[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 v&oE!s#  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of ~$} `R=  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 6-C9[[g<  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ;(M`Wy]2  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 fbp
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%fid=fopen('e21.dat','w'); "2:]9j  
N = 128;                       % Number of Fourier modes (Time domain sampling points) PW)XDo7  
M1 =3000;              % Total number of space steps sxcpWSGA^  
J =100;                % Steps between output of space Cn4o^6?"  
T =10;                  % length of time windows:T*T0 O.4ty)*  
T0=0.1;                 % input pulse width Z{nJ\`  
MN1=0;                 % initial value for the space output location 6( TG/J  
dt = T/N;                      % time step r J'm>&Ps  
n = [-N/2:1:N/2-1]';           % Index 5at\!17TY  
t = n.*dt;  
X?5M)MP+I  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 %IGcn48J  
u20=u10.*0.0;                  % input to waveguide 2 @4dB$QF`&  
u1=u10; u2=u20;                 _
 h\wH;  
U1 = u1;   * Zb-
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U2 = u2;                       % Compute initial condition; save it in U Zn&S7a>7  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. l(|@ dp  
w=2*pi*n./T; D/C,Q|Ya6  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T |KFRC)g  
L=4;                           % length of evoluation to compare with S. Trillo's paper .r!:` 6  
dz=L/M1;                       % space step, make sure nonlinear<0.05 sS#Lnj^`%  
for m1 = 1:1:M1                                    % Start space evolution #MYhKySku  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Z"rrbN1  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; IKSe X  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ImQ?<g8$  
   ca2 = fftshift(fft(u2)); En%PIkxeR  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation bf]W_I]B  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   @mM'V5
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   u2 = ifft(fftshift(c2));                        % Return to physical space #:"F-3A0  
   u1 = ifft(fftshift(c1)); 9qxB/5d_  
if rem(m1,J) == 0                                 % Save output every J steps. 2OFrv=F  
    U1 = [U1 u1];                                  % put solutions in U array #xZ7%   
    U2=[U2 u2]; |4NH}XVYJ>  
    MN1=[MN1 m1]; `PK1zS
r  
    z1=dz*MN1';                                    % output location w7}m T3p,)  
  end ;QbMVY  
end m }I@:s2  
hg=abs(U1').*abs(U1');                             % for data write to excel tpp.
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ha=[z1 hg];                                        % for data write to excel |~vo  
t1=[0 t']; P wL]v.:  
hh=[t1' ha'];                                      % for data write to excel file y\7 -!  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format kx=.K'd5H  
figure(1) 3x2*K_A5:Q  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ]
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figure(2) )Cl!,m)~  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn m~a'  
{w*5uI%%e  
非线性超快脉冲耦合的数值方法的Matlab程序 FWpcWmS`s  
:^".cs?g  
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。   W.b?MPy]  
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 Ng=XH"ce~  
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%  This Matlab script file solves the nonlinear Schrodinger equations (izGF;N+  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of _(=[d  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear b z3&  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Bu4J8eLx  
mD@#,B7A  
C=1;                           yxq+<A4,a  
M1=120,                       % integer for amplitude 9AQMB1D*v4  
M3=5000;                      % integer for length of coupler 8nn%wps  
N = 512;                      % Number of Fourier modes (Time domain sampling points) c zTr_>
  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. U_!Wg|  
T =40;                        % length of time:T*T0. L
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dt = T/N;                     % time step &qfnCM0Y  
n = [-N/2:1:N/2-1]';          % Index \[</|]'[  
t = n.*dt;   d
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ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ,n&@O,XGy  
w=2*pi*n./T; FJ]BB4 K  
g1=-i*ww./2; _ZUtQ49  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Qu4Bd|`(k  
g3=-i*ww./2; ~RdJP'YF-  
P1=0; 2S'{$m)  
P2=0; yu8xTh$:  
P3=1; 0N02E  
P=0; yhnhORSY;  
for m1=1:M1                 (80 Tbi~+  
p=0.032*m1;                %input amplitude r9:Cq  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 :H/CiN  
s1=s10; >jI(^8?  
s20=0.*s10;                %input in waveguide 2 xD[O8vQE  
s30=0.*s10;                %input in waveguide 3 LU$aCw5 B;  
s2=s20; OhUEp g[  
s3=s30; Imi;EHW  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   *fs'%"w-  
%energy in waveguide 1 xb`,9.a7  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   |ymw
])L  
%energy in waveguide 2 8}9B*m  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   K/)*P4C-  
%energy in waveguide 3 t+C9QXY  
for m3 = 1:1:M3                                    % Start space evolution |l5ol@2*  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Af'L=0  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; qfF/X"#
0  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; QoagyL  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform j*2Q{ik>J  
   sca2 = fftshift(fft(s2)); 1eiV[z$?  
   sca3 = fftshift(fft(s3)); XN+~g.0  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   FdrH,  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 5LJUD>f9Z  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Mf [v7\  
   s3 = ifft(fftshift(sc3)); $#|iKi<Y@j  
   s2 = ifft(fftshift(sc2));                       % Return to physical space {J_1.uN=  
   s1 = ifft(fftshift(sc1)); HoA[UT  
end rl#[HbPM  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); VXr'Z  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); %Ot2bhK;  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Snm m(.  
   P1=[P1 p1/p10]; i-6,r[<  
   P2=[P2 p2/p10]; <A
%}  
   P3=[P3 p3/p10]; ldEZ_g^  
   P=[P p*p]; :)/%*<vq,  
end Vn:BasS%  
figure(1) H"~]|@g-p  
plot(P,P1, P,P2, P,P3); 'FVh/};Y.D  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~