[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 i6)7)^nG  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of h%2;B;p]  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 8Jnl!4
  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g>g]qQ  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 WX2:c,%:  
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%fid=fopen('e21.dat','w'); d46PAA{'  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 2@&|/O6_\h  
M1 =3000;              % Total number of space steps A:{PPjs%LA  
J =100;                % Steps between output of space {\HEUIa]w  
T =10;                  % length of time windows:T*T0 w4 R!aWLd  
T0=0.1;                 % input pulse width UJhmhI  
MN1=0;                 % initial value for the space output location OC(S"&D  
dt = T/N;                      % time step ?zFeP6C  
n = [-N/2:1:N/2-1]';           % Index &nJH23h^  
t = n.*dt;   Etv!:\
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u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 6p;G~,bd~  
u20=u10.*0.0;                  % input to waveguide 2 xbZx&`(  
u1=u10; u2=u20;                 M|HW$8V3_2  
U1 = u1;   &Nzq/~uqP  
U2 = u2;                       % Compute initial condition; save it in U U/9i'D[|{  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ly!vbpE_  
w=2*pi*n./T; 4V2}'/|[  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T H]^hEQ3DT  
L=4;                           % length of evoluation to compare with S. Trillo's paper 7FQ&LF46  
dz=L/M1;                       % space step, make sure nonlinear<0.05 UaW,#P
 
for m1 = 1:1:M1                                    % Start space evolution >v sy P  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS j<BW/  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; >h!>Ll  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ef !@|2  
   ca2 = fftshift(fft(u2)); .mr&zq  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation {Kbb4%P+h  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   9FGe(t<  
   u2 = ifft(fftshift(c2));                        % Return to physical space 1=*QMEv1G  
   u1 = ifft(fftshift(c1)); q?&Ap*  
if rem(m1,J) == 0                                 % Save output every J steps. o#p{0y  
    U1 = [U1 u1];                                  % put solutions in U array bSG}I|  
    U2=[U2 u2]; 8Uv2p{ <#  
    MN1=[MN1 m1]; iZ^tLnc  
    z1=dz*MN1';                                    % output location fu=GgD*  
  end R
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end b8QQS#q)V  
hg=abs(U1').*abs(U1');                             % for data write to excel ()Tl\  
ha=[z1 hg];                                        % for data write to excel 1" k_l.\,0  
t1=[0 t']; YI877T9>  
hh=[t1' ha'];                                      % for data write to excel file =hw&2c  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ){D6E9  
figure(1) jV}tjwq  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn sf7~hN*  
figure(2) PUU "k:{  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn xE.yh#?.k  
%oee x1`=  
非线性超快脉冲耦合的数值方法的Matlab程序 Q+i  
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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。   aa-{,X"MF  
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 5]c\{G  
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%  This Matlab script file solves the nonlinear Schrodinger equations B_kjy=]O.  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of l?f%2:}m  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6bE~m<B\`  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 {E 'go]  
2#i*'.  
C=1;                           uQ(C,f[6p  
M1=120,                       % integer for amplitude O ,9,=2j  
M3=5000;                      % integer for length of coupler VR'R7  
N = 512;                      % Number of Fourier modes (Time domain sampling points) t.s;dlx[@  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. l KdY!j"  
T =40;                        % length of time:T*T0. _nn\O3TB  
dt = T/N;                     % time step z1AYXW6F  
n = [-N/2:1:N/2-1]';          % Index 2HX#:y{\l  
t = n.*dt;   *XCgl*% *  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ;YfKG8(0  
w=2*pi*n./T; ,E._A(Z  
g1=-i*ww./2; iXgy/>qgT  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; lTR/o  
g3=-i*ww./2; +";<Kd-  
P1=0; J#/L}h;qH  
P2=0; ~43T$^<w;  
P3=1; 'gaa@ !bg  
P=0; qQ{i2D%)?f  
for m1=1:M1                 _rN1(=J  
p=0.032*m1;                %input amplitude F7"v}K]X  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ES>iM)M  
s1=s10; _u]S/X-  
s20=0.*s10;                %input in waveguide 2 fZ6-ap,u  
s30=0.*s10;                %input in waveguide 3 OL2 b  
s2=s20; &tjv.t  
s3=s30; y@'~fI!E4  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   E*W|>2nx]  
%energy in waveguide 1 'CfM'f3uu  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   &F 3'tf?  
%energy in waveguide 2 (+x!wX( x  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));    L7rEMq  
%energy in waveguide 3 -qDM(zR  
for m3 = 1:1:M3                                    % Start space evolution 
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   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ;,2;J3,pA  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 0]u=GD%  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; z]V%&f  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform >39\u&)  
   sca2 = fftshift(fft(s2)); hLo>jE  
   sca3 = fftshift(fft(s3)); v-MrurQ4  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   U 6`E\?d`  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); P-LdzVt(^  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); gwQk M4  
   s3 = ifft(fftshift(sc3)); p+y2w{{  
   s2 = ifft(fftshift(sc2));                       % Return to physical space h+ggrwg'  
   s1 = ifft(fftshift(sc1)); !C>'a:  
end 8j^3_lD  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); wc~k4B9"  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); lDf:~  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); -udKGrT+  
   P1=[P1 p1/p10]; |WUm;o4E`U  
   P2=[P2 p2/p10]; ?E|be )  
   P3=[P3 p3/p10]; wQR0R~|M  
   P=[P p*p]; ^;DbIo\6H  
end bmd3fJb`r  
figure(1) WvVf+|Km  
plot(P,P1, P,P2, P,P3); E!6Nf[  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~