[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 ,+0_kndR  
GSsot%B u"  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of J?V8u
Ely  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Vg0Rc t  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 8uNq353  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 r'"H8>UZ%  
J 5~bs*a8  
%fid=fopen('e21.dat','w'); 8^2Q ~{i  
N = 128;                       % Number of Fourier modes (Time domain sampling points) [W` _`  
M1 =3000;              % Total number of space steps ((#|>W\&  
J =100;                % Steps between output of space P)4SrqW_  
T =10;                  % length of time windows:T*T0 Z{|wjZb(  
T0=0.1;                 % input pulse width )jvYJ9s  
MN1=0;                 % initial value for the space output location (Zp'|hx8o  
dt = T/N;                      % time step )D Y?Y-n  
n = [-N/2:1:N/2-1]';           % Index zl$'W=[rFs  
t = n.*dt;   c&ymVB?G:1  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 VXQ~PF]z0  
u20=u10.*0.0;                  % input to waveguide 2 +eQg+@u  
u1=u10; u2=u20;                 uN2Ck  
U1 = u1;   jCkYzQUPz  
U2 = u2;                       % Compute initial condition; save it in U f/aSqhAW  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ;>bcI).  
w=2*pi*n./T; Z
J1%  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ar }F^8Ku  
L=4;                           % length of evoluation to compare with S. Trillo's paper )V7bi^r  
dz=L/M1;                       % space step, make sure nonlinear<0.05 7xqTT
N6h  
for m1 = 1:1:M1                                    % Start space evolution dL!PpLR$2  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS #A+ dj| b  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 26?yEd6^Z  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform N2WQrTA:S+  
   ca2 = fftshift(fft(u2)); Eu2@%2}P  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation bejvw?)S.  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   w,n&K6<  
   u2 = ifft(fftshift(c2));                        % Return to physical space Dm2&}{&K  
   u1 = ifft(fftshift(c1)); qf-0 | w  
if rem(m1,J) == 0                                 % Save output every J steps. )cxLpTr  
    U1 = [U1 u1];                                  % put solutions in U array ')
zdI]@M  
    U2=[U2 u2]; <
j^8L^  
    MN1=[MN1 m1]; 1%g%I8W%  
    z1=dz*MN1';                                    % output location K 0R<a~  
  end hX;JMQ915  
end as6a)t.^  
hg=abs(U1').*abs(U1');                             % for data write to excel %|Sh|\6A!  
ha=[z1 hg];                                        % for data write to excel s|FfBG  
t1=[0 t']; (= #EJB1(  
hh=[t1' ha'];                                      % for data write to excel file A%(t'z  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format /x\{cHAt8J  
figure(1) KP
Tp91  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 9\y\{DHd  
figure(2) xA/Ein0  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn r2"B"%;  
WTK )SKa,.  
非线性超快脉冲耦合的数值方法的Matlab程序 @'P\c   
a*/%EP3  
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。   ?QR13l(  
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 e*K1";  
Ls51U7  
!X5n'1&  
I8M^]+c  
%  This Matlab script file solves the nonlinear Schrodinger equations },#@q_E  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of \+3amkBe  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear <l>o6K  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Y~,ZBl,  
[ 'aSPA  
C=1;                           LlbRr.wL  
M1=120,                       % integer for amplitude x:dI:G  
M3=5000;                      % integer for length of coupler U}h
QVpP#  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Ry_"sow4  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05.
n06T6oc  
T =40;                        % length of time:T*T0. df9jT?l  
dt = T/N;                     % time step ( &N`N1  
n = [-N/2:1:N/2-1]';          % Index a\_?zi]s&,  
t = n.*dt;   #ATV#/hW  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. {&3{_Ml  
w=2*pi*n./T; >_esLsPWh]  
g1=-i*ww./2; `!- w^~c  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ,
;%
F\<b  
g3=-i*ww./2; K-X@3&X}  
P1=0; ^&8FwV]  
P2=0; I)s~kA.e  
P3=1; zfGS=@e]G  
P=0; ZlEQzL~  
for m1=1:M1                 ?R#?=<VkG  
p=0.032*m1;                %input amplitude fC|NK+Xd`  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 u"hv _ml  
s1=s10; SobOUly5{  
s20=0.*s10;                %input in waveguide 2 "1I\~]]  
s30=0.*s10;                %input in waveguide 3 "fH"U1Bw  
s2=s20; o%j[]P@4G  
s3=s30; p#A{.6Pa:  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   F4:giu ht  
%energy in waveguide 1 caH!(V}6  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   6O@/Y;5i  
%energy in waveguide 2 M?[~_0_J  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   lX)ZQY:=:  
%energy in waveguide 3 ZkA05wPZ#  
for m3 = 1:1:M3                                    % Start space evolution BK*Bw,KQ<  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS md S`nhb  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Thc"QIk&4  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; mu$0x)  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform .=`r?#0  
   sca2 = fftshift(fft(s2)); JbR;E`8  
   sca3 = fftshift(fft(s3)); sQl`0|VH  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   _+=M)lPm  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 9fhgCu]$  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); AhA4IOG`.  
   s3 = ifft(fftshift(sc3)); 
F
<9S,  
   s2 = ifft(fftshift(sc2));                       % Return to physical space \A%s" O/  
   s1 = ifft(fftshift(sc1)); #0uD&95<  
end Q |1-j  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Z23*`yR  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); SI"y&[iw  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); }eLnTi{  
   P1=[P1 p1/p10]; N.1@!\z@@  
   P2=[P2 p2/p10]; ^.?5!9U  
   P3=[P3 p3/p10]; \""sf{S9  
   P=[P p*p]; ]ucz8('  
end d&G#3}kOb%  
figure(1) kZU v/]Y.  
plot(P,P1, P,P2, P,P3); P/?'ea  
Z]^Ooy[pb  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~