[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 Jvgx+{Xu  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of MZl6J  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 'MVE5  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear H0LEK(K  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 .T#h5[S2x  
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%fid=fopen('e21.dat','w'); 8t25wPlx  
N = 128;                       % Number of Fourier modes (Time domain sampling points) *@^9]$*$  
M1 =3000;              % Total number of space steps X
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J =100;                % Steps between output of space N7=lSBm  
T =10;                  % length of time windows:T*T0 Hyh$-iCa  
T0=0.1;                 % input pulse width XOe)tz L  
MN1=0;                 % initial value for the space output location 6F !B;D-Q  
dt = T/N;                      % time step h/?$~OD  
n = [-N/2:1:N/2-1]';           % Index bwG$\Oe6  
t = n.*dt;   vtk0 j  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 bbddbRj;  
u20=u10.*0.0;                  % input to waveguide 2 suiO%H^t  
u1=u10; u2=u20;                 #Ie/|  
U1 = u1;   t<h[Lb%{T4  
U2 = u2;                       % Compute initial condition; save it in U NGIt~"e7R4  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. rom`%qp^  
w=2*pi*n./T; KW`^uoY$  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T @{n"/6t  
L=4;                           % length of evoluation to compare with S. Trillo's paper (#KSwWo{ed  
dz=L/M1;                       % space step, make sure nonlinear<0.05 O*
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for m1 = 1:1:M1                                    % Start space evolution }$ C;ccWL  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS J[ ;g \  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 40h  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 1u>[0<U~E  
   ca2 = fftshift(fft(u2)); wGy`0c]v?  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation r9sq3z|%  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   GO4IAUA  
   u2 = ifft(fftshift(c2));                        % Return to physical space vJI]ZnL{  
   u1 = ifft(fftshift(c1)); @@uKOFA?  
if rem(m1,J) == 0                                 % Save output every J steps. bAOL<0RS9`  
    U1 = [U1 u1];                                  % put solutions in U array ZP-^10  
    U2=[U2 u2]; #w]UP#^io  
    MN1=[MN1 m1]; e\)r"!?H`  
    z1=dz*MN1';                                    % output location <<WqL?8W  
  end ?$$Xg3w_#  
end )@(IhU)
  
hg=abs(U1').*abs(U1');                             % for data write to excel yrvV<}  
ha=[z1 hg];                                        % for data write to excel *3@ =XY7  
t1=[0 t']; r_>]yp  
hh=[t1' ha'];                                      % for data write to excel file -<0xS.^  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format <DR$WsDG  
figure(1) BcXPgM!Xqz  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 7!sR%h5p  
figure(2) u0;k_6
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn \gCh'3  
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非线性超快脉冲耦合的数值方法的Matlab程序 6K7DZ96L  
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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。   Nb3uDA5R  
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 xyzYY}PS  
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GHWt3K:*w  
%  This Matlab script file solves the nonlinear Schrodinger equations W*;r}!ro  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 0?,<7}"<X  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear M!R=&a=
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9ERyr1-u v  
U%rEW[j  
C=1;                           lJvfgP-j  
M1=120,                       % integer for amplitude 0
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M3=5000;                      % integer for length of coupler g|Tkl  
N = 512;                      % Number of Fourier modes (Time domain sampling points) J.(mg D  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. )ko[_OJj  
T =40;                        % length of time:T*T0. 2`^M OGYk  
dt = T/N;                     % time step yz7Fe  
n = [-N/2:1:N/2-1]';          % Index A$3ll|%j  
t = n.*dt;   O$ARk+  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. #;0F-pt  
w=2*pi*n./T; .^xQtnq  
g1=-i*ww./2; f = 'AI  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; "M3S  
g3=-i*ww./2; a9_KoOa.H  
P1=0; Hkrhd   
P2=0; 50e vWD  
P3=1; %RX!Pi}5+g  
P=0; ':|E$@$W  
for m1=1:M1                 V'FKgzd  
p=0.032*m1;                %input amplitude /H*[~b  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 1*?XI  
s1=s10; soOfk!b  
s20=0.*s10;                %input in waveguide 2 >r>pM(h  
s30=0.*s10;                %input in waveguide 3 l0PXU)>C  
s2=s20; *|OUd7P:hU  
s3=s30; V]Kk=  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   |JiN; O+K  
%energy in waveguide 1 *7{{z%5Pu  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   s54AM]a{j  
%energy in waveguide 2 8/@*6J  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   8dh ?JqX  
%energy in waveguide 3 1()pKBHf  
for m3 = 1:1:M3                                    % Start space evolution W[LQ$uj  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS pmiC|F83!8  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 
z $iI  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; B A i ^t  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform GPrq(  
   sca2 = fftshift(fft(s2)); =%S*h)}@  
   sca3 = fftshift(fft(s3)); !jg< S>S5  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   IN@ =UAc&  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); v2ab84 C*  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); WeIi{<u8R  
   s3 = ifft(fftshift(sc3)); sWq@E6,I  
   s2 = ifft(fftshift(sc2));                       % Return to physical space x|*m ok  
   s1 = ifft(fftshift(sc1)); /&em%/  
end Z*Fn2I4  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Ny$N5/b!!  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); +.a->SZ5"  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); `^)oVs  
   P1=[P1 p1/p10]; 8aY}b($*ZI  
   P2=[P2 p2/p10]; $e%m=@ga  
   P3=[P3 p3/p10]; 8#|PJc  
   P=[P p*p]; &S[>*+}{+  
end =.IAd<C  
figure(1) BO>[\!=y  
plot(P,P1, P,P2, P,P3); b~;M&Y  
L-|u=c-6  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~