[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 WR`NISSp  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of ;gZ/i93:Q  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of $|@vmv0  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear W;cYg.W2  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 "&/2@

 

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%fid=fopen('e21.dat','w'); <xF]ca  
N = 128;                       % Number of Fourier modes (Time domain sampling points) "oNl!<ep  
M1 =3000;              % Total number of space steps xpO;V}M|  
J =100;                % Steps between output of space \o/eF&  
T =10;                  % length of time windows:T*T0 ;Vc|3  
T0=0.1;                 % input pulse width uDXV@;6<  
MN1=0;                 % initial value for the space output location \>pm (gF  
dt = T/N;                      % time step oQ,<Yx%E3  
n = [-N/2:1:N/2-1]';           % Index >$9
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t = n.*dt;   'Etq;^H  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 b=xn(HE8|  
u20=u10.*0.0;                  % input to waveguide 2 KK #E qJ  
u1=u10; u2=u20;                 T@i* F M  
U1 = u1;   _<{<b  
U2 = u2;                       % Compute initial condition; save it in U K0_gMi+bR  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. U|Gy9"  
w=2*pi*n./T; [:#K_EI5%  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
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L=4;                           % length of evoluation to compare with S. Trillo's paper P_NF;v5v  
dz=L/M1;                       % space step, make sure nonlinear<0.05 c`p'5qz  
for m1 = 1:1:M1                                    % Start space evolution t"YsIOT:O"  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS k_,& Q?GtU  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; (DY[OIHI  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ^iJyo&I  
   ca2 = fftshift(fft(u2)); ^d{5GK'  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation M /v@C*c  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   $C5*@`GM$  
   u2 = ifft(fftshift(c2));                        % Return to physical space K)mQcB-"?  
   u1 = ifft(fftshift(c1)); 9$z$yGjl  
if rem(m1,J) == 0                                 % Save output every J steps. [RN]?,  
    U1 = [U1 u1];                                  % put solutions in U array 7+hF1eoI  
    U2=[U2 u2]; &e:+;7  
    MN1=[MN1 m1]; [%^sl>,7  
    z1=dz*MN1';                                    % output location M @-:iP  
  end WEe7\bWF  
end cPuXye  
hg=abs(U1').*abs(U1');                             % for data write to excel  jF0"AA  
ha=[z1 hg];                                        % for data write to excel eBnx$  
t1=[0 t']; oo2d,  
hh=[t1' ha'];                                      % for data write to excel file 86 e13MF  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format >FwK_Zd'  
figure(1) Q
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waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn $8UW^#Bpq  
figure(2) QJ4$) Fr(  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn
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非线性超快脉冲耦合的数值方法的Matlab程序 "4H@&:-(p  
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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。   3MNM<Ih  
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 4xmJQ>/  
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%  This Matlab script file solves the nonlinear Schrodinger equations Dk^AnMx%_  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of {<gv1Yht  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear A8vd@0  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 4BCe;Q^6  
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C=1;                           rx2'].  
M1=120,                       % integer for amplitude IUv#nB3  
M3=5000;                      % integer for length of coupler oC>J{z  
N = 512;                      % Number of Fourier modes (Time domain sampling points) O;<wDh)Yt  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. !P=Cv=  
T =40;                        % length of time:T*T0. ftxL-7y%  
dt = T/N;                     % time step ,.QJS6Yv  
n = [-N/2:1:N/2-1]';          % Index yj&GJuNb~  
t = n.*dt;   U_5`  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. `_OrBu[  
w=2*pi*n./T; "Esl I  
g1=-i*ww./2; #Z2'Y[@.  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Dc-K08c  
g3=-i*ww./2; } jJKE  
P1=0; lEFd^@t  
P2=0; %}9tU>?F#  
P3=1; ErK1j  
P=0; :,JaOn'  
for m1=1:M1                 bKCE;Wu:G  
p=0.032*m1;                %input amplitude hbx4[Pf  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 yqq1a o  
s1=s10; (V6bX]<  
s20=0.*s10;                %input in waveguide 2 apk,\L@sZ  
s30=0.*s10;                %input in waveguide 3 F*PhV|XU  
s2=s20; 2 3PRb<q  
s3=s30; <C'_:&M  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   !\7`I}:  
%energy in waveguide 1 }b(hD|e  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   AuXUD9-  
%energy in waveguide 2 uH9Vj<E$K  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));    *XhlIQ  
%energy in waveguide 3 <@.e.H  
for m3 = 1:1:M3                                    % Start space evolution R}0gIp=  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS f $Agcy  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; XMI*obS'z  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; /@ @F nQ++  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform n;Oe-+oSC  
   sca2 = fftshift(fft(s2)); dw<i)P^   
   sca3 = fftshift(fft(s3)); s0?'mC+p  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   DPzW,
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   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 4@-tT;$  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); )-3~^Y#r_  
   s3 = ifft(fftshift(sc3)); :.*Q@X}-I  
   s2 = ifft(fftshift(sc2));                       % Return to physical space gS+X%  
   s1 = ifft(fftshift(sc1)); pKc!sdC  
end G7 UUx+X  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); AhF@  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); _h-agn4[i  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); XZ |L D#  
   P1=[P1 p1/p10]; <=7nTcO~  
   P2=[P2 p2/p10]; VAL? Z  
   P3=[P3 p3/p10]; k2D*`\ D  
   P=[P p*p]; *m"9F'(Sd  
end ta)gOc)r R  
figure(1) gFTU9k<  
plot(P,P1, P,P2, P,P3); ]%6%rq%9C  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~