[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 @JB9qT  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of /e|vz^#+1,  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of N_jpCCG~  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear P){b"`f  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ^j~CY
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%fid=fopen('e21.dat','w'); R( 2,1f=d  
N = 128;                       % Number of Fourier modes (Time domain sampling points) vndD#/lXq  
M1 =3000;              % Total number of space steps ;iA6[uz  
J =100;                % Steps between output of space 3|++2Z{},  
T =10;                  % length of time windows:T*T0 >|j8j:S[  
T0=0.1;                 % input pulse width vs=8x\W  
MN1=0;                 % initial value for the space output location ~9Xs=S!  
dt = T/N;                      % time step w3hG\2)[HS  
n = [-N/2:1:N/2-1]';           % Index b}&2j3-n,  
t = n.*dt;   LDX>S*cL  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Hs9; &C  
u20=u10.*0.0;                  % input to waveguide 2 |
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u1=u10; u2=u20;                 M
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U1 = u1;   YCBp]xuE  
U2 = u2;                       % Compute initial condition; save it in U q>X
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. {
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w=2*pi*n./T; h7?uM^p  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T \US'tF)/  
L=4;                           % length of evoluation to compare with S. Trillo's paper !+R_Z#gB  
dz=L/M1;                       % space step, make sure nonlinear<0.05 $3yzB9\a"  
for m1 = 1:1:M1                                    % Start space evolution ve3-GWT{C  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 5xb1FH d:  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 77zfRSb+  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform cc0e(\  
   ca2 = fftshift(fft(u2)); GkU]>8E'"  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation "pA24Ze  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Zqi;by%  
   u2 = ifft(fftshift(c2));                        % Return to physical space !3*:
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   u1 = ifft(fftshift(c1)); 0&
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if rem(m1,J) == 0                                 % Save output every J steps. \I-bZ|^  
    U1 = [U1 u1];                                  % put solutions in U array Uo]x6j<  
    U2=[U2 u2]; S+*%u/;l  
    MN1=[MN1 m1]; l|jb}9(J  
    z1=dz*MN1';                                    % output location A?zxF5rfp  
  end <>l!  
end f.e4 C,  
hg=abs(U1').*abs(U1');                             % for data write to excel rCH? R  
ha=[z1 hg];                                        % for data write to excel Lb=4\ _  
t1=[0 t']; RCC~#b
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hh=[t1' ha'];                                      % for data write to excel file ! <O,xI'  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format w~a_FGYX  
figure(1) EJByYk   
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ^2f2g>9j_C  
figure(2) eVvDis  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn .9uw@Eq  
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非线性超快脉冲耦合的数值方法的Matlab程序 @%[ dh@oY  
6\5"36&/rQ  
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。   -
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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  K0 6 E:  
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%  This Matlab script file solves the nonlinear Schrodinger equations ,b${3*PPQ  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of r1]DkX <6  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6Gj69Lr  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 gI5Fzk@:  
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C=1;                           .>^iU}  
M1=120,                       % integer for amplitude ;=i$0w9W  
M3=5000;                      % integer for length of coupler ,!I'0x1OR  
N = 512;                      % Number of Fourier modes (Time domain sampling points) &{=`g+4n  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. \f-HfYG  
T =40;                        % length of time:T*T0. oc0z1u  
dt = T/N;                     % time step 41s[p56+@  
n = [-N/2:1:N/2-1]';          % Index .NX>d@ Kc  
t = n.*dt;   OE8H |?%  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Hphfqdh0`  
w=2*pi*n./T; )K>2  
g1=-i*ww./2; r$/.x6g//  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; S!{Kn ;@  
g3=-i*ww./2; fs3jPHZJ#  
P1=0; <pp<%~_Z  
P2=0; 48W-Tf6v|  
P3=1; ;sZHE&+  
P=0; \+I+Lrj%  
for m1=1:M1                 ?5Ub&{  
p=0.032*m1;                %input amplitude >&DNxw  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 PTf.(B"z  
s1=s10; SHt#%3EU  
s20=0.*s10;                %input in waveguide 2 d_!lRQ^N  
s30=0.*s10;                %input in waveguide 3 nv-_\M   
s2=s20; KX$Q`lM   
s3=s30; =2tl149m/z  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   `mo>~c7  
%energy in waveguide 1 y|O)i I/g  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Ag@R60#  
%energy in waveguide 2 nq3B(  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   3^%sz!jK+  
%energy in waveguide 3 F3,djZq  
for m3 = 1:1:M3                                    % Start space evolution $0wF4$)  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS [R9!Tz  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 1u\kxlZ  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; .
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   sca1 = fftshift(fft(s1));                       % Take Fourier transform
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   sca2 = fftshift(fft(s2)); [-*8S1  
   sca3 = fftshift(fft(s3)); OK1f Y`$z  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   7iM;X2=7}  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); TU,k( `tn<  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); C~([aH@-I  
   s3 = ifft(fftshift(sc3)); ,Z1W3;O  
   s2 = ifft(fftshift(sc2));                       % Return to physical space }N}\<RG  
   s1 = ifft(fftshift(sc1)); /@~&zx&_  
end AcCM W@e  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); cc|"^-j-7  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 9CW
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   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); RI2Or9.  
   P1=[P1 p1/p10]; ZPolE_P
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   P2=[P2 p2/p10]; OcLFVD=  
   P3=[P3 p3/p10]; #Ies yNKZ  
   P=[P p*p]; d;c<" +  
end my(yN|  
figure(1) KJLK]lf}d  
plot(P,P1, P,P2, P,P3); 4 fxD$%9  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~