[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 /3]b!lFZZ  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of RA5*QW  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of (C1@f!Z  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear NTj:+z0  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 r$=YhI/=  
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%fid=fopen('e21.dat','w'); O-5s}RT  
N = 128;                       % Number of Fourier modes (Time domain sampling points) sg=mkkD!g  
M1 =3000;              % Total number of space steps \I3={ii0  
J =100;                % Steps between output of space 7mUpn:U  
T =10;                  % length of time windows:T*T0 J}c`\4gD  
T0=0.1;                 % input pulse width ?AL;m.X-@  
MN1=0;                 % initial value for the space output location fJjtrvNy)  
dt = T/N;                      % time step HOEjLwH  
n = [-N/2:1:N/2-1]';           % Index >_ )~
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t = n.*dt;   hqPpRSv'  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 FN-j@
 
u20=u10.*0.0;                  % input to waveguide 2 &HS6}  
u1=u10; u2=u20;                 YLEk M  
U1 = u1;   :yLSLN  
U2 = u2;                       % Compute initial condition; save it in U AX {~A:B  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. uTSTBI4t  
w=2*pi*n./T; y)5U*\b  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T @A-*XJNS":  
L=4;                           % length of evoluation to compare with S. Trillo's paper =*ZQGM3w  
dz=L/M1;                       % space step, make sure nonlinear<0.05 c5jd q[0  
for m1 = 1:1:M1                                    % Start space evolution d8Keyi8[  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 5LPyPL L  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; vCPiT2G  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ]w)*8 w.)  
   ca2 = fftshift(fft(u2)); 9}\{0;9  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 2N,<~L`FX'  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   .6@qU}  
   u2 = ifft(fftshift(c2));                        % Return to physical space ]i}3
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   u1 = ifft(fftshift(c1)); Do&em8i z  
if rem(m1,J) == 0                                 % Save output every J steps. 6b-

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    U1 = [U1 u1];                                  % put solutions in U array |.]:#)^X?  
    U2=[U2 u2]; 3L;GfYr0  
    MN1=[MN1 m1]; 2J^jSgr50d  
    z1=dz*MN1';                                    % output location *1Q~/<W  
  end
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end o0f{ePZ=  
hg=abs(U1').*abs(U1');                             % for data write to excel k8]uy2R6}  
ha=[z1 hg];                                        % for data write to excel jz\LI  
t1=[0 t']; E"EBj7<s  
hh=[t1' ha'];                                      % for data write to excel file 0K0[mC}ZwM  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format [sM
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figure(1) p6qza @  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn hQm"K~SW
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figure(2) '+!@c&d#%o  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn T8ga)BA  
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非线性超快脉冲耦合的数值方法的Matlab程序 H*l2,0&W  
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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。   U~,~GU
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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 /uTU*Oe  
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%  This Matlab script file solves the nonlinear Schrodinger equations Bf&,ACOf  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of |j[=uS  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear FfDe&/,/  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 f}4bnu3  
CC(At.dd  
C=1;                           |@}Yady@C  
M1=120,                       % integer for amplitude zi^T?<t  
M3=5000;                      % integer for length of coupler 6[-N})  
N = 512;                      % Number of Fourier modes (Time domain sampling points) L_>j SP  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. sknta0^=2  
T =40;                        % length of time:T*T0. kc0YWW Q-:  
dt = T/N;                     % time step ;P` z ?>J:  
n = [-N/2:1:N/2-1]';          % Index Vb=Oz  
t = n.*dt;   0?D`|x_  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 07zbx6:t  
w=2*pi*n./T; g$++\%k&  
g1=-i*ww./2; piZ0KA"  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ebbC`eFD  
g3=-i*ww./2; CM; r\,o  
P1=0; ]Zfg~K(  
P2=0; G~oGBq6Gz  
P3=1; 6cCC+*V{  
P=0; qOyg&]7  
for m1=1:M1                 {x3"/sF  
p=0.032*m1;                %input amplitude .t/XW++  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 D[.;-4"_  
s1=s10; *x^W`i   
s20=0.*s10;                %input in waveguide 2 `@8QQB  
s30=0.*s10;                %input in waveguide 3 ";jj`  
s2=s20; ;QT.|.t6  
s3=s30; Up61Xn  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   29]T:I1d[  
%energy in waveguide 1 oW:p6d  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   u$7od$&S  
%energy in waveguide 2 k79"xyXX  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   *\?tW]8<  
%energy in waveguide 3 [B}$U|V0  
for m3 = 1:1:M3                                    % Start space evolution eq0&8/=  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS wnaT~r@U'  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; CJ*8x7-t  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; f'hrS}e  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform sN6R0YW  
   sca2 = fftshift(fft(s2)); j@jaFsX|  
   sca3 = fftshift(fft(s3)); gr\UI!]F  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   x|#R$^4CY  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 3`ov?T(H  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); PZVh)6f"c  
   s3 = ifft(fftshift(sc3)); !J3dlUFRO  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Tw:j}ERq  
   s1 = ifft(fftshift(sc1)); BDW%cs  
end wS*An
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   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); xPFNH`O&  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 3I87|5V,Z  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); -L;sv0  
   P1=[P1 p1/p10]; 5PY,}1`  
   P2=[P2 p2/p10]; w8!S;~xKI  
   P3=[P3 p3/p10]; oyQp"'|N  
   P=[P p*p]; !f 7CN<  
end Hw 7  
figure(1) +!dWQ=W  
plot(P,P1, P,P2, P,P3); (vX+ Yw  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~