                                  % put solutions in U array m,U`hPJ  
    U2=[U2 u2]; (U |[C*  
    MN1=[MN1 m1]; =/rIXReY  
    z1=dz*MN1';                                    % output location fH7o,U|  
  end 81|Xg5g)b  
end {>cO&eiCt  
hg=abs(U1').*abs(U1');                             % for data write to excel t>T |\WAAL  
ha=[z1 hg];                                        % for data write to excel bG0t7~!{E  
t1=[0 t']; _KkLH\1g$  
hh=[t1' ha'];                                      % for data write to excel file A8R}W=  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ,]'?Gd  
figure(1) :,=no>mMx  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ]64mSB  
figure(2) wKCHG/W  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 8]N+V:  
#U NTD4  
非线性超快脉冲耦合的数值方法的Matlab程序 #is:6Z,OEU  
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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。   %jY/jp=R  
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 <;.Zms${@  
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%  This Matlab script file solves the nonlinear Schrodinger equations 2Ek6YNx  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Eq9TJt'3y  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear F}A@H<?  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 g@.RfX=  
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C=1;                           DLkNL?a  
M1=120,                       % integer for amplitude ~3.
1. 'A  
M3=5000;                      % integer for length of coupler */n)_  
N = 512;                      % Number of Fourier modes (Time domain sampling points)
EW{z?/  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. V$+xJ  m  
T =40;                        % length of time:T*T0. Mrp'wF D  
dt = T/N;                     % time step 6v0^'}  
n = [-N/2:1:N/2-1]';          % Index $LZf&q:\]*  
t = n.*dt;   ]+W+8)f1M  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ;PJWd|3  
w=2*pi*n./T; $Tt@Xu  
g1=-i*ww./2; DEaO=p|  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ZN|DR|cUY  
g3=-i*ww./2; Z xLjh  
P1=0; d(w $! $"h  
P2=0; t#~r'5va  
P3=1; lkV% k1w  
P=0; tgDmHxB]0  
for m1=1:M1                 0
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p=0.032*m1;                %input amplitude glh2CRUj  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 oq=D9  
s1=s10; O k_I}X  
s20=0.*s10;                %input in waveguide 2 1<^"OjQ  
s30=0.*s10;                %input in waveguide 3 8f% @  
s2=s20; SHPaSq'
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s3=s30; 'z2}qJJ)  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   -
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%energy in waveguide 1 (j+C&*u
 
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   wYhWR
gP  
%energy in waveguide 2 *~fZ9EkD  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ~ @Ib:M  
%energy in waveguide 3 *L/_ v  
for m3 = 1:1:M3                                    % Start space evolution *"0
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   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS `pN"T?Pk  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 6z"fBF  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; BG"~yyKA  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform AL}c-#GG  
   sca2 = fftshift(fft(s2)); &TSt/b/+W  
   sca3 = fftshift(fft(s3)); Vf*!m~]Vqi  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   qJFBdJU(1  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); }3Pz{{B&+O  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); <dDGV>n4;  
   s3 = ifft(fftshift(sc3)); 6!/e_a  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 9
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   s1 = ifft(fftshift(sc1)); }+QgRGQ  
end ,>2ijk#  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); J& +s  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); B @UaaWh  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); FgNO#%  
   P1=[P1 p1/p10]; R*E/E  
   P2=[P2 p2/p10]; 4>{q("r,  
   P3=[P3 p3/p10]; PX[taDN  
   P=[P p*p]; 1fQvh/2  
end Et%s,zeA{2  
figure(1) oKz|hks[6  
plot(P,P1, P,P2, P,P3); =XJ SE+ 7  
Q<d\K(<3?:  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~