[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 sAkr-x?+M  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of UPh#YV 0/,  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of D4=*yP
  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear p>B2bv+L  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 VPUVPq~&  
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%fid=fopen('e21.dat','w'); bHwEd%f  
N = 128;                       % Number of Fourier modes (Time domain sampling points) i5 rkP`)j  
M1 =3000;              % Total number of space steps \/NF??k,jk  
J =100;                % Steps between output of space T D_@0Rd  
T =10;                  % length of time windows:T*T0 Q7s@,c!m_  
T0=0.1;                 % input pulse width  js_`L#t  
MN1=0;                 % initial value for the space output location [oLV,O|s|j  
dt = T/N;                      % time step Gnkar[oa&  
n = [-N/2:1:N/2-1]';           % Index Kw -SOFE  
t = n.*dt;   5>x_G#W  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 k +-w%  
u20=u10.*0.0;                  % input to waveguide 2 `geHSx_  
u1=u10; u2=u20;                 }E 'r?N  
U1 = u1;   ~G!JqdKJ0  
U2 = u2;                       % Compute initial condition; save it in U |YJ83nSO~  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. I~GF%$-G  
w=2*pi*n./T; ZwmucY%3  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T <S@jf4  
L=4;                           % length of evoluation to compare with S. Trillo's paper Wc3z7xK1@  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ;5Sdx5`_  
for m1 = 1:1:M1                                    % Start space evolution ?{ir$M  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ( ayAP  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; jJ,_-ui  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform fO*jCl  
   ca2 = fftshift(fft(u2)); QZ a.c  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 8|a./%gixs  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   (`tRJWbdz  
   u2 = ifft(fftshift(c2));                        % Return to physical space OK[J h  
   u1 = ifft(fftshift(c1)); cw Obq\  
if rem(m1,J) == 0                                 % Save output every J steps. 2{OR#v~  
    U1 = [U1 u1];                                  % put solutions in U array %Y^J''  
    U2=[U2 u2]; [{x}# oRSE  
    MN1=[MN1 m1]; AYts &+  
    z1=dz*MN1';                                    % output location t^rw@$"}  
  end Zj`WRH4  
end rpR${%jc  
hg=abs(U1').*abs(U1');                             % for data write to excel n>M`wF>  
ha=[z1 hg];                                        % for data write to excel &gXh:
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t1=[0 t']; %q{q.(M#  
hh=[t1' ha'];                                      % for data write to excel file }r,\0Wm  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 1\.$=N  
figure(1) G=zWhqieh  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Z~5) )5Ye;  
figure(2) hx;f/EPx  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn *IG$"nu  
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非线性超快脉冲耦合的数值方法的Matlab程序 ^t;z;.g  
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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。   J$dwy$n  
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 P15 H[<:Fz  
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%  This Matlab script file solves the nonlinear Schrodinger equations :GHv3hn5  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Fnw:alWr  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear K5""%O+  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 7>vm?a^D2&  
8%?y)K^ D  
C=1;                           {@Mr7*u  
M1=120,                       % integer for amplitude [Kgb#L'{  
M3=5000;                      % integer for length of coupler uV/5f#)  
N = 512;                      % Number of Fourier modes (Time domain sampling points) &p0e)o~Ux  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. UO/sv2CN  
T =40;                        % length of time:T*T0. VtreOJ+  
dt = T/N;                     % time step je4l3Hl  
n = [-N/2:1:N/2-1]';          % Index .g*j]!_]  
t = n.*dt;   PnlI {d  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Gr"CHz/  
w=2*pi*n./T; D
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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; N.F5)04  
g3=-i*ww./2; }pc9uvmIJ  
P1=0; P]E-Wp'p  
P2=0; W U(_N*a  
P3=1; |{jT+  
P=0; *GP2>oEM  
for m1=1:M1                 Y.tx$%
 
p=0.032*m1;                %input amplitude s\ IKSoE  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 nla6QlFYn*  
s1=s10; e~'`x38  
s20=0.*s10;                %input in waveguide 2 my=f}%k=  
s30=0.*s10;                %input in waveguide 3 R%E7 |NAG  
s2=s20; e|~MJu+1  
s3=s30; +n3I\7G>  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   D:)Wr, 26  
%energy in waveguide 1 Bf_$BCyGW  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   eRauyL"Q+  
%energy in waveguide 2 r-2k
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   d|`Ll  
%energy in waveguide 3
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for m3 = 1:1:M3                                    % Start space evolution V7ph^^sC}  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Uv^\[   
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; )8Va%{j  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; NE995;  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform <N<Q9}`V  
   sca2 = fftshift(fft(s2)); }\pI`;*O|  
   sca3 = fftshift(fft(s3)); jvT'N@  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ;"3B,Yj  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 3Ob.OwA  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); sdu?#O+c1  
   s3 = ifft(fftshift(sc3)); Fsx?(?tCMo  
   s2 = ifft(fftshift(sc2));                       % Return to physical space u8e_Lqx?  
   s1 = ifft(fftshift(sc1)); BFLef3~.0  
end 'J|2c;M\x  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); IThd\#=  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ?RRO  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); :Pud%}'  
   P1=[P1 p1/p10]; n ]ikc|  
   P2=[P2 p2/p10]; V"FQVtTx7  
   P3=[P3 p3/p10]; V+d_1] l  
   P=[P p*p]; xO$P C,  
end >r.]a`  
figure(1) 0.aXg"  
plot(P,P1, P,P2, P,P3); 'CLZ7pV  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~