[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 T/7vM6u  
ZV#$Z  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of '8Qw:fh  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of z"av|(?d  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear K!7q!%Ju  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 )[ w&C_>]  
Gx;xj0-"  
%fid=fopen('e21.dat','w'); ,]U[W  
N = 128;                       % Number of Fourier modes (Time domain sampling points) h+xA?[c=  
M1 =3000;              % Total number of space steps 4[_L=zD  
J =100;                % Steps between output of space D@5s8xv  
T =10;                  % length of time windows:T*T0 iha9!kf  
T0=0.1;                 % input pulse width 8vO;IK]9b^  
MN1=0;                 % initial value for the space output location :Fo4O'UC  
dt = T/N;                      % time step -=>U =|  
n = [-N/2:1:N/2-1]';           % Index Lv3XYZ
gW~  
t = n.*dt;   w#
<^RKk  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 kyK'  
u20=u10.*0.0;                  % input to waveguide 2 OT%V{hD  
u1=u10; u2=u20;                 ,$PFI(Whk  
U1 = u1;   'oCm.~;_  
U2 = u2;                       % Compute initial condition; save it in U @jKDj]\  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 5R"
2Wd  
w=2*pi*n./T; rx}*u3x=  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T c G*(C
  
L=4;                           % length of evoluation to compare with S. Trillo's paper 4D GY6PS  
dz=L/M1;                       % space step, make sure nonlinear<0.05 fo;6huz  
for m1 = 1:1:M1                                    % Start space evolution t,1in4sN  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS zw< 4G[u  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; /bi6>GaC:E  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform drs-mt8  
   ca2 = fftshift(fft(u2)); h$|3dz N  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation }!=gP.Zu^  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   j;G[%gi6{  
   u2 = ifft(fftshift(c2));                        % Return to physical space H)`@2~Y  
   u1 = ifft(fftshift(c1)); [Ek42%  
if rem(m1,J) == 0                                 % Save output every J steps. DQMPAj.  
    U1 = [U1 u1];                                  % put solutions in U array _2#zeT5  
    U2=[U2 u2]; OZa88&  
    MN1=[MN1 m1]; =g >.X9lr  
    z1=dz*MN1';                                    % output location F G3Sk!O6  
  end )7k&`?Mh  
end JxnuGkE0[#  
hg=abs(U1').*abs(U1');                             % for data write to excel D{Oq\*  
ha=[z1 hg];                                        % for data write to excel d&5c_6oW  
t1=[0 t']; 8,_ -0_^$  
hh=[t1' ha'];                                      % for data write to excel file hR!}u}ECd  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format T0YDfo  
figure(1) TZ:34\u  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn A3z/Bz4]:#  
figure(2) nW~$ (Qnd  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn )`mbf|,&t{  
Yg[ v/[]  
非线性超快脉冲耦合的数值方法的Matlab程序 ENO? ;  
wZ$tJQO  
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。   abL/Y23 "  
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 RZW$!tyI=  
amMjuyW  
C1KfXC*|L  
-%>8.#~G  
%  This Matlab script file solves the nonlinear Schrodinger equations E2kW=6VO>|  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of `bzr_fJ  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear {>wI8  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 5dqQws-,?1  
;i.I&*t  
C=1;                           d3Y(SPO  
M1=120,                       % integer for amplitude sZ]'DH&_(  
M3=5000;                      % integer for length of coupler ^p$1D  
N = 512;                      % Number of Fourier modes (Time domain sampling points) '!Hhd![\=|  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 7AI3|Ts]p  
T =40;                        % length of time:T*T0. ``+c`F?5  
dt = T/N;                     % time step \{[D|_   
n = [-N/2:1:N/2-1]';          % Index #fwzFS \XL  
t = n.*dt;   ~
B<97x(X  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. y!SF/i?Py  
w=2*pi*n./T; kxygf9I!;  
g1=-i*ww./2; LE8K)i  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; nDyvX1]  
g3=-i*ww./2; I<c@uXXV;!  
P1=0; ;&If9O1  
P2=0; ('T4Db  
P3=1; l8er$8S}  
P=0; (L`l+t1  
for m1=1:M1                 MJ1W*'9</W  
p=0.032*m1;                %input amplitude 5LO4P>f
q  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ^CfM|L8>  
s1=s10; mr@_%U  
s20=0.*s10;                %input in waveguide 2 5woIGO3X  
s30=0.*s10;                %input in waveguide 3 -Uzc"Lx B  
s2=s20; F='Xj@&O  
s3=s30; B{;11u  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   wDB
)&b  
%energy in waveguide 1 NR;q`Xe-  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   9cVn>Fb  
%energy in waveguide 2 4\&H?:c.  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   !O~},pp  
%energy in waveguide 3 l{nB.m2  
for m3 = 1:1:M3                                    % Start space evolution }Vs~RJM)}  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS =t@:F
 
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; '&RZ3@}+  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Dm>T"4B`/  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform n"XdHW0  
   sca2 = fftshift(fft(s2)); se~ *<5  
   sca3 = fftshift(fft(s3)); 9+]ZH.(YE  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   :[A?A4l  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); NdM}xh  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); enPzy:C  
   s3 = ifft(fftshift(sc3)); T^KCB\\<  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 1f+*Tmc5]Q  
   s1 = ifft(fftshift(sc1)); eA~J4k_  
end bq c;.4$  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); &W&7bZ$;  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); yfPCGCOW?  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); bk/.<Rt  
   P1=[P1 p1/p10]; [P.@1mV  
   P2=[P2 p2/p10]; C*"Rd   
   P3=[P3 p3/p10]; vs5 D:cZ}  
   P=[P p*p]; `Mo~EHso.  
end EZ:I$X  
figure(1) &i4 (s%z#  
plot(P,P1, P,P2, P,P3); 6&g!ZE'G  
k\4g|Lya  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~