[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 MO#%w  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of EmY4>lr  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of |x
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 2 yP#:T/z  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 )X^nzhZ2O"  
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%fid=fopen('e21.dat','w'); (rwbF  
N = 128;                       % Number of Fourier modes (Time domain sampling points) g'Xl>q  
M1 =3000;              % Total number of space steps nLtP^ 1~9H  
J =100;                % Steps between output of space ;*Z w}51  
T =10;                  % length of time windows:T*T0 syZ-xE]}  
T0=0.1;                 % input pulse width Y,(eu*Za  
MN1=0;                 % initial value for the space output location {J0^S  
dt = T/N;                      % time step ZTmdS  
n = [-N/2:1:N/2-1]';           % Index Uero!+_  
t = n.*dt;   iD(K*[;lc  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 s\jLIrG8  
u20=u10.*0.0;                  % input to waveguide 2 4UL-j  
u1=u10; u2=u20;                 II<<-Y6  
U1 = u1;   5e2mEQU>  
U2 = u2;                       % Compute initial condition; save it in U `z=MI66Nl  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. D9LwYftZ  
w=2*pi*n./T; XPEjMm'*b3  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T p-7dJ  
L=4;                           % length of evoluation to compare with S. Trillo's paper lHGv:TN  
dz=L/M1;                       % space step, make sure nonlinear<0.05 s{q2C}=$?D  
for m1 = 1:1:M1                                    % Start space evolution kcYR:;y  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS g{J3Ba  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 8Peqm?{5Y5  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform }dXL= ul  
   ca2 = fftshift(fft(u2)); ttw@nv% @  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation |;_ yAL  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   by06!-P0[  
   u2 = ifft(fftshift(c2));                        % Return to physical space 9xKFX|*$  
   u1 = ifft(fftshift(c1)); -xcz+pHQ  
if rem(m1,J) == 0                                 % Save output every J steps. 
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    U1 = [U1 u1];                                  % put solutions in U array +'Ge?(E4_  
    U2=[U2 u2]; 7]v-2 *  
    MN1=[MN1 m1]; n
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;  
    z1=dz*MN1';                                    % output location !c&^b@ yw  
  end 3Q]MT  
end ~*[}O)7#  
hg=abs(U1').*abs(U1');                             % for data write to excel uo{QF5z]  
ha=[z1 hg];                                        % for data write to excel OKU P  
t1=[0 t']; w}1)am&pD  
hh=[t1' ha'];                                      % for data write to excel file 'RA[_Z  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format Qxvz}r.l]  
figure(1) JIQzP?+?  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn [)Ge^yI7  
figure(2) vn_avYwiy  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn an7N<-?
 
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非线性超快脉冲耦合的数值方法的Matlab程序 wd]Yjr#%Ii  
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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。   =['ijD4TW  
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 cnc$^[c  
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%  This Matlab script file solves the nonlinear Schrodinger equations Yx%%+c?.  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of wTW"1M  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 7/1S5yUr|  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 m88~+o<G%  
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C=1;                           'I~dJEW7  
M1=120,                       % integer for amplitude H xlw1(zS  
M3=5000;                      % integer for length of coupler 9C.cz\E  
N = 512;                      % Number of Fourier modes (Time domain sampling points) f LW>-O73  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05.
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T =40;                        % length of time:T*T0. 7h<K)aT  
dt = T/N;                     % time step !+6l.`2WI  
n = [-N/2:1:N/2-1]';          % Index 1=X=jPwO C  
t = n.*dt;   .3&m:P8zV  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ,*4"d._Y  
w=2*pi*n./T; 
:1=?/8h  
g1=-i*ww./2; st2>e1vg  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; \\qg2yI  
g3=-i*ww./2; Dk-L4FS  
P1=0; kT1lOP-Bg  
P2=0; }B-A*TI<h  
P3=1; }rE|\p>  
P=0; H6O\U2+  
for m1=1:M1                 vy#(|[pL{  
p=0.032*m1;                %input amplitude fz&}N`n  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 O>GP>U?]  
s1=s10; %)D7Dr  
s20=0.*s10;                %input in waveguide 2 r
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s30=0.*s10;                %input in waveguide 3 $T4PC5.  
s2=s20; w(j9[  
s3=s30; zT% kx:Fk  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Kv]6 b2HT  
%energy in waveguide 1 *LRGfk+h  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   q T].,?  
%energy in waveguide 2 D'h2 DP!  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   *K(xES!b  
%energy in waveguide 3 [UH5D~Yx
 
for m3 = 1:1:M3                                    % Start space evolution Em,!=v(*  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ~30Wb9eL  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; WI6E3,ejB1  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; t}7wRTG  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform rieQ&Jt"  
   sca2 = fftshift(fft(s2)); eFQi K6`i  
   sca3 = fftshift(fft(s3)); uFm-HR@4  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   76b7-Nj"  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); pqSE|3*l  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); dx}/#jMa  
   s3 = ifft(fftshift(sc3)); u-_$?'l;~  
   s2 = ifft(fftshift(sc2));                       % Return to physical space xgz87d/<:  
   s1 = ifft(fftshift(sc1)); r!^\Q7  
end b-?o?}*  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); w8 $Qh%J'<  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); %SGO"*_  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); <.b$ gX  
   P1=[P1 p1/p10]; v8Zgog)V  
   P2=[P2 p2/p10]; aA`q!s.%A  
   P3=[P3 p3/p10]; hD1AK+y  
   P=[P p*p]; i=N\[&
 
end [bG>qe1}&  
figure(1) 4E>(Y98  
plot(P,P1, P,P2, P,P3); >U<nEnB$?  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~