[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 3IU$  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of y:i[~y  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of >n$EeJ  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear , IMT '*  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 _Ssv:xc,  
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%fid=fopen('e21.dat','w'); .^9/ 0.g8t  
N = 128;                       % Number of Fourier modes (Time domain sampling points) lk+=
26>  
M1 =3000;              % Total number of space steps /\3XARt  
J =100;                % Steps between output of space BZ\EqB  
T =10;                  % length of time windows:T*T0 AT8B!m   
T0=0.1;                 % input pulse width Ybn=Gy  
MN1=0;                 % initial value for the space output location {R
1Cxt}  
dt = T/N;                      % time step +X%fcoc  
n = [-N/2:1:N/2-1]';           % Index ?VOs:sln  
t = n.*dt;   $E4O^0%/p  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ',J%Mv>Yf  
u20=u10.*0.0;                  % input to waveguide 2 0+2Matk>.  
u1=u10; u2=u20;                 =B o4yN  
U1 = u1;   &
t.>^7ELF  
U2 = u2;                       % Compute initial condition; save it in U 3*2&Fw!B  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 2\z`G  
w=2*pi*n./T; HhQPgjZ/  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T A\PV@w%Ai  
L=4;                           % length of evoluation to compare with S. Trillo's paper vU\w3  
dz=L/M1;                       % space step, make sure nonlinear<0.05 !Lg}q!*%>V  
for m1 = 1:1:M1                                    % Start space evolution g*w-"%"O  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ~qLhZR\g^  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; y?R <g^A  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform HZr/0I?  
   ca2 = fftshift(fft(u2)); {C0OrO2:  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation P`IMvOs&  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   t#D\*:Xi  
   u2 = ifft(fftshift(c2));                        % Return to physical space k+m_L{#m5  
   u1 = ifft(fftshift(c1)); p-(ADQS  
if rem(m1,J) == 0                                 % Save output every J steps. c J"]yG)=  
    U1 = [U1 u1];                                  % put solutions in U array On96N|  
    U2=[U2 u2]; ?w5nKpG#RI  
    MN1=[MN1 m1]; =|{,5="  
    z1=dz*MN1';                                    % output location =VX<eV  
  end lA^Kh  
end HU'`kimWb  
hg=abs(U1').*abs(U1');                             % for data write to excel 1Sc~Vb|>  
ha=[z1 hg];                                        % for data write to excel ]BS{,sI  
t1=[0 t']; #35S7G^@`  
hh=[t1' ha'];                                      % for data write to excel file L&gEQDPgq|  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format &_%+r5  
figure(1) O,xAu}6f+  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn E6^S2J2  
figure(2) #V9hG9%8  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn hk$nlc|$  
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非线性超快脉冲耦合的数值方法的Matlab程序 t+)GB=C  
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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。   ofrlTw&o  
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 U-]PWt?C{  
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%  This Matlab script file solves the nonlinear Schrodinger equations pvwnza1  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of PA-0FlV|  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 1.d9{LO[-  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 X9`C2fyVd  
:~A1Ud4c  
C=1;                           +uGP(ONY  
M1=120,                       % integer for amplitude #y9K-}u  
M3=5000;                      % integer for length of coupler zl8\jP  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Y 
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dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. .LTFa.jxA  
T =40;                        % length of time:T*T0. ZT-
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dt = T/N;                     % time step +&zuI  
n = [-N/2:1:N/2-1]';          % Index 2mp>Mn~K^  
t = n.*dt;   NwuBe:"@  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. jvKaxB;e  
w=2*pi*n./T; 7u3b aM  
g1=-i*ww./2; Q@.9wEAJ  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; {8p?we3l1  
g3=-i*ww./2; m=l3O:~J  
P1=0;  !+VN  
P2=0; X1z0'gvh  
P3=1; 9M~$W-5  
P=0; jxOVH+?l%  
for m1=1:M1                 ?}Ptb&Vk(  
p=0.032*m1;                %input amplitude 8JO\%DFJ  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 1#_j6Q2  
s1=s10; OuIW|gIu0  
s20=0.*s10;                %input in waveguide 2 mt]YY<l  
s30=0.*s10;                %input in waveguide 3 EsxTBg  
s2=s20; [Ik B/Xbw|  
s3=s30; 9oN'.H^  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   (']z\4o  
%energy in waveguide 1 9d(v^T  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   p~;z"Z  
%energy in waveguide 2 pC.P  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   2<./HH*f  
%energy in waveguide 3 /@}# KP=  
for m3 = 1:1:M3                                    % Start space evolution Us~wv"L=UX  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS zyn =Xv@p  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; b020U>)v  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; (S 3kP5:F  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform E1Aa2  
   sca2 = fftshift(fft(s2)); Jj!tRZT  
   sca3 = fftshift(fft(s3)); <1%XN  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   _Wsk3AP  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);  X_S]8Aa  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); t"Rf67  
   s3 = ifft(fftshift(sc3)); |N.q[>^R  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Kyiez]T6%q  
   s1 = ifft(fftshift(sc1)); ) G&3V  
end >d[vHyA~!D  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); m64\@ [  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); WSccR  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); n&{N't  
   P1=[P1 p1/p10]; nE$ V<Co}  
   P2=[P2 p2/p10]; ?O^:j!C6  
   P3=[P3 p3/p10]; T<,tC"  
   P=[P p*p]; APm[)vw#f  
end J3E:r_+  
figure(1) `,=p\g|D  
plot(P,P1, P,P2, P,P3);  xyCcd=  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~