[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 S=_vv)6+4  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of kJWN.  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of x.8TRMk^  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear s"Pf+aTW
 
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 =K{\p`?  
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%fid=fopen('e21.dat','w'); `tjH<  
N = 128;                       % Number of Fourier modes (Time domain sampling points) GA7}K:LP'k  
M1 =3000;              % Total number of space steps 6JKqn~0Kk  
J =100;                % Steps between output of space ~"UV]Udn  
T =10;                  % length of time windows:T*T0 &WNf M+
 
T0=0.1;                 % input pulse width %Y!Yvw^&P(  
MN1=0;                 % initial value for the space output location )M__ t5L  
dt = T/N;                      % time step ~ek$
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n = [-N/2:1:N/2-1]';           % Index |9~GM  
t = n.*dt;   j"AU z)x  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Q#nOJ(KV  
u20=u10.*0.0;                  % input to waveguide 2 #j *d^j&  
u1=u10; u2=u20;                 gJ2>(k03y  
U1 = u1;   71vkyn@"  
U2 = u2;                       % Compute initial condition; save it in U ]E]2o  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. E;<l(.Ar  
w=2*pi*n./T; kOh{l: 2-+  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T $.9{if#o&  
L=4;                           % length of evoluation to compare with S. Trillo's paper )T;?^kho  
dz=L/M1;                       % space step, make sure nonlinear<0.05 6252N]*  
for m1 = 1:1:M1                                    % Start space evolution i hh/sPi  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS KiJT!moB  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; < yC  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform &3yD_P_3  
   ca2 = fftshift(fft(u2)); wm+/e#'&  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ID#I`}h.k  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Ug&,Y/tFw2  
   u2 = ifft(fftshift(c2));                        % Return to physical space q$aaA`E%  
   u1 = ifft(fftshift(c1)); R
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if rem(m1,J) == 0                                 % Save output every J steps. Q>n|^y6  
    U1 = [U1 u1];                                  % put solutions in U array }1>[  
    U2=[U2 u2]; F'hHK.tT  
    MN1=[MN1 m1]; msVOH%wH  
    z1=dz*MN1';                                    % output location v%f
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  end h,Q3oy\s1  
end JA)] _H P  
hg=abs(U1').*abs(U1');                             % for data write to excel ei rzYt  
ha=[z1 hg];                                        % for data write to excel <vXGi  
t1=[0 t']; )c8j}  
hh=[t1' ha'];                                      % for data write to excel file ?(R]9.5S  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format gdkwWoN.  
figure(1) =2@
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waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Vb9',a?#n  
figure(2) -YsLd 9^4  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn \?jeWyo  
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非线性超快脉冲耦合的数值方法的Matlab程序 IEU^#=n  
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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。   o`Ta("9^  
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 &gjF4~W]  
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%  This Matlab script file solves the nonlinear Schrodinger equations J9=m]R8T  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 9]e V?yoA8  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear y
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Q:5KZm[[  
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C=1;                           ~q~MoN<R  
M1=120,                       % integer for amplitude X$yN_7|+  
M3=5000;                      % integer for length of coupler hXA6D)
  
N = 512;                      % Number of Fourier modes (Time domain sampling points) a<@N-Exr  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Z ,EvQ8i  
T =40;                        % length of time:T*T0. G_SG  
dt = T/N;                     % time step v'BZs   
n = [-N/2:1:N/2-1]';          % Index ,u/aT5\_  
t = n.*dt;   @WI2hHD  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. hiUD]5Kp  
w=2*pi*n./T; D&S26jrZ  
g1=-i*ww./2; &o<F7U'R  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 6,9o>zT%H  
g3=-i*ww./2; /IsS;0K%L  
P1=0; I}t#%/'YA  
P2=0; 7[.6axL  
P3=1; . Z%{'CC  
P=0; lIProF0  
for m1=1:M1                 AhNq/?Q Q~  
p=0.032*m1;                %input amplitude Hbpqyl%O>  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ##4GK08!  
s1=s10; 4)("v-p  
s20=0.*s10;                %input in waveguide 2 &Sr
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s30=0.*s10;                %input in waveguide 3 *f?4   
s2=s20; ZfB" E  
s3=s30; *<J*S#]  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   KhMSL  
%energy in waveguide 1 qs QNjt  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   CXC`sPY  
%energy in waveguide 2 rs~wv('  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   'Tc]KXD6  
%energy in waveguide 3 &0`) Q
 
for m3 = 1:1:M3                                    % Start space evolution [B|MlrZ  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS EbdfV-E  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; *Q,0W:~-  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 7R\oj
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   sca1 = fftshift(fft(s1));                       % Take Fourier transform .<Zy|1 4  
   sca2 = fftshift(fft(s2)); -*XCxU'  
   sca3 = fftshift(fft(s3)); ]Ei0d8Uo  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   |Z*J/v'@p  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); }|XtypbL  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); (e[}/hf6  
   s3 = ifft(fftshift(sc3)); D`VM6/iQR  
   s2 = ifft(fftshift(sc2));                       % Return to physical space VL*ovD%-  
   s1 = ifft(fftshift(sc1)); |P%DkM*X  
end 67VT\f  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); iURk=*Z=  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); fF V!)Zj  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); )lZp9O  
   P1=[P1 p1/p10]; YWxc-fPZ  
   P2=[P2 p2/p10];  0gfA#|'  
   P3=[P3 p3/p10]; zNIsf"  
   P=[P p*p]; %y%j*B!%  
end YE9,KVV;$n  
figure(1) pb=cBZ$  
plot(P,P1, P,P2, P,P3); ZAXN6h  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~