[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 o.Rv<a5.L  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of /1v9U|j  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of tV
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ^a_a%ws
 
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 *;]}`r  
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%fid=fopen('e21.dat','w'); WA"~6U*  
N = 128;                       % Number of Fourier modes (Time domain sampling points)  L"%SU  
M1 =3000;              % Total number of space steps <y] 67:"<v  
J =100;                % Steps between output of space |Rz.Pt6  
T =10;                  % length of time windows:T*T0 {\(MMTQ  
T0=0.1;                 % input pulse width F{!pii5O9  
MN1=0;                 % initial value for the space output location 8>,w8(Nt  
dt = T/N;                      % time step sqtz^K ROM  
n = [-N/2:1:N/2-1]';           % Index w|-
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t = n.*dt;   - ~|Gwr"  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Leb|YX
 
u20=u10.*0.0;                  % input to waveguide 2 ;//9,x9;t  
u1=u10; u2=u20;                 *H/3xPh,*  
U1 = u1;   twq~.:<o  
U2 = u2;                       % Compute initial condition; save it in U NFZ(*v1U  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. [i/!o
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w=2*pi*n./T; ZQ_6I}i")  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T T5."3i  
L=4;                           % length of evoluation to compare with S. Trillo's paper L|T?,^  
dz=L/M1;                       % space step, make sure nonlinear<0.05 R-S<7Q3E0=  
for m1 = 1:1:M1                                    % Start space evolution hc[ K VLpS  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Qk:Lo*!  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; [jzsB:;XB&  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform GQn:lu3j:  
   ca2 = fftshift(fft(u2)); PY.K_(D  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation {h7 vJ^  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   31a,i2Q4  
   u2 = ifft(fftshift(c2));                        % Return to physical space "mW'tm1+  
   u1 = ifft(fftshift(c1)); L^ J|cgmNw  
if rem(m1,J) == 0                                 % Save output every J steps. dA~:L`A|X  
    U1 = [U1 u1];                                  % put solutions in U array ]=qauf>3  
    U2=[U2 u2]; ^w\22 Q  
    MN1=[MN1 m1]; bGH#s {'5  
    z1=dz*MN1';                                    % output location wW@e#:  
  end \D?'.Wo%  
end |(3y09  
hg=abs(U1').*abs(U1');                             % for data write to excel $u!(F]^  
ha=[z1 hg];                                        % for data write to excel 2!J#XzR0W  
t1=[0 t']; Nrr}) g  
hh=[t1' ha'];                                      % for data write to excel file sv%X8  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 7Ed0BJTa  
figure(1) THp_ dTD  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn FBNLszT{L  
figure(2) ^?`fN'!p  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn RW. qw4  
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非线性超快脉冲耦合的数值方法的Matlab程序 't5ufAT  
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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。   Yub}AuU`v  
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 G;G*!nlWf  
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%  This Matlab script file solves the nonlinear Schrodinger equations Svn7.Ivep  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of \34vE@V*  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear BV~J*e  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 bkV<ZUW|;  
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C=1;                           rv*{[K  
M1=120,                       % integer for amplitude pux IJ  
M3=5000;                      % integer for length of coupler |u>(~6  
N = 512;                      % Number of Fourier modes (Time domain sampling points) '@t$3 hk  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. kw#X,hP  
T =40;                        % length of time:T*T0. 1&=)Bxg4  
dt = T/N;                     % time step IgX &aW
 
n = [-N/2:1:N/2-1]';          % Index +
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t = n.*dt;   Ib#-M;{  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. *-nO,K>y`  
w=2*pi*n./T; !/XNpQP  
g1=-i*ww./2; @
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g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; } {1IB  
g3=-i*ww./2; PEf yHf7`  
P1=0; w \b+OW  
P2=0; M}\h?s   
P3=1; O+}py{ st  
P=0; |U|>YA1[b  
for m1=1:M1                 u9hd%}9Qd?  
p=0.032*m1;                %input amplitude 
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 i/9iM\2  
s1=s10; c;VqEpsbl  
s20=0.*s10;                %input in waveguide 2 y8k8Hd1<f  
s30=0.*s10;                %input in waveguide 3 6'Q{xJe?  
s2=s20; =0Z
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s3=s30; #rkq ?:Q  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   [H}> 2Q  
%energy in waveguide 1 &u>dKf)5  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   PILpWhjL$9  
%energy in waveguide 2 :V'99Esv`  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   "2cOSPpQL  
%energy in waveguide 3 q?}C`5%D  
for m3 = 1:1:M3                                    % Start space evolution #r'MfTr  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Q@W/~~N  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 2RkW/)A9  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; &i5@4,p y9  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform E_ns4k#uG  
   sca2 = fftshift(fft(s2)); Ehx9-*]
 
   sca3 = fftshift(fft(s3)); bJ^h{]  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   iOk;o=  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); h=#w< @  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); >rd#,r  
   s3 = ifft(fftshift(sc3)); xb;{<~`71  
   s2 = ifft(fftshift(sc2));                       % Return to physical space b#_RZ  
   s1 = ifft(fftshift(sc1)); 0g?)j-  
end ;st0Ekni)  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 7:jLZ!mgi  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); {kpF etXt?  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); *ub2dH4/  
   P1=[P1 p1/p10]; gNCS*a  
   P2=[P2 p2/p10]; =)Xj[NNRT
 
   P3=[P3 p3/p10]; %O\@rws  
   P=[P p*p]; E 2nz  
end /|?$C7%a\D  
figure(1) 5BVvT `<  
plot(P,P1, P,P2, P,P3); *] ihc u  
&,&+p0CSI!  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~