[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 AC;ja$A#  
}ac0}  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of *^e06xc:  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 0l=g$G \%  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear B~K@o.%  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 FJDx80J  
&i179Qg!  
%fid=fopen('e21.dat','w'); MA0}BJoW  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 99j^<)  
M1 =3000;              % Total number of space steps 6}zargu(;  
J =100;                % Steps between output of space M}2a/}4
 
T =10;                  % length of time windows:T*T0 MwMv[];I  
T0=0.1;                 % input pulse width :Lu=t3#  
MN1=0;                 % initial value for the space output location f-6
-!  
dt = T/N;                      % time step [+<lm 5t  
n = [-N/2:1:N/2-1]';           % Index
*Y8nea^$  
t = n.*dt;   {WfZE&B  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 >|Ps23J#  
u20=u10.*0.0;                  % input to waveguide 2 !8S$tk  
u1=u10; u2=u20;                 Khp`KPxz%  
U1 = u1;   <
pJeiMo  
U2 = u2;                       % Compute initial condition; save it in U 4d~Sn81xW  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. b3]QH h/  
w=2*pi*n./T; uf4C+c
i  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T f'._{"  
L=4;                           % length of evoluation to compare with S. Trillo's paper ',`GdfAsH  
dz=L/M1;                       % space step, make sure nonlinear<0.05 '}3@D$YiM%  
for m1 = 1:1:M1                                    % Start space evolution faH113nc  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS yzJ
VU0s  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Ni"n_Yun  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform hZ6CiEJB  
   ca2 = fftshift(fft(u2)); 1Z-f@PoM  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation vZ3/t8$*  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   JtA tG%  
   u2 = ifft(fftshift(c2));                        % Return to physical space ]@YBa4}w  
   u1 = ifft(fftshift(c1)); $KDH"J  
if rem(m1,J) == 0                                 % Save output every J steps. P(B:tg  
    U1 = [U1 u1];                                  % put solutions in U array uXD?s3Wv  
    U2=[U2 u2]; [AgS@^"sf5  
    MN1=[MN1 m1]; /sHWJ?`&/,  
    z1=dz*MN1';                                    % output location )w\E^  
  end kex4U6&OQB  
end x`:zC#  
hg=abs(U1').*abs(U1');                             % for data write to excel #J&4
5  
ha=[z1 hg];                                        % for data write to excel 5>{  
t1=[0 t']; <Sw>5M!j  
hh=[t1' ha'];                                      % for data write to excel file ZmM/YPy  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format cF6eMml;  
figure(1) rm}OVL  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 8JYF0r7  
figure(2) cbsU!8
 
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn CF
"u8yE  
N0`v;4gF$]  
非线性超快脉冲耦合的数值方法的Matlab程序 DdO$&/`)YP  
Y*oT(  
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。   6%N.'wf  
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 zl~`>  
(vL-Z[M!  
wCT. (d_  
u17e  
%  This Matlab script file solves the nonlinear Schrodinger equations HHd;<%q  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of FwD"Pc2  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 'L$%)`;e  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 MA9Oi(L)K  
C9+`sFau@  
C=1;                           )<Cf,R  
M1=120,                       % integer for amplitude eRV4XB:  
M3=5000;                      % integer for length of coupler DK-V3}`q}  
N = 512;                      % Number of Fourier modes (Time domain sampling points) #9=as Y  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ZV:cgv  
T =40;                        % length of time:T*T0. 1$1s0yg  
dt = T/N;                     % time step 8#?jYhT7  
n = [-N/2:1:N/2-1]';          % Index Ns3k(j16  
t = n.*dt;   E RnuM  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. (- ]A1WQ?  
w=2*pi*n./T; c& &^Do  
g1=-i*ww./2; 4rpx  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Pr|:nJs  
g3=-i*ww./2; ){'Ef_/R  
P1=0; w0`aW6t#  
P2=0; .&|Ivz6  
P3=1; W ='c+3O6  
P=0; 2h Wtpus  
for m1=1:M1                 8Jnl!4
  
p=0.032*m1;                %input amplitude g>g]qQ  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 WX2:c,%:  
s1=s10; HfQZRDH  
s20=0.*s10;                %input in waveguide 2 d46PAA{'  
s30=0.*s10;                %input in waveguide 3 2@&|/O6_\h  
s2=s20; A:{PPjs%LA  
s3=s30; heLWVI[so  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   6xDYEvHS  
%energy in waveguide 1 _tl  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   8 K7.; t1  
%energy in waveguide 2 vUlGE  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   $>Y2N5  
%energy in waveguide 3 gG^A
6Ol%D  
for m3 = 1:1:M3                                    % Start space evolution }@+3QHwYU  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS R8Kj3wp  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
>a6{y  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; $ NNd4d*  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform cM'\u~m{  
   sca2 = fftshift(fft(s2)); b#h}g>l  
   sca3 = fftshift(fft(s3)); zk#NM"C+  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   %3"xn!'vf  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); wNNInS6  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Z>9uVBE02  
   s3 = ifft(fftshift(sc3)); QJeL&mf  
   s2 = ifft(fftshift(sc2));                       % Return to physical space )9oF?l^q  
   s1 = ifft(fftshift(sc1)); ?p&CR[  
end ](^$5Am  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); PTt#Ixn,  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
X`,=tM  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); he/WqCZg  
   P1=[P1 p1/p10]; D9hV`fA  
   P2=[P2 p2/p10]; Bf)}g4nYn  
   P3=[P3 p3/p10]; eootHK  
   P=[P p*p]; !06 !`LT  
end 3e)W_P*0?  
figure(1) CrvL[6i  
plot(P,P1, P,P2, P,P3); !+<OED=qe  

[UP-BX(  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~